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units av-main-archive' role="main" itemprop="mainContentOfPage" itemscope="itemscope" itemtype="https://schema.org/Blog" ><div class='category-term-description'><h1>Math Articles</h1><p>Here is our every growing collection of expert math articles that deal with all mathematics disciplines. These cover all areas of math and all skill ranges from algebra to advanced calculus.</p></div><div class="entry-content-wrapper"><div data-slideshow-options="{"animation":"fade","autoplay":false,"loop_autoplay":"once","interval":5,"loop_manual":"manual-endless","autoplay_stopper":false,"noNavigation":false,"show_slide_delay":90}" class='avia-content-slider avia-content-grid-active avia-content-slider1 avia-content-slider-odd avia-builder-el-no-sibling av-slideshow-ui av-control-default av-no-slider-navigation av-slideshow-manual av-loop-once av-loop-manual-endless ' itemscope="itemscope" itemtype="https://schema.org/Blog" ><div class="avia-content-slider-inner"><div class="slide-entry-wrap"><article class='slide-entry flex_column post-entry post-entry-47569 slide-entry-overview slide-loop-1 slide-parity-odd av_one_third first real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/brownian-motions-and-quantifying-randomness-in-physical-systems/' data-rel='slide-1' class='slide-image' title='Brownian Motions and Quantifying Randomness in Physical Systems'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2024/08/brownian-motion.png" class="wp-image-47594 avia-img-lazy-loading-not-47594 attachment-portfolio size-portfolio wp-post-image" alt="brownian motion" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2024/08/brownian-motion.png" class="wp-image-47594 avia-img-lazy-loading-not-47594 attachment-portfolio size-portfolio wp-post-image" alt="brownian motion" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: Brownian Motions and Quantifying Randomness in Physical Systems"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/brownian-motions-and-quantifying-randomness-in-physical-systems/' title='Brownian Motions and Quantifying Randomness in Physical Systems'>Brownian Motions and Quantifying Randomness in Physical Systems</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2024-08-26T07:14:45-05:00" >August 26, 2024</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/brownian-motions-and-quantifying-randomness-in-physical-systems/#comments'>1 Comment</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >Stochastic calculus has come a long way since Robert Brown described the motion of pollen through a microscope in 1827. It's now a key player in data science,…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2024/08/brownian-motion.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>ergospherical</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>ergospherical</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2024-08-26 07:14:45</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2024-11-16 10:39:17</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>Brownian Motions and Quantifying Randomness in Physical Systems</span></span></span></article><article class='slide-entry flex_column post-entry post-entry-46007 slide-entry-overview slide-loop-2 slide-parity-even av_one_third real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/views-on-complex-numbers/' data-rel='slide-1' class='slide-image' title='Views On Complex Numbers'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2024/06/complex-numbers-views.png" class="wp-image-46207 avia-img-lazy-loading-not-46207 attachment-portfolio size-portfolio wp-post-image" alt="complex numbers views" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2024/06/complex-numbers-views.png" class="wp-image-46207 avia-img-lazy-loading-not-46207 attachment-portfolio size-portfolio wp-post-image" alt="complex numbers views" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: Views On Complex Numbers"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/views-on-complex-numbers/' title='Views On Complex Numbers'>Views On Complex Numbers</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2024-06-07T06:10:00-05:00" >June 7, 2024</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/views-on-complex-numbers/#comments'>70 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >Abstract Why do we need yet another article about complex numbers? This is a valid question and I have asked it myself. I could mention that I wanted…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2024/06/complex-numbers-views.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>fresh_42</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>fresh_42</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2024-06-07 06:10:00</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2024-09-30 09:01:04</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>Views On Complex Numbers</span></span></span></article><article class='slide-entry flex_column post-entry post-entry-44731 slide-entry-overview slide-loop-3 slide-parity-odd av_one_third real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/the-lambert-w-function-in-finance/' data-rel='slide-1' class='slide-image' title='The Lambert W Function in Finance'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2024/02/Lambert-W-Function-in-Finance.png" class="wp-image-45299 avia-img-lazy-loading-not-45299 attachment-portfolio size-portfolio wp-post-image" alt="Lambert W Function in Finance" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2024/02/Lambert-W-Function-in-Finance.png" class="wp-image-45299 avia-img-lazy-loading-not-45299 attachment-portfolio size-portfolio wp-post-image" alt="Lambert W Function in Finance" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: The Lambert W Function in Finance"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/the-lambert-w-function-in-finance/' title='The Lambert W Function in Finance'>The Lambert W Function in Finance</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2024-02-09T08:25:09-06:00" >February 9, 2024</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/the-lambert-w-function-in-finance/#respond'>0 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >Preamble The classical mathematician practically by instinct views the continuous process as the "real" process, and the discrete process as an approximation…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2024/02/Lambert-W-Function-in-Finance.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>Neil Parker</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>Neil Parker</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2024-02-09 08:25:09</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2024-02-09 08:25:09</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>The Lambert W Function in Finance</span></span></span></article></div><div class="slide-entry-wrap"><article class='slide-entry flex_column post-entry post-entry-44769 slide-entry-overview slide-loop-4 slide-parity-odd av_one_third first real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/why-division-by-zero-is-a-bad-idea/' data-rel='slide-1' class='slide-image' title='Why Division by Zero is a Bad Idea'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2015/09/infinity.png" class="wp-image-4849 avia-img-lazy-loading-not-4849 attachment-portfolio size-portfolio wp-post-image" alt="infinity" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2015/09/infinity.png" class="wp-image-4849 avia-img-lazy-loading-not-4849 attachment-portfolio size-portfolio wp-post-image" alt="infinity" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: Why Division by Zero is a Bad Idea"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/why-division-by-zero-is-a-bad-idea/' title='Why Division by Zero is a Bad Idea'>Why Division by Zero is a Bad Idea</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2024-01-11T10:41:33-06:00" >January 11, 2024</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/why-division-by-zero-is-a-bad-idea/#comments'>33 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >A division by zero is primarily an algebraic question. The reasoning therefore follows the indirect pattern of most algebraic proofs: What if it was allowed? Then…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2015/09/infinity.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>fresh_42</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>fresh_42</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2024-01-11 10:41:33</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2024-11-04 08:08:37</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>Why Division by Zero is a Bad Idea</span></span></span></article><article class='slide-entry flex_column post-entry post-entry-44496 slide-entry-overview slide-loop-5 slide-parity-even av_one_third real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/series-in-mathematics-from-zeno-to-quantum-theory/' data-rel='slide-1' class='slide-image' title='Series in Mathematics: From Zeno to Quantum Theory'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2023/11/geometric-series.png" class="wp-image-44636 avia-img-lazy-loading-not-44636 attachment-portfolio size-portfolio wp-post-image" alt="geometric series" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2023/11/geometric-series.png" class="wp-image-44636 avia-img-lazy-loading-not-44636 attachment-portfolio size-portfolio wp-post-image" alt="geometric series" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: Series in Mathematics: From Zeno to Quantum Theory"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/series-in-mathematics-from-zeno-to-quantum-theory/' title='Series in Mathematics: From Zeno to Quantum Theory'>Series in Mathematics: From Zeno to Quantum Theory</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2023-11-07T20:13:49-06:00" >November 7, 2023</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/series-in-mathematics-from-zeno-to-quantum-theory/#comments'>2 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >Introduction Series play a decisive role in many branches of mathematics. They accompanied mathematical developments from Zeno of Elea (##5##-th century…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2023/11/geometric-series.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>fresh_42</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>fresh_42</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2023-11-07 20:13:49</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2023-12-19 13:21:53</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>Series in Mathematics: From Zeno to Quantum Theory</span></span></span></article><article class='slide-entry flex_column post-entry post-entry-44253 slide-entry-overview slide-loop-6 slide-parity-odd av_one_third real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/differential-equation-systems-and-nature/' data-rel='slide-1' class='slide-image' title='Differential Equation Systems and Nature'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2023/08/Differential-Equation-Systems-and-Nature.png" class="wp-image-44413 avia-img-lazy-loading-not-44413 attachment-portfolio size-portfolio wp-post-image" alt="Differential Equation Systems and Nature" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2023/08/Differential-Equation-Systems-and-Nature.png" class="wp-image-44413 avia-img-lazy-loading-not-44413 attachment-portfolio size-portfolio wp-post-image" alt="Differential Equation Systems and Nature" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: Differential Equation Systems and Nature"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/differential-equation-systems-and-nature/' title='Differential Equation Systems and Nature'>Differential Equation Systems and Nature</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2023-08-27T07:20:35-05:00" >August 27, 2023</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/differential-equation-systems-and-nature/#comments'>12 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >Abstract "Mathematics is the native language of nature." is a phrase that is often used when it comes to explaining why mathematics is all around in natural…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2023/08/Differential-Equation-Systems-and-Nature.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>fresh_42</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>fresh_42</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2023-08-27 07:20:35</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2024-01-09 07:51:58</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>Differential Equation Systems and Nature</span></span></span></article></div><div class="slide-entry-wrap"><article class='slide-entry flex_column post-entry post-entry-43710 slide-entry-overview slide-loop-7 slide-parity-odd av_one_third first real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/precalculus-calculus-and-infinitesimals/' data-rel='slide-1' class='slide-image' title='Beginners Guide to Precalculus, Calculus and Infinitesimals'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2023/08/calc-precalc.png" class="wp-image-44245 avia-img-lazy-loading-not-44245 attachment-portfolio size-portfolio wp-post-image" alt="calc precalc" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2023/08/calc-precalc.png" class="wp-image-44245 avia-img-lazy-loading-not-44245 attachment-portfolio size-portfolio wp-post-image" alt="calc precalc" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: Beginners Guide to Precalculus, Calculus and Infinitesimals"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/precalculus-calculus-and-infinitesimals/' title='Beginners Guide to Precalculus, Calculus and Infinitesimals'>Beginners Guide to Precalculus, Calculus and Infinitesimals</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2023-08-18T01:04:41-05:00" >August 18, 2023</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/precalculus-calculus-and-infinitesimals/#comments'>3 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >Introduction I am convinced students learn Calculus far too late. In my view, there has never been a good reason for this.In the US, they go through…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2023/08/calc-precalc.