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class="category-term-description"><h1>mathematics self-study Articles</h1></div><div class="entry-content-wrapper"><h3 class='post-title tag-page-post-type-title '>Tag Archive for: <span>mathematics self-study</span></h3><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-41907 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/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="2015-11-17T21:13:09-06:00" >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-38245 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/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="2015-11-17T21:13:09-06:00" >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><article class='slide-entry flex_column post-entry post-entry-30011 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/how-to-solve-second-order-partial-derivatives/' data-rel='slide-1' class='slide-image' title='How to Solve Second-Order Partial Derivatives'><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/2020/05/second-order-derivitive.png" class="wp-image-30056 avia-img-lazy-loading-not-30056 attachment-portfolio size-portfolio wp-post-image" alt="calculus" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2020/05/second-order-derivitive.png" class="wp-image-30056 avia-img-lazy-loading-not-30056 attachment-portfolio size-portfolio wp-post-image" alt="calculus" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: How to Solve Second-Order Partial Derivatives"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/how-to-solve-second-order-partial-derivatives/' title='How to Solve Second-Order Partial Derivatives'>How to Solve Second-Order Partial Derivatives</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2020-05-19T14:09:30-05:00" >May 19, 2020</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/how-to-solve-second-order-partial-derivatives/#comments'>1 Comment</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >Introduction A frequent concern among students is how to carry out higher order partial derivatives where a change of variables and the chain rule are…</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/2020/05/second-order-derivitive.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="2015-11-17T21:13:09-06:00" >2020-05-19 14:09:30</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2021-01-05 08:59:33</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>How to Solve Second-Order Partial Derivatives</span></span></span></article></div><div class="slide-entry-wrap"><article class='slide-entry flex_column post-entry post-entry-29836 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/the-analytic-continuation-of-the-lerch-and-the-zeta-functions/' data-rel='slide-1' class='slide-image' title='The Analytic Continuation of the Lerch and the Zeta Functions'><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/2020/04/lerch-zeta-functions.png" class="wp-image-29958 avia-img-lazy-loading-not-29958 attachment-portfolio size-portfolio wp-post-image" alt="lerch and zeta functions" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2020/04/lerch-zeta-functions.png" class="wp-image-29958 avia-img-lazy-loading-not-29958 attachment-portfolio size-portfolio wp-post-image" alt="lerch and zeta functions" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: The Analytic Continuation of the Lerch and the Zeta Functions"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/the-analytic-continuation-of-the-lerch-and-the-zeta-functions/' title='The Analytic Continuation of the Lerch and the Zeta Functions'>The Analytic Continuation of the Lerch and the Zeta Functions</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2020-04-27T08:07:42-05:00" >April 27, 2020</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/the-analytic-continuation-of-the-lerch-and-the-zeta-functions/#respond'>0 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >Introduction In this brief Insight article the analytic continuations of the Lerch Transcendent and Riemann Zeta Functions are achieved via the Euler's…</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/2020/04/lerch-zeta-functions.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'>benorin</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'>benorin</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-11-17T21:13:09-06:00" >2020-04-27 08:07:42</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2021-04-20 08:01:46</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>The Analytic Continuation of the Lerch and the Zeta Functions</span></span></span></article><article class='slide-entry flex_column post-entry post-entry-28956 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/a-path-to-fractional-integral-representations-of-some-special-functions/' data-rel='slide-1' class='slide-image' title='A Path to Fractional Integral Representations of Some Special Functions'><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/Integral-Representations-of-Some-Special-Functions.png" class="wp-image-29157 avia-img-lazy-loading-not-29157 attachment-portfolio size-portfolio wp-post-image" alt="Integral Representations of Some Special Functions" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2020/03/Integral-Representations-of-Some-Special-Functions.png" class="wp-image-29157 avia-img-lazy-loading-not-29157 attachment-portfolio size-portfolio wp-post-image" alt="Integral Representations of Some Special Functions" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: A Path to Fractional Integral Representations of Some Special Functions"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/a-path-to-fractional-integral-representations-of-some-special-functions/' title='A Path to Fractional Integral Representations of Some Special Functions'>A Path to Fractional Integral Representations of Some Special Functions</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2020-03-23T08:23:05-05:00" >March 23, 2020</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/a-path-to-fractional-integral-representations-of-some-special-functions/#comments'>9 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >Introduction This bit is what new thing you can learn reading this:) As for original content, I only have hope that the method of using the sets $$C_N^n:…</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/Integral-Representations-of-Some-Special-Functions.