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id="mw-content-text" class="mw-body-content"> <div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"> <table role="presentation" style="width: 100%; background-color: transparent; vertical-align: top; border: 0px; border-spacing: 0; margin:0;"> <tbody> <tr> <td style="width: 1%; border-bottom: 2px solid #246"> </td> <td style="text-align: center; border-radius:0.5em 0.5em 0 0; padding:0.3em; border: 2px solid #246; font-size: 110%; background-color: #BDF; border-bottom-color: #BDF; font-weight:bold;" width="3%"><a class="mw-selflink selflink">Portal:Mathematics</a></td> <td style="width: 2%; border-bottom: 2px solid #246"> </td> <td style="text-align: center; border-radius:0.5em 0.5em 0 0; padding:0.3em; border: 2px solid #246; font-size: 110%; background-color: #EEE;" width="3%"><a href="https://en-wikiversity-org.translate.goog/wiki/Portal:Mathematics/Learn?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Portal:Mathematics/Learn">Learn</a></td> <td style="width: 2%; 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href="https://en-wikiversity-org.translate.goog/w/index.php?title=Portal:Mathematics/Introduction&action=edit&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB"><span style="background: #48B; color: white">edit</span></a> </div> <div style="font-family:sans-serif; font-size:100%; font-weight:bold; border: none; margin: 0; padding:0 0 .1em 1em; background: #48B; color:white;"> The Mathematics Portal </div> </div> <div style="border: 1px solid #246; border-top-width: 1px; vertical-align: top; background: #f9fcff; opacity: 1; color: black; text-align: left; margin: 0 0 .1em 0; padding: 1em; padding-top: .3em; padding-bottom: .5em;"> <figure class="mw-halign-right" typeof="mw:File/Thumb"> <a href="https://en-wikiversity-org.translate.goog/wiki/File:Pythagorean.svg?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Pythagorean.svg/150px-Pythagorean.svg.png" decoding="async" width="150" height="137" class="mw-file-element" srcset="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Pythagorean.svg/225px-Pythagorean.svg.png 1.5x,https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Pythagorean.svg/300px-Pythagorean.svg.png 2x" data-file-width="512" data-file-height="466"></a> <figcaption> <a href="https://en-wikiversity-org.translate.goog/wiki/Our_Playground:_The_Real_Numbers_and_Their_Development?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-redirect" title="Our Playground: The Real Numbers and Their Development">Pythagorean Theorem</a> </figcaption> </figure> <figure class="mw-halign-left" typeof="mw:File/Thumb"> <a href="https://en-wikiversity-org.translate.goog/wiki/File:Torus.png?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/17/Torus.png/200px-Torus.png" decoding="async" width="200" height="128" class="mw-file-element" srcset="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://upload.wikimedia.org/wikipedia/commons/thumb/1/17/Torus.png/300px-Torus.png 1.5x,https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://upload.wikimedia.org/wikipedia/commons/thumb/1/17/Torus.png/400px-Torus.png 2x" data-file-width="784" data-file-height="502"></a> <figcaption> <a href="https://en-wikiversity-org.translate.goog/wiki/Topology?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Topology">Topology</a> </figcaption> </figure> <p>Welcome to the Mathematics Portal! This page connects visitors to the learning resources that have been developed by various Wikiversity <a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://en.wikipedia.org/wiki/Portal:Mathematics/WikiProjects" class="extiw" title="w:Portal:Mathematics/WikiProjects">content development projects</a>. Wikiversity participants who are interested in mathematics are invited to create and develop <a href="https://en-wikiversity-org.translate.goog/wiki/Portal:Learning_Projects?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Portal:Learning Projects">learning projects</a> and <a href="https://en-wikiversity-org.translate.goog/wiki/Portal:Learning_Materials?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Portal:Learning Materials">learning resources</a> and help organize them by developing this portal.