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>Bill Hobba</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>Bill Hobba</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2023-08-18 01:04:41</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2023-08-19 06:58:25</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>Beginners Guide to Precalculus, Calculus and Infinitesimals</span></span></span></article><article class='slide-entry flex_column post-entry post-entry-43536 slide-entry-overview slide-loop-8 slide-parity-even av_one_third real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/what-are-numbers/' data-rel='slide-1' class='slide-image' title='What Are Numbers?'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2023/08/what-are-numbers.png" class="wp-image-44224 avia-img-lazy-loading-not-44224 attachment-portfolio size-portfolio wp-post-image" alt="what are numbers" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2023/08/what-are-numbers.png" class="wp-image-44224 avia-img-lazy-loading-not-44224 attachment-portfolio size-portfolio wp-post-image" alt="what are numbers" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: What Are Numbers?"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/what-are-numbers/' title='What Are Numbers?'>What Are Numbers?</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2023-08-14T22:43:45-05:00" >August 14, 2023</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/what-are-numbers/#comments'>7 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >Introduction When doing mathematics, we usually take for granted what natural numbers, integers, and rationals are. They are pretty intuitive. Going…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2023/08/what-are-numbers.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>Bill Hobba</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>Bill Hobba</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2023-08-14 22:43:45</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2023-11-01 18:53:56</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>What Are Numbers?</span></span></span></article><article class='slide-entry flex_column post-entry post-entry-43587 slide-entry-overview slide-loop-9 slide-parity-odd av_one_third real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/introduction-to-the-world-of-algebras/' data-rel='slide-1' class='slide-image' title='Introduction to the World of Algebras'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2023/07/world-of-algebras.png" class="wp-image-43690 avia-img-lazy-loading-not-43690 attachment-portfolio size-portfolio wp-post-image" alt="world of algebras" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2023/07/world-of-algebras.png" class="wp-image-43690 avia-img-lazy-loading-not-43690 attachment-portfolio size-portfolio wp-post-image" alt="world of algebras" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: Introduction to the World of Algebras"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/introduction-to-the-world-of-algebras/' title='Introduction to the World of Algebras'>Introduction to the World of Algebras</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2023-07-08T07:35:07-05:00" >July 8, 2023</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/introduction-to-the-world-of-algebras/#respond'>0 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >Abstract Richard Pierce describes the intention of his book [2] about associative algebras as his attempt to prove that there is algebra after Galois…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2023/07/world-of-algebras.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>fresh_42</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>fresh_42</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2023-07-08 07:35:07</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2023-07-22 09:22:21</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>Introduction to the World of Algebras</span></span></span></article></div><div class="slide-entry-wrap"><article class='slide-entry flex_column post-entry post-entry-43241 slide-entry-overview slide-loop-10 slide-parity-odd av_one_third first real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/what-are-infinitesimals/' data-rel='slide-1' class='slide-image' title='What Are Infinitesimals – Advanced Version'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2023/05/Infinitesimals.png" class="wp-image-43343 avia-img-lazy-loading-not-43343 attachment-portfolio size-portfolio wp-post-image" alt="Infinitesimals" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2023/05/Infinitesimals.png" class="wp-image-43343 avia-img-lazy-loading-not-43343 attachment-portfolio size-portfolio wp-post-image" alt="Infinitesimals" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: What Are Infinitesimals - Advanced Version"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/what-are-infinitesimals/' title='What Are Infinitesimals – Advanced Version'>What Are Infinitesimals – Advanced Version</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2023-05-24T03:01:58-05:00" >May 24, 2023</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/what-are-infinitesimals/#respond'>0 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >Introduction When I learned calculus, the intuitive idea of infinitesimal was used. These are real numbers so small that, for all practical purposes (say…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2023/05/Infinitesimals.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>Bill Hobba</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>Bill Hobba</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2023-05-24 03:01:58</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2024-08-18 09:51:21</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>What Are Infinitesimals – Advanced Version</span></span></span></article><article class='slide-entry flex_column post-entry post-entry-42892 slide-entry-overview slide-loop-11 slide-parity-even av_one_third real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/an-overview-of-complex-differentiation-and-integration/' data-rel='slide-1' class='slide-image' title='An Overview of Complex Differentiation and Integration'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2023/03/integration_differentiation.png" class="wp-image-42943 avia-img-lazy-loading-not-42943 attachment-portfolio size-portfolio wp-post-image" alt="integration and complex differentiation" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2023/03/integration_differentiation.png" class="wp-image-42943 avia-img-lazy-loading-not-42943 attachment-portfolio size-portfolio wp-post-image" alt="integration and complex differentiation" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: An Overview of Complex Differentiation and Integration"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/an-overview-of-complex-differentiation-and-integration/' title='An Overview of Complex Differentiation and Integration'>An Overview of Complex Differentiation and Integration</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2023-03-14T08:24:25-05:00" >March 14, 2023</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/an-overview-of-complex-differentiation-and-integration/#respond'>0 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >Abstract I want to shed some light on complex analysis without getting all the technical details in the way which are necessary for the precise treatments…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2023/03/integration_differentiation.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>fresh_42</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>fresh_42</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2023-03-14 08:24:25</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2024-06-02 15:46:27</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>An Overview of Complex Differentiation and Integration</span></span></span></article><article class='slide-entry flex_column post-entry post-entry-42711 slide-entry-overview slide-loop-12 slide-parity-odd av_one_third real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/when-lie-groups-became-physics/' data-rel='slide-1' class='slide-image' title='When Lie Groups Became Physics'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2023/02/lie-group-physics.png" class="wp-image-42798 avia-img-lazy-loading-not-42798 attachment-portfolio size-portfolio wp-post-image" alt="lie group physics" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2023/02/lie-group-physics.png" class="wp-image-42798 avia-img-lazy-loading-not-42798 attachment-portfolio size-portfolio wp-post-image" alt="lie group physics" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: When Lie Groups Became Physics"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/when-lie-groups-became-physics/' title='When Lie Groups Became Physics'>When Lie Groups Became Physics</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2023-02-08T07:44:28-06:00" >February 8, 2023</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/when-lie-groups-became-physics/#respond'>0 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >Abstract We explain by simple examples (one-parameter Lie groups), partly in the original language, and along the historical papers of Sophus Lie, Abraham…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2023/02/lie-group-physics.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>fresh_42</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>fresh_42</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2023-02-08 07:44:28</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2023-04-05 20:15:42</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>When Lie Groups Became Physics</span></span></span></article></div><div class="slide-entry-wrap"><article class='slide-entry flex_column post-entry post-entry-42189 slide-entry-overview slide-loop-13 slide-parity-odd av_one_third first real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/classification-of-mathematics-by-42-branches/' data-rel='slide-1' class='slide-image' title='Classification of Mathematics by 42 Branches'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2022/10/math-classifications.png" class="wp-image-42262 avia-img-lazy-loading-not-42262 attachment-portfolio size-portfolio wp-post-image" alt="math classifications" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2022/10/math-classifications.png" class="wp-image-42262 avia-img-lazy-loading-not-42262 attachment-portfolio size-portfolio wp-post-image" alt="math classifications" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: Classification of Mathematics by 42 Branches"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/classification-of-mathematics-by-42-branches/' title='Classification of Mathematics by 42 Branches'>Classification of Mathematics by 42 Branches</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2022-10-25T09:06:07-05:00" >October 25, 2022</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/classification-of-mathematics-by-42-branches/#respond'>0 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" > I often read questions about our classification scheme that we use on physicsforums.com to sort posts by science fields and subjects, what has…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2022/10/math-classifications.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>fresh_42</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>fresh_42</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2022-10-25 09:06:07</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2024-09-30 08:54:18</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>Classification of Mathematics by 42 Branches</span></span></span></article><article class='slide-entry flex_column post-entry post-entry-42071 slide-entry-overview slide-loop-14 slide-parity-even av_one_third real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/counting-to-p-adic-calculus-all-number-systems-that-we-have/' data-rel='slide-1' class='slide-image' title='Counting to p-adic Calculus: All Number Systems That We Have'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2022/09/history-of-numbers.png" class="wp-image-42106 avia-img-lazy-loading-not-42106 attachment-portfolio size-portfolio wp-post-image" alt="history of numbers" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2022/09/history-of-numbers.png" class="wp-image-42106 avia-img-lazy-loading-not-42106 attachment-portfolio size-portfolio wp-post-image" alt="history of numbers" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: Counting to p-adic Calculus: All Number Systems That We Have"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/counting-to-p-adic-calculus-all-number-systems-that-we-have/' title='Counting to p-adic Calculus: All Number Systems That We Have'>Counting to p-adic Calculus: All Number Systems That We Have</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2022-09-18T15:11:13-05:00" >September 18, 2022</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/counting-to-p-adic-calculus-all-number-systems-that-we-have/#respond'>0 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >An entire book could easily be written about the history of numbers from ancient Babylon and India, over Abu Dscha'far Muhammad ibn Musa al-Chwarizmi (##\sim…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2022/09/history-of-numbers.