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'>benorin</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'>benorin</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-11-17T21:13:09-06:00" >2020-03-23 08:23:05</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'>A Path to Fractional Integral Representations of Some Special Functions</span></span></span></article><article class='slide-entry flex_column post-entry post-entry-22662 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/a-numerical-insight-for-the-fundamental-theorem-of-calculus/' data-rel='slide-1' class='slide-image' title='A Numerical Insight for the Fundamental Theorem of Calculus'><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/2018/11/calc_therom.png" class="wp-image-22664 avia-img-lazy-loading-not-22664 attachment-portfolio size-portfolio wp-post-image" alt="Calculus Therom" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2018/11/calc_therom.png" class="wp-image-22664 avia-img-lazy-loading-not-22664 attachment-portfolio size-portfolio wp-post-image" alt="Calculus Therom" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: A Numerical Insight for the Fundamental Theorem of Calculus"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/a-numerical-insight-for-the-fundamental-theorem-of-calculus/' title='A Numerical Insight for the Fundamental Theorem of Calculus'>A Numerical Insight for the Fundamental Theorem of Calculus</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2018-11-08T21:43:46-06:00" >November 8, 2018</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/a-numerical-insight-for-the-fundamental-theorem-of-calculus/#comments'>9 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >The purpose of this article is not to provide some rigorous statement, neither a rigorous clever proof of the fundamental theorem of calculus. It is rather…</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/2018/11/calc_therom.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'>Delta2</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'>Delta2</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-11-17T21:13:09-06:00" >2018-11-08 21:43:46</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2021-04-18 15:12:03</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>A Numerical Insight for the Fundamental Theorem of Calculus</span></span></span></article></div><div class="slide-entry-wrap"><article class='slide-entry flex_column post-entry post-entry-21213 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/the-10-commandments-of-index-expressions-and-tensor-calculus/' data-rel='slide-1' class='slide-image' title='The 10 Commandments of Index Expressions and Tensor Calculus'><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/2018/07/tensorcalculus.png" class="wp-image-21224 avia-img-lazy-loading-not-21224 attachment-portfolio size-portfolio wp-post-image" alt="tensor calculus" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2018/07/tensorcalculus.png" class="wp-image-21224 avia-img-lazy-loading-not-21224 attachment-portfolio size-portfolio wp-post-image" alt="tensor calculus" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: The 10 Commandments of Index Expressions and Tensor Calculus"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/the-10-commandments-of-index-expressions-and-tensor-calculus/' title='The 10 Commandments of Index Expressions and Tensor Calculus'>The 10 Commandments of Index Expressions and Tensor Calculus</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2018-07-28T08:15:26-05:00" >July 28, 2018</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/the-10-commandments-of-index-expressions-and-tensor-calculus/#comments'>16 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >Having more than 10 years of experience in teaching vector and tensor calculus and special and general relativity, I have noted that many people have 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/2018/07/tensorcalculus.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'>Orodruin</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'>Orodruin</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-11-17T21:13:09-06:00" >2018-07-28 08:15:26</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2024-08-17 16:44:26</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>The 10 Commandments of Index Expressions and Tensor Calculus</span></span></span></article><article class='slide-entry flex_column post-entry post-entry-16491 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/homopolar-generator-analytical-example/' data-rel='slide-1' class='slide-image' title='What is the Homopolar Generator: An Analytical Example'><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/2017/11/maxwell.png" class="wp-image-16528 avia-img-lazy-loading-not-16528 attachment-portfolio size-portfolio wp-post-image" alt="Maxwell equations" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2017/11/maxwell.png" class="wp-image-16528 avia-img-lazy-loading-not-16528 attachment-portfolio size-portfolio wp-post-image" alt="Maxwell equations" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: What is the Homopolar Generator: An Analytical Example"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/homopolar-generator-analytical-example/' title='What is the Homopolar Generator: An Analytical Example'>What is the Homopolar Generator: An Analytical Example</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2017-11-27T16:48:13-06:00" >November 27, 2017</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/homopolar-generator-analytical-example/#comments'>8 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >Introduction It is surprising that the homopolar generator, invented in one of Faraday's ingenious experiments in 1831, still seems to create confusion…</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/2017/11/maxwell.