</p> <div style="clear:both;"></div> </div> <div class="noprint" style="text-align:center; margin:0 0 .5em 0px; padding:0.25em 0.25em 0.25em 0.25em; font-weight: bold"> </div> <div style="clear:both;"></div> <div style="float:left; width:66%; min-width:300px;"> <div style="clear: both; border: solid #246; border-width: 1px 1px 0; background: #48B; color: white; padding: .15em; text-align: center; font-family: sans-serif; font-size:100%; margin-bottom: 0px;"> <div class="plainlinks" style="float:right; margin-bottom:.1em; font-size:80%; background: #48B; color: white;"> <a class="external text" href="https://en-wikiversity-org.translate.goog/w/index.php?title=Portal:Mathematics/Featured_Resource&action=edit&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB"><span style="background: #48B; color: white">edit</span></a> </div> <div style="font-family:sans-serif; font-size:100%; font-weight:bold; border: none; margin: 0; padding:0 0 .1em 1em; background: #48B; color:white;"> Featured Resource </div> </div> <div style="border: 1px solid #246; border-top-width: 1px; vertical-align: top; background: #f9fcff; opacity: 1; color: black; text-align: left; margin: 0 0 .1em 0; padding: 1em; padding-top: .3em; padding-bottom: .5em;"> <div class="center" style="width:auto; margin-left:auto; margin-right:auto;"> <b><a href="https://en-wikiversity-org.translate.goog/wiki/Mathematics_for_Applied_Sciences_(Osnabr%C3%BCck_2023-2024)/Part_I/Link_on_portal?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Mathematics for Applied Sciences (Osnabrück 2023-2024)/Part I/Link on portal">Mathematics for Applied Sciences (Osnabrück 2023-2024)/Part I/Link on portal</a></b> </div> <p>Mathematics for Applied Sciences (Osnabrück 2023-2024)/Part I</p> <p>This mathematical course is for beginners at the University of Osnabrück in the subjects Computer sciences, Cognitive sciences, Physics and System sciences. Of course, everybody interested can study the material. It is an introduction to advanced mathematics on the academic level. It covers logical foundation, sets, mappings, algebraic structures like fields and polynomials, the basics of analysis like sequences, continuity, differentiability, primitive functions and the basics of linear algebra like vector spaces, bases, linear maps, eigenvalues. Enjoy!</p> <p>To the <a href="https://en-wikiversity-org.translate.goog/wiki/Mathematics_for_Applied_Sciences_(Osnabr%C3%BCck_2023-2024)/Part_I?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Mathematics for Applied Sciences (Osnabrück 2023-2024)/Part I">course</a>. <a href="https://en-wikiversity-org.translate.goog/wiki/Mathematics_for_Applied_Sciences_(Osnabr%C3%BCck_2023-2024)/Part_I/Link_on_portal?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Mathematics for Applied Sciences (Osnabrück 2023-2024)/Part I/Link on portal">(more...)</a></p> <div style="clear:both;"></div> </div> <div class="noprint" style="text-align:center; margin:0 0 .5em 0px; padding:0.25em 0.25em 0.25em 0.25em; font-weight: bold"> </div> <div style="clear:both;"></div> <div style="clear: both; border: solid #246; border-width: 1px 1px 0; background: #48B; color: white; padding: .15em; text-align: center; font-family: sans-serif; font-size:100%; margin-bottom: 0px;"> <div class="plainlinks" style="float:right; margin-bottom:.1em; font-size:80%; background: #48B; color: white;"> <a class="external text" href="https://en-wikiversity-org.translate.goog/w/index.php?title=Portal:Mathematics/Featured_Picture&action=edit&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB"><span style="background: #48B; color: white">edit</span></a> </div> <div style="font-family:sans-serif; font-size:100%; font-weight:bold; border: none; margin: 0; padding:0 0 .1em 1em; background: #48B; color:white;"> Featured Picture </div> </div> <div style="border: 1px solid #246; border-top-width: 1px; vertical-align: top; background: #f9fcff; opacity: 1; color: black; text-align: left; margin: 0 0 .1em 0; padding: 1em; padding-top: .3em; padding-bottom: .5em;"> <figure class="mw-halign-center" typeof="mw:File/Thumb"> <a href="https://en-wikiversity-org.translate.goog/wiki/File:EnneperSurfaceAnimated.gif?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/0/06/EnneperSurfaceAnimated.gif" decoding="async" width="220" height="220" class="mw-file-element" data-file-width="220" data-file-height="220"></a> <figcaption> A portion of the Weierstrass-Enneper Surface(geometry and complex analysis) </figcaption> </figure> </div> <div class="noprint" style="text-align:center; margin:0 0 .5em 0px; padding:0.25em 0.25em 0.25em 0.25em; font-weight: bold"> </div> <div style="clear:both;"></div> <div style="clear: both; border: solid #246; border-width: 1px 1px 0; background: #48B; color: white; padding: .15em; text-align: center; font-family: sans-serif; font-size:100%; margin-bottom: 0px;"> <div class="plainlinks" style="float:right; margin-bottom:.1em; font-size:80%; background: #48B; color: white;"> <a class="external text" href="https://en-wikiversity-org.translate.goog/w/index.php?title=Portal:Mathematics/Suggested_Courses&action=edit&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB"><span style="background: #48B; color: white">edit</span></a> </div> <div style="font-family:sans-serif; font-size:100%; font-weight:bold; border: none; margin: 0; padding:0 0 .1em 1em; background: #48B; color:white;"> Suggested Courses </div> </div> <div style="border: 1px solid #246; border-top-width: 1px; vertical-align: top; background: #f9fcff; opacity: 1; color: black; text-align: left; margin: 0 0 .1em 0; padding: 1em; padding-top: .3em; padding-bottom: .5em;"> <p>One could learn the following topics in the following order, although it is also possible to skip certain courses according to one's interests. These courses are also the most commonly found courses in a mathematics undergraduate concentration in English-speaking universities. However, universities will differ in their course titles and content, so that there is no universal list of undergraduate courses.