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>fresh_42</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>fresh_42</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2022-09-18 15:11:13</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2023-08-15 09:04:11</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>Counting to p-adic Calculus: All Number Systems That We Have</span></span></span></article><article class='slide-entry flex_column post-entry post-entry-42024 slide-entry-overview slide-loop-15 slide-parity-odd av_one_third real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/intro-to-evariste-galois-and-galois-theory/' data-rel='slide-1' class='slide-image' title='Évariste Galois and His Theory'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2022/09/evariste-galois.png" class="wp-image-42059 avia-img-lazy-loading-not-42059 attachment-portfolio size-portfolio wp-post-image" alt="evariste galois" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2022/09/evariste-galois.png" class="wp-image-42059 avia-img-lazy-loading-not-42059 attachment-portfolio size-portfolio wp-post-image" alt="evariste galois" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: Évariste Galois and His Theory"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/intro-to-evariste-galois-and-galois-theory/' title='Évariste Galois and His Theory'>Évariste Galois and His Theory</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2022-09-05T19:40:52-05:00" >September 5, 2022</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/intro-to-evariste-galois-and-galois-theory/#respond'>0 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" > * Oct. 25th, 1811 † May 31st, 1832 ... or why squaring the circle is doomed. Galois died in a duel at the age of twenty. Yet, he gave…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2022/09/evariste-galois.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>fresh_42</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>fresh_42</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2022-09-05 19:40:52</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2023-08-15 09:04:12</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>Évariste Galois and His Theory</span></span></span></article></div><div class="slide-entry-wrap"><article class='slide-entry flex_column post-entry post-entry-41907 slide-entry-overview slide-loop-16 slide-parity-odd av_one_third first real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/yardsticks-to-metric-tensor-fields/' data-rel='slide-1' class='slide-image' title='Yardsticks to Metric Tensor Fields'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2022/08/definition-differences.png" class="wp-image-41991 avia-img-lazy-loading-not-41991 attachment-portfolio size-portfolio wp-post-image" alt="definition differences" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2022/08/definition-differences.png" class="wp-image-41991 avia-img-lazy-loading-not-41991 attachment-portfolio size-portfolio wp-post-image" alt="definition differences" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: Yardsticks to Metric Tensor Fields"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/yardsticks-to-metric-tensor-fields/' title='Yardsticks to Metric Tensor Fields'>Yardsticks to Metric Tensor Fields</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2022-08-27T10:57:47-05:00" >August 27, 2022</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/yardsticks-to-metric-tensor-fields/#comments'>1 Comment</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >I asked myself why different scientists understand the same thing seemingly differently, especially the concept of a metric tensor. If we ask a topologist,…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2022/08/definition-differences.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>fresh_42</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>fresh_42</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2022-08-27 10:57:47</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2024-09-30 09:20:21</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>Yardsticks to Metric Tensor Fields</span></span></span></article><article class='slide-entry flex_column post-entry post-entry-41797 slide-entry-overview slide-loop-17 slide-parity-even av_one_third real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/p-vs-np-conjecture-calculations-and-meaning/' data-rel='slide-1' class='slide-image' title='P vs. NP and what is a Turing Machine (TM)?'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2022/07/pvsnp.png" class="wp-image-41832 avia-img-lazy-loading-not-41832 attachment-portfolio size-portfolio wp-post-image" alt="pvsnp" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2022/07/pvsnp.png" class="wp-image-41832 avia-img-lazy-loading-not-41832 attachment-portfolio size-portfolio wp-post-image" alt="pvsnp" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: P vs. NP and what is a Turing Machine (TM)?"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/p-vs-np-conjecture-calculations-and-meaning/' title='P vs. NP and what is a Turing Machine (TM)?'>P vs. NP and what is a Turing Machine (TM)?</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2022-07-25T08:13:16-05:00" >July 25, 2022</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/p-vs-np-conjecture-calculations-and-meaning/#comments'>1 Comment</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >P or NP This article deals with the complexity of calculations and in particular the meaning of ##P\stackrel{?}{\neq}NP## Before we explain what P and…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2022/07/pvsnp.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>fresh_42</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>fresh_42</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2022-07-25 08:13:16</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2022-07-25 09:22:26</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>P vs. NP and what is a Turing Machine (TM)?</span></span></span></article><article class='slide-entry flex_column post-entry post-entry-40500 slide-entry-overview slide-loop-18 slide-parity-odd av_one_third real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/the-history-and-importance-of-the-riemann-hypothesis/' data-rel='slide-1' class='slide-image' title='The History and Importance of the Riemann Hypothesis'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2022/05/Riemann-Hypothesis-History.png" class="wp-image-41099 avia-img-lazy-loading-not-41099 attachment-portfolio size-portfolio wp-post-image" alt="Riemann Hypothesis History" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2022/05/Riemann-Hypothesis-History.png" class="wp-image-41099 avia-img-lazy-loading-not-41099 attachment-portfolio size-portfolio wp-post-image" alt="Riemann Hypothesis History" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: The History and Importance of the Riemann Hypothesis"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/the-history-and-importance-of-the-riemann-hypothesis/' title='The History and Importance of the Riemann Hypothesis'>The History and Importance of the Riemann Hypothesis</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2022-05-21T11:29:54-05:00" >May 21, 2022</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/the-history-and-importance-of-the-riemann-hypothesis/#respond'>0 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >Riemann Hypothesis History The Riemann Hypothesis is one of the most famous and long-standing unsolved problems in mathematics, specifically in the field…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2022/05/Riemann-Hypothesis-History.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>fresh_42</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>fresh_42</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2022-05-21 11:29:54</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2024-09-30 09:04:58</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>The History and Importance of the Riemann Hypothesis</span></span></span></article></div><div class="slide-entry-wrap"><article class='slide-entry flex_column post-entry post-entry-40428 slide-entry-overview slide-loop-19 slide-parity-odd av_one_third first real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/the-amazing-relationship-between-integration-and-eulers-number/' data-rel='slide-1' class='slide-image' title='The Amazing Relationship Between Integration And Euler’s Number'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2022/03/Hyperbola-1.png" class="wp-image-40492 avia-img-lazy-loading-not-40492 attachment-portfolio size-portfolio wp-post-image" alt="Hyperbola" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2022/03/Hyperbola-1.png" class="wp-image-40492 avia-img-lazy-loading-not-40492 attachment-portfolio size-portfolio wp-post-image" alt="Hyperbola" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: The Amazing Relationship Between Integration And Euler's Number"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/the-amazing-relationship-between-integration-and-eulers-number/' title='The Amazing Relationship Between Integration And Euler’s Number'>The Amazing Relationship Between Integration And Euler’s Number</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2022-03-28T17:09:06-05:00" >March 28, 2022</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/the-amazing-relationship-between-integration-and-eulers-number/#respond'>0 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >We use integration to measure lengths, areas, or volumes. This is a geometrical interpretation, but we want to examine an analytical interpretation that…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2022/03/Hyperbola-1.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>fresh_42</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>fresh_42</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2022-03-28 17:09:06</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2022-03-29 07:39:28</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>The Amazing Relationship Between Integration And Euler’s Number</span></span></span></article><article class='slide-entry flex_column post-entry post-entry-40064 slide-entry-overview slide-loop-20 slide-parity-even av_one_third real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/probabilistic-factors-involved-in-disease-and-virus-testing/' data-rel='slide-1' class='slide-image' title='Probabilistic Factors Involved in Disease and Virus Testing'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2022/02/probabilities-virus-testing.png" class="wp-image-40097 avia-img-lazy-loading-not-40097 attachment-portfolio size-portfolio wp-post-image" alt="probabilities virus testing" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2022/02/probabilities-virus-testing.png" class="wp-image-40097 avia-img-lazy-loading-not-40097 attachment-portfolio size-portfolio wp-post-image" alt="probabilities virus testing" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: Probabilistic Factors Involved in Disease and Virus Testing"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/probabilistic-factors-involved-in-disease-and-virus-testing/' title='Probabilistic Factors Involved in Disease and Virus Testing'>Probabilistic Factors Involved in Disease and Virus Testing</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2022-02-06T17:13:53-06:00" >February 6, 2022</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/probabilistic-factors-involved-in-disease-and-virus-testing/#comments'>2 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >Introduction This Insight looks at the various probabilistic factors and related terminology involved in disease and virus testing.As we all know,…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2022/02/probabilities-virus-testing.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>PeroK</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>PeroK</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2022-02-06 17:13:53</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2024-08-18 09:37:26</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>Probabilistic Factors Involved in Disease and Virus Testing</span></span></span></article><article class='slide-entry flex_column post-entry post-entry-38245 slide-entry-overview slide-loop-21 slide-parity-odd av_one_third real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/10-math-things-we-all-learnt-wrong-at-school/' data-rel='slide-1' class='slide-image' title='10 Math Things We All Learnt Wrong At School'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2021/04/blackboard.png" class="wp-image-38292 avia-img-lazy-loading-not-38292 attachment-portfolio size-portfolio wp-post-image" alt="blackboard" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2021/04/blackboard.png" class="wp-image-38292 avia-img-lazy-loading-not-38292 attachment-portfolio size-portfolio wp-post-image" alt="blackboard" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: 10 Math Things We All Learnt Wrong At School"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/10-math-things-we-all-learnt-wrong-at-school/' title='10 Math Things We All Learnt Wrong At School'>10 Math Things We All Learnt Wrong At School</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2021-04-21T16:20:23-05:00" >April 21, 2021</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/10-math-things-we-all-learnt-wrong-at-school/#comments'>10 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >Some of these could even lead to heavy debates within the scientific community, so maybe I should say: from my point of view. So before you get excited…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2021/04/blackboard.