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'>vanhees71</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'>vanhees71</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-11-17T21:13:09-06:00" >2017-11-27 16:48:13</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2021-04-18 15:04:23</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>What is the Homopolar Generator: An Analytical Example</span></span></span></article><article class='slide-entry flex_column post-entry post-entry-14577 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/what-is-a-tensor/' data-rel='slide-1' class='slide-image' title='What Is a Tensor? The mathematical point of view.'><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/2017/06/whatisatensor.png" class="wp-image-14688 avia-img-lazy-loading-not-14688 attachment-portfolio size-portfolio wp-post-image" alt="whatisatensor" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2017/06/whatisatensor.png" class="wp-image-14688 avia-img-lazy-loading-not-14688 attachment-portfolio size-portfolio wp-post-image" alt="whatisatensor" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: What Is a Tensor? The mathematical point of view."><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/what-is-a-tensor/' title='What Is a Tensor? The mathematical point of view.'>What Is a Tensor? The mathematical point of view.</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2017-06-18T23:49:07-05:00" >June 18, 2017</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/what-is-a-tensor/#comments'>58 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >Tensor Key pointsThe author begins by questioning the nature of numbers and their deeper significance. Numbers can represent various 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/2017/06/whatisatensor.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="2015-11-17T21:13:09-06:00" >2017-06-18 23:49:07</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2024-09-30 09:18:15</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>What Is a Tensor? The mathematical point of view.</span></span></span></article></div><div class="slide-entry-wrap"><article class='slide-entry flex_column post-entry post-entry-11032 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/solving-cubic-equation-dummies/' data-rel='slide-1' class='slide-image' title='Learn How to Solve the Cubic Equation for Dummies'><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/2016/10/cubicfunction.png" class="wp-image-11050 avia-img-lazy-loading-not-11050 attachment-portfolio size-portfolio wp-post-image" alt="cubicfunction" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2016/10/cubicfunction.png" class="wp-image-11050 avia-img-lazy-loading-not-11050 attachment-portfolio size-portfolio wp-post-image" alt="cubicfunction" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: Learn How to Solve the Cubic Equation for Dummies"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/solving-cubic-equation-dummies/' title='Learn How to Solve the Cubic Equation for Dummies'>Learn How to Solve the Cubic Equation for Dummies</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2016-10-01T21:39:50-05:00" >October 1, 2016</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/solving-cubic-equation-dummies/#comments'>5 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >Everybody learns the "quadratic formula" for solving equations of the form [itex]A x^2 + B x + C = 0[/itex], even though you don't really need such a formula,…</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/2016/10/cubicfunction.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'>stevendaryl</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'>stevendaryl</span></span><span class='av-structured-data' itemprop="datePublished" datetime="2015-11-17T21:13:09-06:00" >2016-10-01 21:39:50</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2021-04-17 14:21:20</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>Learn How to Solve the Cubic Equation for Dummies</span></span></span></article><article class='slide-entry flex_column post-entry post-entry-10360 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/omissions-mathematics-education-gauge-integration/' data-rel='slide-1' class='slide-image' title='Omissions in Mathematics Education: Gauge 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/2016/07/omissionguage.png" class="wp-image-10363 avia-img-lazy-loading-not-10363 attachment-portfolio size-portfolio wp-post-image" alt="omissionguage" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2016/07/omissionguage.png" class="wp-image-10363 avia-img-lazy-loading-not-10363 attachment-portfolio size-portfolio wp-post-image" alt="omissionguage" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: Omissions in Mathematics Education: Gauge Integration"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/omissions-mathematics-education-gauge-integration/' title='Omissions in Mathematics Education: Gauge Integration'>Omissions in Mathematics Education: Gauge Integration</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2016-07-22T15:27:57-05:00" >July 22, 2016</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/omissions-mathematics-education-gauge-integration/#comments'>31 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >The current (pure) mathematics curriculum at the university is well-established. Most of the choices made are sensible. But still, some important topics…</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/2016/07/omissionguage.