</p> <ol> <li><a href="https://en-wikiversity-org.translate.goog/wiki/Portal:Arithmetic?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Portal:Arithmetic">Arithmetic</a> (no prerequisites)</li> <li><a href="https://en-wikiversity-org.translate.goog/wiki/Portal:Algebra_and_Geometry?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Portal:Algebra and Geometry">Algebra and Geometry</a> (requires arithmetic)</li> <li><a href="https://en-wikiversity-org.translate.goog/wiki/Portal:Discrete_Mathematics?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Portal:Discrete Mathematics">Discrete Mathematics</a> (requires algebra)</li> <li><a href="https://en-wikiversity-org.translate.goog/wiki/Portal:Introductory_Statistics?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Portal:Introductory Statistics">Introductory Statistics</a> (requires algebra)</li> <li><a href="https://en-wikiversity-org.translate.goog/w/index.php?title=Portal:Calculus_1&action=edit&redlink=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="new" title="Portal:Calculus 1 (page does not exist)">Calculus 1</a> (requires algebra and geometry)</li> <li><a href="https://en-wikiversity-org.translate.goog/w/index.php?title=Portal:Linear_Algebra&action=edit&redlink=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="new" title="Portal:Linear Algebra (page does not exist)">Linear Algebra</a> (requires algebra and geometry)</li> <li><a href="https://en-wikiversity-org.translate.goog/w/index.php?title=Portal:Calculus_2&action=edit&redlink=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="new" title="Portal:Calculus 2 (page does not exist)">Calculus 2</a> (requires calculus 1)</li> <li><a href="https://en-wikiversity-org.translate.goog/w/index.php?title=Portal:Differential_Equations&action=edit&redlink=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="new" title="Portal:Differential Equations (page does not exist)">Differential Equations</a> (requires calculus 2 and linear algebra)</li> <li><a href="https://en-wikiversity-org.translate.goog/w/index.php?title=Portal:Calculus_3&action=edit&redlink=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="new" title="Portal:Calculus 3 (page does not exist)">Calculus 3</a> (requires calculus 2 and linear algebra)</li> <li><a href="https://en-wikiversity-org.translate.goog/w/index.php?title=Portal:Mathematical_Statistics&action=edit&redlink=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="new" title="Portal:Mathematical Statistics (page does not exist)">Mathematical Statistics</a> (requires calculus 3)</li> <li><a href="https://en-wikiversity-org.translate.goog/w/index.php?title=Portal:Mathematical_Logic&action=edit&redlink=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="new" title="Portal:Mathematical Logic (page does not exist)">Mathematical Logic</a> (requires discrete math)</li> <li>Modern Analysis (requires calculus 1 and linear algebra)</li> <li><a href="https://en-wikiversity-org.translate.goog/wiki/Portal:Modern_Algebra?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Portal:Modern Algebra">Modern Algebra</a> (requires discrete mathematics)</li> <li>Set Theory (requires discrete mathematics)</li> <li>Number Theory (requires discrete mathematics)</li> <li>Complex Analysis (requires modern analysis)</li> <li>General Topology (requires modern analysis)</li> <li>Combinatorics (requires discrete mathematics)</li> <li>Differential Geometry</li> <li>Partial Differential Equations</li> <li><a href="https://en-wikiversity-org.translate.goog/wiki/Portal:Measure_Theory?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Portal:Measure Theory">Measure and Integration Theory</a> (requires modern analysis)</li> <li><a href="https://en-wikiversity-org.translate.goog/wiki/Portal:Functional_Analysis?