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>fresh_42</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>fresh_42</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2021-04-21 16:20:23</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2024-08-18 09:26:59</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>10 Math Things We All Learnt Wrong At School</span></span></span></article></div><div class="slide-entry-wrap"><article class='slide-entry flex_column post-entry post-entry-34731 slide-entry-overview slide-loop-22 slide-parity-odd av_one_third first real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/how-bayesian-inference-works-in-the-context-of-science/' data-rel='slide-1' class='slide-image' title='How Bayesian Inference Works in the Context of Science'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2020/12/bayesian-inference.png" class="wp-image-34755 avia-img-lazy-loading-not-34755 attachment-portfolio size-portfolio wp-post-image" alt="bayesian inference" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2020/12/bayesian-inference.png" class="wp-image-34755 avia-img-lazy-loading-not-34755 attachment-portfolio size-portfolio wp-post-image" alt="bayesian inference" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: How Bayesian Inference Works in the Context of Science"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/how-bayesian-inference-works-in-the-context-of-science/' title='How Bayesian Inference Works in the Context of Science'>How Bayesian Inference Works in the Context of Science</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2020-12-17T08:08:29-06:00" >December 17, 2020</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/how-bayesian-inference-works-in-the-context-of-science/#comments'>12 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >Confessions of a moderate Bayesian part 3 Read part 1: How to Get Started with Bayesian Statistics Read part 2: Frequentist Probability vs Bayesian ProbabilityBayesian…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2020/12/bayesian-inference.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>Dale</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>Dale</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2020-12-17 08:08:29</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2024-09-30 09:19:48</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>How Bayesian Inference Works in the Context of Science</span></span></span></article><article class='slide-entry flex_column post-entry post-entry-34181 slide-entry-overview slide-loop-23 slide-parity-even av_one_third real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/frequentist-probability-vs-bayesian-probability/' data-rel='slide-1' class='slide-image' title='Exploring Frequentist Probability vs Bayesian Probability'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2020/12/bayesian-statistics-part-2.png" class="wp-image-34193 avia-img-lazy-loading-not-34193 attachment-portfolio size-portfolio wp-post-image" alt="bayesian statistics part 2" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2020/12/bayesian-statistics-part-2.png" class="wp-image-34193 avia-img-lazy-loading-not-34193 attachment-portfolio size-portfolio wp-post-image" alt="bayesian statistics part 2" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: Exploring Frequentist Probability vs Bayesian Probability"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/frequentist-probability-vs-bayesian-probability/' title='Exploring Frequentist Probability vs Bayesian Probability'>Exploring Frequentist Probability vs Bayesian Probability</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2020-12-03T07:23:02-06:00" >December 3, 2020</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/frequentist-probability-vs-bayesian-probability/#comments'>38 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >Confessions of a moderate Bayesian, part 2 Read Part 1: Confessions of a moderate Bayesian, part 1Bayesian statistics by and for non-statisticianshttps://www.cafepress.com/physicsforums.13280237 Background One…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2020/12/bayesian-statistics-part-2.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>Dale</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>Dale</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2020-12-03 07:23:02</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2024-08-18 09:16:54</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>Exploring Frequentist Probability vs Bayesian Probability</span></span></span></article><article class='slide-entry flex_column post-entry post-entry-34157 slide-entry-overview slide-loop-24 slide-parity-odd av_one_third real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/how-to-get-started-with-bayesian-stats-confessions-of-a-moderate-bayesian/' data-rel='slide-1' class='slide-image' title='How to Get Started with Bayesian Statistics'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2020/11/bayesian-statistics.png" class="wp-image-34174 avia-img-lazy-loading-not-34174 attachment-portfolio size-portfolio wp-post-image" alt="bayesian statistics" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2020/11/bayesian-statistics.png" class="wp-image-34174 avia-img-lazy-loading-not-34174 attachment-portfolio size-portfolio wp-post-image" alt="bayesian statistics" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: How to Get Started with Bayesian Statistics"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/how-to-get-started-with-bayesian-stats-confessions-of-a-moderate-bayesian/' title='How to Get Started with Bayesian Statistics'>How to Get Started with Bayesian Statistics</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2020-11-28T09:32:47-06:00" >November 28, 2020</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/how-to-get-started-with-bayesian-stats-confessions-of-a-moderate-bayesian/#comments'>13 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >Confessions of a moderate Bayesian, part 1 Bayesian statistics by and for non-statisticianshttps://www.cafepress.com/physicsforums.13265286 Background I…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2020/11/bayesian-statistics.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>Dale</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>Dale</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2020-11-28 09:32:47</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2024-08-18 09:16:06</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>How to Get Started with Bayesian Statistics</span></span></span></article></div><div class="slide-entry-wrap"><article class='slide-entry flex_column post-entry post-entry-29325 slide-entry-overview slide-loop-25 slide-parity-odd av_one_third first real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/mary-somerville-features-in-google-doodle/' data-rel='slide-1' class='slide-image' title='Mathematician Mary Somerville Features in Google Doodle'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2020/03/mary-Somerville.png" class="wp-image-29490 avia-img-lazy-loading-not-29490 attachment-portfolio size-portfolio wp-post-image" alt="mary Somerville" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2020/03/mary-Somerville.png" class="wp-image-29490 avia-img-lazy-loading-not-29490 attachment-portfolio size-portfolio wp-post-image" alt="mary Somerville" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: Mathematician Mary Somerville Features in Google Doodle"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/mary-somerville-features-in-google-doodle/' title='Mathematician Mary Somerville Features in Google Doodle'>Mathematician Mary Somerville Features in Google Doodle</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2020-02-02T07:35:03-06:00" >February 2, 2020</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/mary-somerville-features-in-google-doodle/#respond'>0 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >The Google Doodle for 2 February 2020 celebrated Mary Somerville, the Scottish polymath and science writer, and Caroline Herschel, the joint first-ever…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2020/03/mary-Somerville.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>Mark R Smith</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>Mark R Smith</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2020-02-02 07:35:03</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2024-08-17 17:24:05</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>Mathematician Mary Somerville Features in Google Doodle</span></span></span></article><article class='slide-entry flex_column post-entry post-entry-24632 slide-entry-overview slide-loop-26 slide-parity-even av_one_third real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/how-most-proofs-are-structured-and-how-to-write-them/' data-rel='slide-1' class='slide-image' title='How to Write a Math Proof and Their Structure'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2019/05/writing_proofs.png" class="wp-image-24732 avia-img-lazy-loading-not-24732 attachment-portfolio size-portfolio wp-post-image" alt="writing proofs" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2019/05/writing_proofs.png" class="wp-image-24732 avia-img-lazy-loading-not-24732 attachment-portfolio size-portfolio wp-post-image" alt="writing proofs" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: How to Write a Math Proof and Their Structure"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/how-most-proofs-are-structured-and-how-to-write-them/' title='How to Write a Math Proof and Their Structure'>How to Write a Math Proof and Their Structure</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2019-06-03T07:17:08-05:00" >June 3, 2019</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/how-most-proofs-are-structured-and-how-to-write-them/#comments'>1 Comment</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >Proofs in mathematics are what mathematics is all about. They are subject to entire books, created entire theories like Fermat's last theorem, are hard…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/05/writing_proofs.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>fresh_42</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>fresh_42</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2019-06-03 07:17:08</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2024-08-17 17:03:38</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>How to Write a Math Proof and Their Structure</span></span></span></article><article class='slide-entry flex_column post-entry post-entry-24050 slide-entry-overview slide-loop-27 slide-parity-odd av_one_third real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/a-pure-hamiltonian-proof-of-the-maupertuis-principle/' data-rel='slide-1' class='slide-image' title='A Pure Hamiltonian Proof of the Maupertuis Principle'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2019/03/Maupertuis_Principle_1.png" class="wp-image-24084 avia-img-lazy-loading-not-24084 attachment-portfolio size-portfolio wp-post-image" alt="Maupertuis Principle" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2019/03/Maupertuis_Principle_1.png" class="wp-image-24084 avia-img-lazy-loading-not-24084 attachment-portfolio size-portfolio wp-post-image" alt="Maupertuis Principle" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: A Pure Hamiltonian Proof of the Maupertuis Principle"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/a-pure-hamiltonian-proof-of-the-maupertuis-principle/' title='A Pure Hamiltonian Proof of the Maupertuis Principle'>A Pure Hamiltonian Proof of the Maupertuis Principle</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2019-03-18T13:36:26-05:00" >March 18, 2019</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/a-pure-hamiltonian-proof-of-the-maupertuis-principle/#respond'>0 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >Here is another version of proof of Maupertuis's principle. This version is pure Hamiltonian and independent of the Lagrangian approach.The proof…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/03/Maupertuis_Principle_1.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>wrobel</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>wrobel</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2019-03-18 13:36:26</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2021-04-20 07:50:31</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>A Pure Hamiltonian Proof of the Maupertuis Principle</span></span></span></article></div><div class="slide-entry-wrap"><article class='slide-entry flex_column post-entry post-entry-23610 slide-entry-overview slide-loop-28 slide-parity-odd av_one_third first real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/the-sum-of-geometric-series-from-probability-theory/' data-rel='slide-1' class='slide-image' title='The Sum of Geometric Series from Probability Theory'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2019/02/probability_theory.png" class="wp-image-23623 avia-img-lazy-loading-not-23623 attachment-portfolio size-portfolio wp-post-image" alt="The Sum of Geometric Series from Probability Theory" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2019/02/probability_theory.png" class="wp-image-23623 avia-img-lazy-loading-not-23623 attachment-portfolio size-portfolio wp-post-image" alt="The Sum of Geometric Series from Probability Theory" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: The Sum of Geometric Series from Probability Theory"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/the-sum-of-geometric-series-from-probability-theory/' title='The Sum of Geometric Series from Probability Theory'>The Sum of Geometric Series from Probability Theory</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2019-02-18T06:14:21-06:00" >February 18, 2019</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/the-sum-of-geometric-series-from-probability-theory/#comments'>12 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >Here I present a simple (but to the best of my knowledge, new) derivation of the formula for the sum of the infinite geometric series. The derivation is…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/probability_theory.