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="2015-11-17T21:13:09-06:00" >2016-07-22 15:27:57</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2024-08-17 09:29:42</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>Omissions in Mathematics Education: Gauge Integration</span></span></span></article><article class='slide-entry flex_column post-entry post-entry-10208 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/misconceptions-indefinite-integrals/' data-rel='slide-1' class='slide-image' title='Some Misconceptions on Indefinite Integrals'><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/2016/07/integralmisconceptions.png" class="wp-image-10212 avia-img-lazy-loading-not-10212 attachment-portfolio size-portfolio wp-post-image" alt="integralmisconceptions" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2016/07/integralmisconceptions.png" class="wp-image-10212 avia-img-lazy-loading-not-10212 attachment-portfolio size-portfolio wp-post-image" alt="integralmisconceptions" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: Some Misconceptions on Indefinite Integrals"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/misconceptions-indefinite-integrals/' title='Some Misconceptions on Indefinite Integrals'>Some Misconceptions on Indefinite Integrals</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2016-07-03T13:22:25-05:00" >July 3, 2016</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/misconceptions-indefinite-integrals/#comments'>40 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >Integration is an incredibly useful technique taught in all calculus classes. Nevertheless, there are certain paradoxes involved with integration 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/2016/07/integralmisconceptions.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="2015-11-17T21:13:09-06:00" >2016-07-03 13:22:25</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2021-01-04 23:01:56</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>Some Misconceptions on Indefinite Integrals</span></span></span></article></div><div class="slide-entry-wrap"><article class='slide-entry flex_column post-entry post-entry-10144 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/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="2015-11-17T21:13:09-06:00" >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-9857 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/problems-self-studying/' data-rel='slide-1' class='slide-image' title='5 Problems with Students Self Studying Mathematics'><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/selfstudy.png" class="wp-image-9860 avia-img-lazy-loading-not-9860 attachment-portfolio size-portfolio wp-post-image" alt="selfstudy" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2016/05/selfstudy.png" class="wp-image-9860 avia-img-lazy-loading-not-9860 attachment-portfolio size-portfolio wp-post-image" alt="selfstudy" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: 5 Problems with Students Self Studying Mathematics"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/problems-self-studying/' title='5 Problems with Students Self Studying Mathematics'>5 Problems with Students Self Studying Mathematics</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2016-05-27T20:37:15-05:00" >May 27, 2016</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/problems-self-studying/#comments'>49 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >For several years already I have been trying to help students who have been self-studying math. I did this completely free with no compensation for me.…</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/selfstudy.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="2015-11-17T21:13:09-06:00" >2016-05-27 20:37:15</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2024-08-17 09:23:43</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>5 Problems with Students Self Studying Mathematics</span></span></span></article><article class='slide-entry flex_column post-entry post-entry-9333 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/high-school-want-advanced-mathematics/' data-rel='slide-1' class='slide-image' title='In High School and Want to Do Advanced Mathematics?'><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/2016/04/highschool-math.png" class="wp-image-10438 avia-img-lazy-loading-not-10438 attachment-portfolio size-portfolio wp-post-image" alt="highschoolmath" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2016/04/highschool-math.png" class="wp-image-10438 avia-img-lazy-loading-not-10438 attachment-portfolio size-portfolio wp-post-image" alt="highschoolmath" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: In High School and Want to Do Advanced Mathematics?"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/high-school-want-advanced-mathematics/' title='In High School and Want to Do Advanced Mathematics?'>In High School and Want to Do Advanced Mathematics?</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2016-04-07T13:48:55-05:00" >April 7, 2016</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/high-school-want-advanced-mathematics/#comments'>21 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >This insight is written for high school students who don't feel very challenged by their high school courses. Or maybe those high school students who want…</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/2016/04/highschool-math.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="2015-11-17T21:13:09-06:00" >2016-04-07 13:48:55</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2024-08-17 09:17:09</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>In High School and Want to Do Advanced Mathematics?