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Portal:Functional Analysis">Functional Analysis</a> (requires measure and integration theory)</li> <li>Probability Theory (requires modern analysis and mathematical statistics)</li> <li>Algebraic Topology</li> </ol> </div> <div class="noprint" style="text-align:center; margin:0 0 .5em 0px; padding:0.25em 0.25em 0.25em 0.25em; font-weight: bold"> </div> <div style="clear:both;"></div> <p><br></p> </div> <div style="float:right; width:33%; min-width:150px;"> <div style="clear: both; border: solid #246; border-width: 1px 1px 0; background: #48B; color: white; padding: .15em; text-align: center; font-family: sans-serif; font-size:100%; margin-bottom: 0px;"> <div class="plainlinks" style="float:right; margin-bottom:.1em; font-size:80%; background: #48B; color: white;"> <a class="external text" href="https://en-wikiversity-org.translate.goog/w/index.php?title=Portal:Mathematics/Categories&action=edit&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB"><span style="background: #48B; color: white">edit</span></a> </div> <div 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cats, 344 pgs, 1 file)</span> </div> <div class="CategoryTreeChildren"> <div class="CategoryTreeSection"> <div class="CategoryTreeItem"> <span class="CategoryTreeBullet"><a class="CategoryTreeToggle" data-ct-title="Algebra" aria-expanded="false"></a> </span> <bdi dir="ltr"><a href="https://en-wikiversity-org.translate.goog/wiki/Category:Algebra?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Category:Algebra">Algebra</a></bdi> <span title="Contains 13 subcategories, 50 pages, and 1 file" dir="ltr">(13 cats, 50 pgs, 1 file)</span> </div> <div class="CategoryTreeChildren" style="display:none"></div> </div> <div class="CategoryTreeSection"> <div class="CategoryTreeItem"> <span class="CategoryTreeBullet"><a class="CategoryTreeToggle" data-ct-title="Mathematical_analysis" aria-expanded="false"></a> </span> <bdi dir="ltr"><a href="https://en-wikiversity-org.translate.goog/wiki/Category:Mathematical_analysis?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Category:Mathematical analysis">Mathematical analysis</a></bdi> <span title="Contains 5 subcategories, 5 pages, and 0 files" dir="ltr">(5 cats, 5 pgs)</span> </div> <div class="CategoryTreeChildren" style="display:none"></div> </div> <div class="CategoryTreeSection"> <div class="CategoryTreeItem"> <span class="CategoryTreeEmptyBullet"></span> <bdi dir="ltr"><a href="https://en-wikiversity-org.translate.goog/wiki/Category:Analytic_functions?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Category:Analytic functions">Analytic functions</a></bdi> <span title="Contains 0 subcategories, 1 page, and 0 files" dir="ltr">(1 pg)</span> </div> <div class="CategoryTreeChildren" style="display:none"></div> </div> <div class="CategoryTreeSection"> <div class="CategoryTreeItem"> <span class="CategoryTreeBullet"><a class="CategoryTreeToggle" data-ct-title="Applied_mathematics" aria-expanded="false"></a> </span> <bdi dir="ltr"><a 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src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png" decoding="async" width="18" height="25" class="mw-file-element" srcset="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/28px-Commons-logo.svg.png 1.5x,https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/37px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376"></a> <figcaption></figcaption> </figure> </div> <div style="float:left; margin:0 3px 3px 3px; font-size:91%;"> <p><b><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://en.wikinews.org/wiki/Special:Search/Portal:Mathematics" class="extiw" title="wikinews:Special:Search/Portal:Mathematics">Wikinews</a></b> <br> News<br></p> <figure class="mw-default-size mw-halign-center" typeof="mw:File"> <a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://en.wikinews.org/wiki/Special:Search/Portal:Mathematics"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/24/Wikinews-logo.svg/46px-Wikinews-logo.svg.png" decoding="async" width="46" height="25" class="mw-file-element" srcset="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://upload.wikimedia.org/wikipedia/commons/thumb/2/24/Wikinews-logo.svg/70px-Wikinews-logo.svg.png 1.5x,https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://upload.wikimedia.org/wikipedia/commons/thumb/2/24/Wikinews-logo.svg/92px-Wikinews-logo.svg.png 2x" data-file-width="759" data-file-height="415"></a> <figcaption></figcaption> </figure> </div> <div style="float:left; margin:0 3px 3px 3px; font-size:91%;"> <p><b><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://en.wikiquote.org/wiki/Special:Search/Portal:Mathematics" class="extiw" 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href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://en.wikisource.org/wiki/Special:Search/Portal:Mathematics" class="extiw" title="wikisource:Special:Search/Portal:Mathematics">Wikisource</a></b> <br> Texts<br></p> <figure class="mw-halign-center" typeof="mw:File"> <a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://en.wikisource.org/wiki/Special:Search/Portal:Mathematics"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/24px-Wikisource-logo.svg.png" decoding="async" width="24" height="25" class="mw-file-element" srcset="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/36px-Wikisource-logo.svg.png 1.5x,https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/48px-Wikisource-logo.svg.png 2x" data-file-width="410" 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