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>Demystifier</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>Demystifier</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2019-02-18 06:14:21</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2021-04-18 15:06:11</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>The Sum of Geometric Series from Probability Theory</span></span></span></article><article class='slide-entry flex_column post-entry post-entry-23125 slide-entry-overview slide-loop-29 slide-parity-even av_one_third real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/lie-algebras-a-walkthrough-the-representations/' data-rel='slide-1' class='slide-image' title='Lie Algebras: A Walkthrough The Representations'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2019/01/lie_algebra_representations.png" class="wp-image-23401 avia-img-lazy-loading-not-23401 attachment-portfolio size-portfolio wp-post-image" alt="lie algebra representations" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2019/01/lie_algebra_representations.png" class="wp-image-23401 avia-img-lazy-loading-not-23401 attachment-portfolio size-portfolio wp-post-image" alt="lie algebra representations" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: Lie Algebras: A Walkthrough The Representations"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/lie-algebras-a-walkthrough-the-representations/' title='Lie Algebras: A Walkthrough The Representations'>Lie Algebras: A Walkthrough The Representations</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2019-01-25T08:33:44-06:00" >January 25, 2019</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/lie-algebras-a-walkthrough-the-representations/#comments'>1 Comment</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >  Part III: Representations  10. Sums and Products. Frobenius began in ##1896## to generalize Weber's group characters and soon investigated…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/01/lie_algebra_representations.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>fresh_42</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>fresh_42</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2019-01-25 08:33:44</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2023-10-06 08:45:35</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>Lie Algebras: A Walkthrough The Representations</span></span></span></article><article class='slide-entry flex_column post-entry post-entry-23123 slide-entry-overview slide-loop-30 slide-parity-odd av_one_third real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/lie-algebras-a-walkthrough-the-structures/' data-rel='slide-1' class='slide-image' title='Learn Lie Algebras: A Walkthrough The Structures'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2019/01/lie_algebra_structure.png" class="wp-image-23259 avia-img-lazy-loading-not-23259 attachment-portfolio size-portfolio wp-post-image" alt="Lie Algebra Structure" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2019/01/lie_algebra_structure.png" class="wp-image-23259 avia-img-lazy-loading-not-23259 attachment-portfolio size-portfolio wp-post-image" alt="Lie Algebra Structure" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: Learn Lie Algebras: A Walkthrough The Structures"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/lie-algebras-a-walkthrough-the-structures/' title='Learn Lie Algebras: A Walkthrough The Structures'>Learn Lie Algebras: A Walkthrough The Structures</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2019-01-07T13:36:58-06:00" >January 7, 2019</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/lie-algebras-a-walkthrough-the-structures/#comments'>2 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >  Part II: Structures5. Decompositions.Lie algebra theory is to a large extend the classification of the semisimple Lie algebras…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/01/lie_algebra_structure.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>fresh_42</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>fresh_42</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2019-01-07 13:36:58</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2024-09-30 08:59:26</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>Learn Lie Algebras: A Walkthrough The Structures</span></span></span></article></div><div class="slide-entry-wrap"><article class='slide-entry flex_column post-entry post-entry-23114 slide-entry-overview slide-loop-31 slide-parity-odd av_one_third first real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/lie-algebras-a-walkthrough-the-basics/' data-rel='slide-1' class='slide-image' title='Learn Lie Algebras: A Walkthrough The Basics'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2019/01/lie_algebra_basics.png" class="wp-image-23193 avia-img-lazy-loading-not-23193 attachment-portfolio size-portfolio wp-post-image" alt="lie algebra basics" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2019/01/lie_algebra_basics.png" class="wp-image-23193 avia-img-lazy-loading-not-23193 attachment-portfolio size-portfolio wp-post-image" alt="lie algebra basics" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: Learn Lie Algebras: A Walkthrough The Basics"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/lie-algebras-a-walkthrough-the-basics/' title='Learn Lie Algebras: A Walkthrough The Basics'>Learn Lie Algebras: A Walkthrough The Basics</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2019-01-03T13:22:45-06:00" >January 3, 2019</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/lie-algebras-a-walkthrough-the-basics/#comments'>7 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >  Part I: Basics 1. Introduction. This article is meant to provide a quick reference guide to Lie algebras: the terminology, important theorems,…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/01/lie_algebra_basics.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>fresh_42</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>fresh_42</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2019-01-03 13:22:45</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2021-04-02 10:56:37</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>Learn Lie Algebras: A Walkthrough The Basics</span></span></span></article><article class='slide-entry flex_column post-entry post-entry-21426 slide-entry-overview slide-loop-32 slide-parity-even av_one_third real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/a-simplified-synthesis-of-financial-options-pricing/' data-rel='slide-1' class='slide-image' title='Learn a Simplified Synthesis of Financial Options Pricing'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2018/08/stock_options.png" class="wp-image-21511 avia-img-lazy-loading-not-21511 attachment-portfolio size-portfolio wp-post-image" alt="stock options math" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2018/08/stock_options.png" class="wp-image-21511 avia-img-lazy-loading-not-21511 attachment-portfolio size-portfolio wp-post-image" alt="stock options math" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: Learn a Simplified Synthesis of Financial Options Pricing"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/a-simplified-synthesis-of-financial-options-pricing/' title='Learn a Simplified Synthesis of Financial Options Pricing'>Learn a Simplified Synthesis of Financial Options Pricing</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2018-08-17T22:42:01-05:00" >August 17, 2018</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/a-simplified-synthesis-of-financial-options-pricing/#comments'>19 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >Financial options (the right to purchase ("call") or sell ("put") stock (or other assets)) at a fixed price at a future date have been around for a long…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2018/08/stock_options.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>rude man</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>rude man</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2018-08-17 22:42:01</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2024-08-17 16:46:33</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>Learn a Simplified Synthesis of Financial Options Pricing</span></span></span></article><article class='slide-entry flex_column post-entry post-entry-18465 slide-entry-overview slide-loop-33 slide-parity-odd av_one_third real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/hilbert-spaces-relatives-part-ii/' data-rel='slide-1' class='slide-image' title='Learn the Basics of Hilbert Spaces and Their Relatives: Operators'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2018/03/hilbertspaces2.png" class="wp-image-18612 avia-img-lazy-loading-not-18612 attachment-portfolio size-portfolio wp-post-image" alt="hilbertspaces2" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2018/03/hilbertspaces2.png" class="wp-image-18612 avia-img-lazy-loading-not-18612 attachment-portfolio size-portfolio wp-post-image" alt="hilbertspaces2" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: Learn the Basics of Hilbert Spaces and Their Relatives: Operators"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/hilbert-spaces-relatives-part-ii/' title='Learn the Basics of Hilbert Spaces and Their Relatives: Operators'>Learn the Basics of Hilbert Spaces and Their Relatives: Operators</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2018-03-06T18:25:08-06:00" >March 6, 2018</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/hilbert-spaces-relatives-part-ii/#comments'>4 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >  Operators. The Maze Of Definitions. We will use the conventions of part I (Basics), which are ##\mathbb{F}\in \{\mathbb{R},\mathbb{C}\}##,…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2018/03/hilbertspaces2.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>fresh_42</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>fresh_42</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2018-03-06 18:25:08</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2021-04-02 09:32:29</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>Learn the Basics of Hilbert Spaces and Their Relatives: Operators</span></span></span></article></div><div class="slide-entry-wrap"><article class='slide-entry flex_column post-entry post-entry-18356 slide-entry-overview slide-loop-34 slide-parity-odd av_one_third first real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/hilbert-spaces-relatives/' data-rel='slide-1' class='slide-image' title='Learn the Basics of Hilbert Spaces and Their Relatives'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2018/02/hilbertspaces.png" class="wp-image-18410 avia-img-lazy-loading-not-18410 attachment-portfolio size-portfolio wp-post-image" alt="hilbertspaces" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2018/02/hilbertspaces.png" class="wp-image-18410 avia-img-lazy-loading-not-18410 attachment-portfolio size-portfolio wp-post-image" alt="hilbertspaces" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: Learn the Basics of Hilbert Spaces and Their Relatives"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/hilbert-spaces-relatives/' title='Learn the Basics of Hilbert Spaces and Their Relatives'>Learn the Basics of Hilbert Spaces and Their Relatives</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2018-02-16T15:25:53-06:00" >February 16, 2018</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/hilbert-spaces-relatives/#comments'>2 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >  Basics Language first: There is no such thing as the Hilbert space.Hilbert spaces can look rather different, and which one is used in…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2018/02/hilbertspaces.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>fresh_42</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>fresh_42</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2018-02-16 15:25:53</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2021-04-02 09:24:03</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>Learn the Basics of Hilbert Spaces and Their Relatives</span></span></span></article><article class='slide-entry flex_column post-entry post-entry-16627 slide-entry-overview slide-loop-35 slide-parity-even av_one_third real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/intransitive-dice-twist/' data-rel='slide-1' class='slide-image' title='Learn About Intransitive Dice with a Twist'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2017/12/dice.png" class="wp-image-16687 avia-img-lazy-loading-not-16687 attachment-portfolio size-portfolio wp-post-image" alt="dice" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2017/12/dice.png" class="wp-image-16687 avia-img-lazy-loading-not-16687 attachment-portfolio size-portfolio wp-post-image" alt="dice" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: Learn About Intransitive Dice with a Twist"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/intransitive-dice-twist/' title='Learn About Intransitive Dice with a Twist'>Learn About Intransitive Dice with a Twist</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2017-12-07T15:44:45-06:00" >December 7, 2017</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/intransitive-dice-twist/#comments'>6 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >Intransitive dice are sets of dice that don't follow the usual rules for "is better/larger than". If A<B and B<C, then A<C. If Bob runs faster…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2017/12/dice.