</span></span></span></article></div><div class="slide-entry-wrap"><article class='slide-entry flex_column post-entry post-entry-6447 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/self-study-basic-high-school-mathematics/' data-rel='slide-1' class='slide-image' title='How to Self-Study Basic High School Mathematics'><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/2015/11/studymath-2.png" class="wp-image-6508 avia-img-lazy-loading-not-6508 attachment-portfolio size-portfolio wp-post-image" alt="studymath" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2015/11/studymath-2.png" class="wp-image-6508 avia-img-lazy-loading-not-6508 attachment-portfolio size-portfolio wp-post-image" alt="studymath" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: How to Self-Study Basic High School Mathematics"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/self-study-basic-high-school-mathematics/' title='How to Self-Study Basic High School Mathematics'>How to Self-Study Basic High School Mathematics</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2015-11-19T15:10:39-06:00" >November 19, 2015</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/self-study-basic-high-school-mathematics/#comments'>5 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >  IntroductionWe often get questions here from people self-studying mathematics. One of those questions is what mathematics should I study…</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/2015/11/studymath-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'>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="2015-11-17T21:13:09-06:00" >2015-11-19 15:10:39</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2024-08-17 06:25:14</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>How to Self-Study Basic High School Mathematics</span></span></span></article><article class='slide-entry flex_column post-entry post-entry-6450 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/self-study-calculus/' data-rel='slide-1' class='slide-image' title='A Guide to Self Study Calculus'><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/2015/11/studymath2.png" class="wp-image-6505 avia-img-lazy-loading-not-6505 attachment-portfolio size-portfolio wp-post-image" alt="studymath2" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2015/11/studymath2.png" class="wp-image-6505 avia-img-lazy-loading-not-6505 attachment-portfolio size-portfolio wp-post-image" alt="studymath2" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: A Guide to Self Study Calculus"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/self-study-calculus/' title='A Guide to Self Study Calculus'>A Guide to Self Study Calculus</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2015-11-18T19:12:52-06:00" >November 18, 2015</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/self-study-calculus/#comments'>26 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >  We often get questions here from people self-studying mathematics. One of those questions is what mathematics should I study and in what order.…</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/2015/11/studymath2.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="2015-11-17T21:13:09-06:00" >2015-11-18 19:12:52</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2024-08-17 06:24:00</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>A Guide to Self Study Calculus</span></span></span></article><article class='slide-entry flex_column post-entry post-entry-6444 slide-entry-overview slide-loop-18 slide-parity-odd post-entry-last 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-study-mathematics/' data-rel='slide-1' class='slide-image' title='The Essential Guide to Self Study Mathematics'><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/2015/11/studymath1.png" class="wp-image-6489 avia-img-lazy-loading-not-6489 attachment-portfolio size-portfolio wp-post-image" alt="studymath1" decoding="async" /><noscript><img fetchpriority="high" width="240" height="135" src="https://www.physicsforums.com/insights/wp-content/uploads/2015/11/studymath1.png" class="wp-image-6489 avia-img-lazy-loading-not-6489 attachment-portfolio size-portfolio wp-post-image" alt="studymath1" decoding="async" /></noscript></a><div class="slide-content"><header class="entry-content-header" aria-label="Slide: The Essential Guide to Self Study Mathematics"><h3 class='slide-entry-title entry-title ' itemprop="headline" ><a href='https://www.physicsforums.com/insights/how-to-study-mathematics/' title='The Essential Guide to Self Study Mathematics'>The Essential Guide to Self Study Mathematics</a></h3><span class="av-vertical-delimiter"></span></header><div class="slide-meta"><time class='slide-meta-time updated' itemprop="datePublished" datetime="2015-11-17T21:13:09-06:00" >November 17, 2015</time><div class="slide-meta-del">/</div><div class="slide-meta-comments"><a href='https://www.physicsforums.com/insights/how-to-study-mathematics/#comments'>13 Comments</a></div></div><div class='slide-entry-excerpt entry-content' itemprop="text" >  How to self-study mathematics? People self-study mathematics for a lot of reasons. Either out of pure interest, because they want to get ahead,…</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/2015/11/studymath1.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="2015-11-17T21:13:09-06:00" >2015-11-17 21:13:09</span><span class='av-structured-data' itemprop="dateModified" itemtype="https://schema.org/dateModified" >2024-08-17 06:22:44</span><span class='av-structured-data' itemprop="mainEntityOfPage" itemtype="https://schema.org/mainEntityOfPage" ><span itemprop='name'>The Essential Guide to Self Study Mathematics</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/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: 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/what-is-a-tensor/" class="wpp-post-title" target="_self">What Is a Tensor? 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