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>mfb</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>mfb</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2017-12-07 15:44:45</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2024-08-17 16:12:00</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>Learn About Intransitive Dice with a Twist</span></span></span></article><article class='slide-entry flex_column post-entry post-entry-15554 slide-entry-overview slide-loop-36 slide-parity-odd av_one_third real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/journey-manifold-su2mathbbc-part/' data-rel='slide-1' class='slide-image' title='A Journey to The Manifold SU(2): Differentiation, Spheres, and Fiber Bundles'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2017/10/manifold1.png" class="wp-image-15769 avia-img-lazy-loading-not-15769 attachment-portfolio size-portfolio wp-post-image" alt="" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2017/10/manifold1.png" class="wp-image-15769 avia-img-lazy-loading-not-15769 attachment-portfolio size-portfolio wp-post-image" alt="" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: A Journey to The Manifold SU(2): Differentiation, Spheres, and Fiber Bundles"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/journey-manifold-su2mathbbc-part/' title='A Journey to The Manifold SU(2): Differentiation, Spheres, and Fiber Bundles'>A Journey to The Manifold SU(2): Differentiation, Spheres, and Fiber Bundles</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2017-10-16T12:06:58-05:00" >October 16, 2017</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/journey-manifold-su2mathbbc-part/#comments'>3 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >Part 2  Differentiation, Spheres, and Fiber Bundles Image source: [24]The special unitary groups play a significant role in the standard…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2017/10/manifold1.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>fresh_42</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>fresh_42</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2017-10-16 12:06:58</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2021-04-01 10:40:51</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>A Journey to The Manifold SU(2): Differentiation, Spheres, and Fiber Bundles</span></span></span></article></div><div class="slide-entry-wrap"><article class='slide-entry flex_column post-entry post-entry-14889 slide-entry-overview slide-loop-37 slide-parity-odd av_one_third first real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/tell-operations-operators-functionals-representations-apart/' data-rel='slide-1' class='slide-image' title='How to Tell Operations, Operators, Functionals, and Representations Apart'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2017/07/operators.png" class="wp-image-14945 avia-img-lazy-loading-not-14945 attachment-portfolio size-portfolio wp-post-image" alt="mathoperators" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2017/07/operators.png" class="wp-image-14945 avia-img-lazy-loading-not-14945 attachment-portfolio size-portfolio wp-post-image" alt="mathoperators" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: How to Tell Operations, Operators, Functionals, and Representations Apart"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/tell-operations-operators-functionals-representations-apart/' title='How to Tell Operations, Operators, Functionals, and Representations Apart'>How to Tell Operations, Operators, Functionals, and Representations Apart</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2017-07-21T03:45:25-05:00" >July 21, 2017</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/tell-operations-operators-functionals-representations-apart/#comments'>24 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" > All these concepts belong to the toolbox of physicists. I read them quite often on our forum and their usage is sometimes a bit confusing.…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2017/07/operators.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>fresh_42</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>fresh_42</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2017-07-21 03:45:25</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2024-08-17 14:52:07</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>How to Tell Operations, Operators, Functionals, and Representations Apart</span></span></span></article><article class='slide-entry flex_column post-entry post-entry-12270 slide-entry-overview slide-loop-38 slide-parity-even av_one_third real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/simple-geometry-deep-math/' data-rel='slide-1' class='slide-image' title='When Simple Geometry Unveils Deep Math'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2017/01/geometrysimple.png" class="wp-image-12350 avia-img-lazy-loading-not-12350 attachment-portfolio size-portfolio wp-post-image" alt="geometrysimple" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2017/01/geometrysimple.png" class="wp-image-12350 avia-img-lazy-loading-not-12350 attachment-portfolio size-portfolio wp-post-image" alt="geometrysimple" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: When Simple Geometry Unveils Deep Math"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/simple-geometry-deep-math/' title='When Simple Geometry Unveils Deep Math'>When Simple Geometry Unveils Deep Math</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2017-01-21T15:05:30-06:00" >January 21, 2017</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/simple-geometry-deep-math/#comments'>28 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >Introduction It is a remarkable fact that consideration of very elementary concepts in geometry often leads quickly into deep and unexpected mathematical…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2017/01/geometrysimple.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>trilobite</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>trilobite</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2017-01-21 15:05:30</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2021-04-02 13:02:35</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>When Simple Geometry Unveils Deep Math</span></span></span></article><article class='slide-entry flex_column post-entry post-entry-11596 slide-entry-overview slide-loop-39 slide-parity-odd av_one_third real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/representations-precision-important/' data-rel='slide-1' class='slide-image' title='Linear Representations and Why Precision is Important in Math'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2016/11/representations.png" class="wp-image-11646 avia-img-lazy-loading-not-11646 attachment-portfolio size-portfolio wp-post-image" alt="representations" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2016/11/representations.png" class="wp-image-11646 avia-img-lazy-loading-not-11646 attachment-portfolio size-portfolio wp-post-image" alt="representations" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: Linear Representations and Why Precision is Important in Math"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/representations-precision-important/' title='Linear Representations and Why Precision is Important in Math'>Linear Representations and Why Precision is Important in Math</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2016-11-16T14:40:43-06:00" >November 16, 2016</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/representations-precision-important/#comments'>2 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >First of all: What is a representation? It is the description of a mathematical object like a Lie group or a Lie algebra by its actions on another space…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2016/11/representations.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>fresh_42</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>fresh_42</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2016-11-16 14:40:43</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2024-06-07 06:16:02</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>Linear Representations and Why Precision is Important in Math</span></span></span></article></div><div class="slide-entry-wrap"><article class='slide-entry flex_column post-entry post-entry-11505 slide-entry-overview slide-loop-40 slide-parity-odd av_one_third first real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/can-angles-assigned-dimension/' data-rel='slide-1' class='slide-image' title='Can Angles be Assigned a Dimension?'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2016/11/angledimensions.png" class="wp-image-11520 avia-img-lazy-loading-not-11520 attachment-portfolio size-portfolio wp-post-image" alt="angledimensions" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2016/11/angledimensions.png" class="wp-image-11520 avia-img-lazy-loading-not-11520 attachment-portfolio size-portfolio wp-post-image" alt="angledimensions" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: Can Angles be Assigned a Dimension?"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/can-angles-assigned-dimension/' title='Can Angles be Assigned a Dimension?'>Can Angles be Assigned a Dimension?</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2016-11-12T15:48:20-06:00" >November 12, 2016</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/can-angles-assigned-dimension/#comments'>106 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" > 1. Some Background on Dimensional Analysis ... if you are not already familiar with it. 1.1 Dimensions Dimensional Analysis is a way of analyzing…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2016/11/angledimensions.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>Derek Bolton</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>Derek Bolton</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2016-11-12 15:48:20</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2024-06-07 06:16:03</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>Can Angles be Assigned a Dimension?</span></span></span></article><article class='slide-entry flex_column post-entry post-entry-10144 slide-entry-overview slide-loop-41 slide-parity-even av_one_third real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/groups-and-geometry/' data-rel='slide-1' class='slide-image' title='Exploring the Relationship Between Group Theory and Geometry'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2016/06/groupsandgeometry.png" class="wp-image-10182 avia-img-lazy-loading-not-10182 attachment-portfolio size-portfolio wp-post-image" alt="groupsandgeometry" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2016/06/groupsandgeometry.png" class="wp-image-10182 avia-img-lazy-loading-not-10182 attachment-portfolio size-portfolio wp-post-image" alt="groupsandgeometry" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: Exploring the Relationship Between Group Theory and Geometry"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/groups-and-geometry/' title='Exploring the Relationship Between Group Theory and Geometry'>Exploring the Relationship Between Group Theory and Geometry</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2016-06-30T22:17:49-05:00" >June 30, 2016</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/groups-and-geometry/#comments'>7 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >There is a very deep link between group theory and geometry. Sadly, this link is not emphasized a lot in most courses of group theory, even though it is…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2016/06/groupsandgeometry.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>Micromass</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>Micromass</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2016-06-30 22:17:49</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2024-06-07 06:16:03</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>Exploring the Relationship Between Group Theory and Geometry</span></span></span></article><article class='slide-entry flex_column post-entry post-entry-10074 slide-entry-overview slide-loop-42 slide-parity-odd av_one_third real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/friends-strangers-7825-computers/' data-rel='slide-1' class='slide-image' title='An Interesting Ramsey Theory Riddle'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2016/06/aastock2.png" class="wp-image-11309 avia-img-lazy-loading-not-11309 attachment-portfolio size-portfolio wp-post-image" alt="computers" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2016/06/aastock2.png" class="wp-image-11309 avia-img-lazy-loading-not-11309 attachment-portfolio size-portfolio wp-post-image" alt="computers" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: An Interesting Ramsey Theory Riddle"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/friends-strangers-7825-computers/' title='An Interesting Ramsey Theory Riddle'>An Interesting Ramsey Theory Riddle</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2016-06-22T04:29:42-05:00" >June 22, 2016</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/friends-strangers-7825-computers/#comments'>5 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >Ramsey theory has its origins in a very nice riddle Consider a party of 6 people. Any two of these 6 will either be meeting each other for the first time…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2016/06/aastock2.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>Micromass</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>Micromass</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2016-06-22 04:29:42</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2021-04-02 10:18:50</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>An Interesting Ramsey Theory Riddle</span></span></span></article></div><div class="slide-entry-wrap"><article class='slide-entry flex_column post-entry post-entry-9649 slide-entry-overview slide-loop-43 slide-parity-odd av_one_third first real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/scientific-inference-come-know-stuff-part-3/' data-rel='slide-1' class='slide-image' title='Scientific Inference: Balancing Predictive Success with Falsifiability'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2016/05/logicp3.png" class="wp-image-9701 avia-img-lazy-loading-not-9701 attachment-portfolio size-portfolio wp-post-image" alt="logicp3" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2016/05/logicp3.png" class="wp-image-9701 avia-img-lazy-loading-not-9701 attachment-portfolio size-portfolio wp-post-image" alt="logicp3" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: Scientific Inference: Balancing Predictive Success with Falsifiability"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/scientific-inference-come-know-stuff-part-3/' title='Scientific Inference: Balancing Predictive Success with Falsifiability'>Scientific Inference: Balancing Predictive Success with Falsifiability</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2016-05-12T13:06:37-05:00" >May 12, 2016</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/scientific-inference-come-know-stuff-part-3/#comments'>9 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >  Bayes' Theorem: Balancing predictive success with falsifiability Despite its murky logical pedigree, confirmation is a key part of learning.…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2016/05/logicp3.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>Brian Powell</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>Brian Powell</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2016-05-12 13:06:37</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2024-08-17 09:22:00</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>Scientific Inference: Balancing Predictive Success with Falsifiability</span></span></span></article><article class='slide-entry flex_column post-entry post-entry-8943 slide-entry-overview slide-loop-44 slide-parity-even av_one_third real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/perfect-secrecy-unbreakable-cipher/' data-rel='slide-1' class='slide-image' title='Is It Possible to Design an Unbreakable Cipher?'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2016/03/encryption.png" class="wp-image-9100 avia-img-lazy-loading-not-9100 attachment-portfolio size-portfolio wp-post-image" alt="encryption" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2016/03/encryption.png" class="wp-image-9100 avia-img-lazy-loading-not-9100 attachment-portfolio size-portfolio wp-post-image" alt="encryption" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: Is It Possible to Design an Unbreakable Cipher?"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/perfect-secrecy-unbreakable-cipher/' title='Is It Possible to Design an Unbreakable Cipher?'>Is It Possible to Design an Unbreakable Cipher?</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2016-04-01T14:35:17-05:00" >April 1, 2016</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/perfect-secrecy-unbreakable-cipher/#comments'>10 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >Is it possible to design an unbreakable cipher? Do methods of encryption exist that guarantee privacy from even the most capable and highly-resourced…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2016/03/encryption.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>Brian Powell</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>Brian Powell</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2016-04-01 14:35:17</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2024-09-30 08:56:14</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>Is It Possible to Design an Unbreakable Cipher?</span></span></span></article><article class='slide-entry flex_column post-entry post-entry-8616 slide-entry-overview slide-loop-45 slide-parity-odd av_one_third real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/monographic-substitution-cipher-julius-caesar-kgb/' data-rel='slide-1' class='slide-image' title='The Monographic Substitution Cipher: From Julius Caesar to the KGB'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2016/03/cipher.png" class="wp-image-8729 avia-img-lazy-loading-not-8729 attachment-portfolio size-portfolio wp-post-image" alt="cipher" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2016/03/cipher.png" class="wp-image-8729 avia-img-lazy-loading-not-8729 attachment-portfolio size-portfolio wp-post-image" alt="cipher" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: The Monographic Substitution Cipher: From Julius Caesar to the KGB"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/monographic-substitution-cipher-julius-caesar-kgb/' title='The Monographic Substitution Cipher: From Julius Caesar to the KGB'>The Monographic Substitution Cipher: From Julius Caesar to the KGB</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2016-03-13T22:03:57-05:00" >March 13, 2016</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/monographic-substitution-cipher-julius-caesar-kgb/#comments'>7 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >A monographic substitution cipher works by replacing individual characters of plaintext with corresponding characters of ciphertext. It is perhaps the…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2016/03/cipher.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>Brian Powell</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>Brian Powell</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2016-03-13 22:03:57</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2024-08-17 07:21:10</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>The Monographic Substitution Cipher: From Julius Caesar to the KGB</span></span></span></article></div><div class="slide-entry-wrap"><article class='slide-entry flex_column post-entry post-entry-7753 slide-entry-overview slide-loop-46 slide-parity-odd av_one_third first real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/case-learning-complex-math/' data-rel='slide-1' class='slide-image' title='Hear the Case for Learning Complex Math'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2016/02/complexmath.png" class="wp-image-8255 avia-img-lazy-loading-not-8255 attachment-portfolio size-portfolio wp-post-image" alt="complexmath" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2016/02/complexmath.png" class="wp-image-8255 avia-img-lazy-loading-not-8255 attachment-portfolio size-portfolio wp-post-image" alt="complexmath" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: Hear the Case for Learning Complex Math"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/case-learning-complex-math/' title='Hear the Case for Learning Complex Math'>Hear the Case for Learning Complex Math</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2016-02-03T22:59:20-06:00" >February 3, 2016</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/case-learning-complex-math/#comments'>15 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >Resistance to complex math seems to never die out. I see it frequently in PF posts. Often it takes the form of challenges rather than questions. …</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2016/02/complexmath.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>anorlunda</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>anorlunda</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2016-02-03 22:59:20</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2024-09-02 09:36:36</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>Hear the Case for Learning Complex Math</span></span></span></article><article class='slide-entry flex_column post-entry post-entry-7469 slide-entry-overview slide-loop-47 slide-parity-even av_one_third real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/things-can-go-wrong-complex-numbers/' data-rel='slide-1' class='slide-image' title='Things Which Can Go Wrong with Complex Numbers'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2016/01/complexnumbers.png" class="wp-image-7575 avia-img-lazy-loading-not-7575 attachment-portfolio size-portfolio wp-post-image" alt="complexnumbers" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2016/01/complexnumbers.png" class="wp-image-7575 avia-img-lazy-loading-not-7575 attachment-portfolio size-portfolio wp-post-image" alt="complexnumbers" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: Things Which Can Go Wrong with Complex Numbers"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/things-can-go-wrong-complex-numbers/' title='Things Which Can Go Wrong with Complex Numbers'>Things Which Can Go Wrong with Complex Numbers</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2016-01-14T20:20:21-06:00" >January 14, 2016</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/things-can-go-wrong-complex-numbers/#comments'>3 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >At the first sight, there are many paradoxes in complex number theory. Here are some nice examples of things that don't seem to work:Example A [itex]-1=i^2=\sqrt{-1}\cdot\sqrt{-1}=\sqrt{(-1)(-1)}=\sqrt{1}=1[/itex]Example…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2016/01/complexnumbers.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>Micromass</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>Micromass</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2016-01-14 20:20:21</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2021-04-02 08:23:51</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>Things Which Can Go Wrong with Complex Numbers</span></span></span></article><article class='slide-entry flex_column post-entry post-entry-4634 slide-entry-overview slide-loop-48 slide-parity-odd av_one_third real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/millennium-prize-problems-part-i/' data-rel='slide-1' class='slide-image' title='Intro to the Millennium Prize Problems'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2016/01/MillenniumPrize.png" class="wp-image-7496 avia-img-lazy-loading-not-7496 attachment-portfolio size-portfolio wp-post-image" alt="MillenniumPrize" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2016/01/MillenniumPrize.png" class="wp-image-7496 avia-img-lazy-loading-not-7496 attachment-portfolio size-portfolio wp-post-image" alt="MillenniumPrize" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: Intro to the Millennium Prize Problems"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/millennium-prize-problems-part-i/' title='Intro to the Millennium Prize Problems'>Intro to the Millennium Prize Problems</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2016-01-07T14:59:39-06:00" >January 7, 2016</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/millennium-prize-problems-part-i/#comments'>13 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >IntroductionIn this Insight, I will go over the background information for the Millennium Prize problems and briefly describe three of them. A future…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2016/01/MillenniumPrize.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>Josh Meyer</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>Josh Meyer</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2016-01-07 14:59:39</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2024-08-17 06:58:56</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>Intro to the Millennium Prize Problems</span></span></span></article></div><div class="slide-entry-wrap"><article class='slide-entry flex_column post-entry post-entry-17375 slide-entry-overview slide-loop-49 slide-parity-odd av_one_third first real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/axioms-natural-numbers/' data-rel='slide-1' class='slide-image' title='Learn Axioms for the Natural Numbers'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2018/01/micro2.png" class="wp-image-17383 avia-img-lazy-loading-not-17383 attachment-portfolio size-portfolio wp-post-image" alt="micro2" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2018/01/micro2.png" class="wp-image-17383 avia-img-lazy-loading-not-17383 attachment-portfolio size-portfolio wp-post-image" alt="micro2" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: Learn Axioms for the Natural Numbers"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/axioms-natural-numbers/' title='Learn Axioms for the Natural Numbers'>Learn Axioms for the Natural Numbers</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2016-01-04T21:59:12-06:00" >January 4, 2016</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/axioms-natural-numbers/#respond'>0 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >** Bloch Chapter 1.2The Peano system in Bloch has a special element ##1\in \mathbb{N}##. The intuitive idea here is that ##\mathbb{N} = \{1,2,3,...\}##.…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2018/01/micro2.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>Micromass</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>Micromass</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2016-01-04 21:59:12</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2023-08-15 09:04:11</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>Learn Axioms for the Natural Numbers</span></span></span></article><article class='slide-entry flex_column post-entry post-entry-17368 slide-entry-overview slide-loop-50 slide-parity-even av_one_third real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/forward-real-numbers-real-analysis/' data-rel='slide-1' class='slide-image' title='An Intro on Real Numbers and Real Analysis'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2018/01/micro3.png" class="wp-image-17384 avia-img-lazy-loading-not-17384 attachment-portfolio size-portfolio wp-post-image" alt="micro3" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2018/01/micro3.png" class="wp-image-17384 avia-img-lazy-loading-not-17384 attachment-portfolio size-portfolio wp-post-image" alt="micro3" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: An Intro on Real Numbers and Real Analysis"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/forward-real-numbers-real-analysis/' title='An Intro on Real Numbers and Real Analysis'>An Intro on Real Numbers and Real Analysis</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2016-01-03T22:00:30-06:00" >January 3, 2016</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/forward-real-numbers-real-analysis/#respond'>0 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >It is important to realize that in standard mathematics, we attempt to characterize everything in terms of sets. This means that notions such as natural…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2018/01/micro3.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>Micromass</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>Micromass</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2016-01-03 22:00:30</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2024-08-17 06:56:39</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>An Intro on Real Numbers and Real Analysis</span></span></span></article><article class='slide-entry flex_column post-entry post-entry-7094 slide-entry-overview slide-loop-51 slide-parity-odd av_one_third real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/trials-tribulations-physicist-became-math-geek/' data-rel='slide-1' class='slide-image' title='Trials and Tribulations of a Physicist who Became a Math Geek'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2015/12/physicsturnedmath.png" class="wp-image-7104 avia-img-lazy-loading-not-7104 attachment-portfolio size-portfolio wp-post-image" alt="physicsturnedmath" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2015/12/physicsturnedmath.png" class="wp-image-7104 avia-img-lazy-loading-not-7104 attachment-portfolio size-portfolio wp-post-image" alt="physicsturnedmath" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: Trials and Tribulations of a Physicist who Became a Math Geek"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/trials-tribulations-physicist-became-math-geek/' title='Trials and Tribulations of a Physicist who Became a Math Geek'>Trials and Tribulations of a Physicist who Became a Math Geek</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2015-12-06T16:33:10-06:00" >December 6, 2015</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/trials-tribulations-physicist-became-math-geek/#comments'>6 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >How did I go from the brink of changing my major from physics to ceramics (no more math) to the Math faculty of the Air Force Academy? How did I go from…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2015/12/physicsturnedmath.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>Dr. Courtney</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>Dr. Courtney</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2015-12-06 16:33:10</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2024-08-17 06:33:34</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>Trials and Tribulations of a Physicist who Became a Math Geek</span></span></span></article></div><div class="slide-entry-wrap"><article class='slide-entry flex_column post-entry post-entry-3783 slide-entry-overview slide-loop-52 slide-parity-odd av_one_third first real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/math-and-the-obvious/' data-rel='slide-1' class='slide-image' title='Lessons From My Experience Teaching Math'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2015/07/mathobvious.png" class="wp-image-3861 avia-img-lazy-loading-not-3861 attachment-portfolio size-portfolio wp-post-image" alt="math obvious" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2015/07/mathobvious.png" class="wp-image-3861 avia-img-lazy-loading-not-3861 attachment-portfolio size-portfolio wp-post-image" alt="math obvious" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: Lessons From My Experience Teaching Math"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/math-and-the-obvious/' title='Lessons From My Experience Teaching Math'>Lessons From My Experience Teaching Math</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2015-07-17T15:49:36-05:00" >July 17, 2015</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/math-and-the-obvious/#comments'>20 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >My #1 goal, when I teach a math class, is to convey a certain way of thinking about math. It's quite different from what my students have done before,…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2015/07/mathobvious.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>Kenny Felder</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>Kenny Felder</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2015-07-17 15:49:36</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2024-08-16 08:19:08</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>Lessons From My Experience Teaching Math</span></span></span></article><article class='slide-entry flex_column post-entry post-entry-1488 slide-entry-overview slide-loop-53 slide-parity-even av_one_third real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/brachistochrone-subway/' data-rel='slide-1' class='slide-image' title='A Brachistochrone Subway Is Not a Cost-effective Idea'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2015/05/subwayarticle.png" class="wp-image-2281 avia-img-lazy-loading-not-2281 attachment-portfolio size-portfolio wp-post-image" alt="subway" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2015/05/subwayarticle.png" class="wp-image-2281 avia-img-lazy-loading-not-2281 attachment-portfolio size-portfolio wp-post-image" alt="subway" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: A Brachistochrone Subway Is Not a Cost-effective Idea"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/brachistochrone-subway/' title='A Brachistochrone Subway Is Not a Cost-effective Idea'>A Brachistochrone Subway Is Not a Cost-effective Idea</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2015-05-14T14:38:24-05:00" >May 14, 2015</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/brachistochrone-subway/#comments'>6 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >It is apparent that a subway tunnel could be built without the need for supplied energy like electricity, assuming zero friction everywhere. The tunnel…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2015/05/subwayarticle.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>rude man</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>rude man</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2015-05-14 14:38:24</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2021-04-17 09:13:17</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>A Brachistochrone Subway Is Not a Cost-effective Idea</span></span></span></article><article class='slide-entry flex_column post-entry post-entry-17978 slide-entry-overview slide-loop-54 slide-parity-odd av_one_third real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/abstract-algebra-natural-numbers/' data-rel='slide-1' class='slide-image' title='Is Zero a Natural Number?'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2018/01/abstract_algebra.png" class="wp-image-17983 avia-img-lazy-loading-not-17983 attachment-portfolio size-portfolio wp-post-image" alt="abstract_algebra" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2018/01/abstract_algebra.png" class="wp-image-17983 avia-img-lazy-loading-not-17983 attachment-portfolio size-portfolio wp-post-image" alt="abstract_algebra" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: Is Zero a Natural Number?"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/abstract-algebra-natural-numbers/' title='Is Zero a Natural Number?'>Is Zero a Natural Number?</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2015-01-23T20:08:09-06:00" >January 23, 2015</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/abstract-algebra-natural-numbers/#respond'>0 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >Using: Anderson-Feil Chapter 1.1 Is zero a natural number? This is a pretty controversial question. Many mathematicians - especially those working in…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2018/01/abstract_algebra.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>Micromass</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>Micromass</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2015-01-23 20:08:09</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2024-11-10 15:03:38</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>Is Zero a Natural Number?</span></span></span></article></div><div class="slide-entry-wrap"><article class='slide-entry flex_column post-entry post-entry-17379 slide-entry-overview slide-loop-55 slide-parity-odd post-entry-last av_one_third first real-thumbnail posttype-post post-format-standard' itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost" ><a href='https://www.physicsforums.com/insights/what-is-a-property-formally/' data-rel='slide-1' class='slide-image' title='What is a Property Formally in Mathematical Logic'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDAiIGhlaWdodD0iMTM1IiB2aWV3Qm94PSIwIDAgMjQwIDEzNSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" fetchpriority="high" width="240" height="135" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2018/01/micro1.png" class="wp-image-17382 avia-img-lazy-loading-not-17382 attachment-portfolio size-portfolio wp-post-image" alt="micro1" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2018/01/micro1.png" class="wp-image-17382 avia-img-lazy-loading-not-17382 attachment-portfolio size-portfolio wp-post-image" alt="micro1" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: What is a Property Formally in Mathematical Logic"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/what-is-a-property-formally/' title='What is a Property Formally in Mathematical Logic'>What is a Property Formally in Mathematical Logic</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >January 4, 2015</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/what-is-a-property-formally/#respond'>0 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >** Hrbacek-Jech Chapter 1.2Hrbacek and Jech do not go into full detail about what a property is formally. This is a part of mathematical logic, but…</div></div><footer class="entry-footer"></footer><span class='hidden'> <span class='av-structured-data' itemprop="image" itemscope="itemscope" itemtype="https://schema.org/ImageObject" > <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2018/01/micro1.png</span> <span itemprop='height'>135</span> <span itemprop='width'>240</span> </span> <span class='av-structured-data' itemprop="publisher" itemtype="https://schema.org/Organization" itemscope="itemscope" > <span itemprop='name'>Micromass</span> <span itemprop='logo' itemscope itemtype='https://schema.org/ImageObject'> <span itemprop='url'>https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png</span> </span> </span><span class='av-structured-data' itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person" ><span itemprop='name'>Micromass</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-01-04T21:54:48-06:00" >2015-01-04 21:54:48</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2024-08-16 07:25:51</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>What is a Property Formally in Mathematical Logic</span></span></span></article></div></div></div></div></main><aside class='sidebar sidebar_right smartphones_sidebar_active alpha units' aria-label="Sidebar" role="complementary" itemscope="itemscope" itemtype="https://schema.org/WPSideBar" ><div class="inner_sidebar extralight-border"><section id="custom_html-2" class="widget_text widget clearfix widget_custom_html"><div class="textwidget custom-html-widget"><h2 class="widgettitle">Trending Articles</h2><ul class="wpp-list wpp-sunset"><li class="" style="--item-position: 1;--total-items: 10"><div class="item-position"></div><div class="item-data"><a href="https://www.physicsforums.com/insights/hand-wavy-discussion-planck-length/" class="wpp-post-title" target="_self">What Planck Length Is and It’s Common Misconceptions</a></div></li><li class="" style="--item-position: 2;--total-items: 10"><div class="item-position"></div><div class="item-data"><a href="https://www.physicsforums.com/insights/pbs-video-comment-what-if-physics-is-not-describing-reality/" class="wpp-post-title" target="_self">PBS Video Comment: “What If Physics IS NOT Describing Reality”</a></div></li><li class="" style="--item-position: 3;--total-items: 10"><div class="item-position"></div><div class="item-data"><a href="https://www.physicsforums.com/insights/can-see-atom/" class="wpp-post-title" target="_self">Can We See an Atom?</a></div></li><li class="" style="--item-position: 4;--total-items: 10"><div class="item-position"></div><div class="item-data"><a href="https://www.physicsforums.com/insights/the-7-basic-rules-of-quantum-mechanics/" class="wpp-post-title" target="_self">The 7 Basic Rules of Quantum Mechanics</a></div></li><li class="" style="--item-position: 5;--total-items: 10"><div class="item-position"></div><div class="item-data"><a href="https://www.physicsforums.com/insights/how-to-better-define-information-in-physics/" class="wpp-post-title" target="_self">How to Better Define Information in Physics</a></div></li><li class="" style="--item-position: 6;--total-items: 10"><div class="item-position"></div><div class="item-data"><a href="https://www.physicsforums.com/insights/what-is-a-tensor/" class="wpp-post-title" target="_self">What Is a Tensor? 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