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MATH-4020: Introduction to Number Theory
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<meta property="og:title" content="MATH-4020: Introduction to Number Theory">
<meta property="og:description" content="Topics include the history of number representation systems, divisibility, greatest common divisor and prime factorization, linear Diophantine equations, congruences, and condition congruences. Additional topics may be chosen from cryptology, the perpetual calendar, hashing functions, computer operations and complexity, continued fractions, multiplicative functions, primitive roots, pseudo-random numbers, nonlinear Diophantine equations, Fermat's last theorem, algebraic numbers, and approximation of numbers by rationals.">
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<h1 id="name">
Introduction to Number Theory
</h1>
<h2 id="code">
MATH-4020
</h2>
<p>
Topics include the history of number representation systems, divisibility, greatest common divisor and prime factorization, linear Diophantine equations, congruences, and condition congruences. Additional topics may be chosen from cryptology, the perpetual calendar, hashing functions, computer operations and complexity, continued fractions, multiplicative functions, primitive roots, pseudo-random numbers, nonlinear Diophantine equations, Fermat's last theorem, algebraic numbers, and approximation of numbers by rationals.
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4 credits
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<table id="years-table">
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<tr>
<th></th>
<th class="spring season-label">Spring</th>
<th class="summer season-label" colspan="2">Summer</th>
<th class="fall season-label">Fall</th>
</tr>
<tr>
<th colspan="2"></th>
<th class="summer2 midsum-label">(Session 1)</th>
<th class="summer3 midsum-label">(Session 2)</th>
<th></th>
</tr>
</thead>
<tbody>
<tr>
<th class="year">2023</th>
<td class="term spring offered">
<div class="view-container detail-view-container">
<span class="term-course-info">
<a href="https://sis.rpi.edu/rss/bwckctlg.p_disp_listcrse?term_in=202301&subj_in=MATH&crse_in=4020&schd_in=">Intro To Number Theory (4c)</a>
</span>
<ul class="prof-list">
<li>Bruce Piper</li>
</ul>
<span class="course-capacity">
Seats Taken: 44/60
</span>
</div>
</td>
<td colspan="2" class="term summer not-offered">
</td>
<td class="term fall not-offered">
</td>
</tr>
<tr>
<th class="year">2022</th>
<td class="term spring not-offered">
</td>
<td colspan="2" class="term summer not-offered">
</td>
<td class="term fall not-offered">
</td>
</tr>
<tr>
<th class="year">2021</th>
<td class="term spring offered">
<div class="view-container detail-view-container">
<span class="term-course-info">
<a href="https://sis.rpi.edu/rss/bwckctlg.p_disp_listcrse?term_in=202101&subj_in=MATH&crse_in=4020&schd_in=">Intro To Number Theory (4c)</a>
</span>
<ul class="prof-list">
<li>Bruce Piper</li>
</ul>
<span class="course-capacity">
Seats Taken: 78/90
</span>
</div>
</td>
<td colspan="2" class="term summer not-offered">
</td>
<td class="term fall not-offered">
</td>
</tr>
<tr>
<th class="year">2020</th>
<td class="term spring not-offered">
</td>
<td colspan="2" class="term summer not-offered">
</td>
<td class="term fall not-offered">
</td>
</tr>
<tr>
<th class="year">2019</th>
<td class="term spring offered">
<div class="view-container detail-view-container">
<span class="term-course-info">
<a href="https://sis.rpi.edu/rss/bwckctlg.p_disp_listcrse?term_in=201901&subj_in=MATH&crse_in=4020&schd_in=">Intro To Number Theory (4c)</a>
</span>
<ul class="prof-list">
<li>Bruce Piper</li>
</ul>
<span class="course-capacity">
Seats Taken: 71/80
</span>
</div>
</td>
<td colspan="2" class="term summer not-offered">
</td>
<td class="term fall not-offered">
</td>
</tr>
<tr>
<th class="year">2018</th>
<td class="term spring not-offered">
</td>
<td colspan="2" class="term summer not-offered">
</td>
<td class="term fall not-offered">
</td>
</tr>
<tr>
<th class="year">2017</th>
<td class="term spring offered">
<div class="view-container detail-view-container">
<span class="term-course-info">
<a href="https://sis.rpi.edu/rss/bwckctlg.p_disp_listcrse?term_in=201701&subj_in=MATH&crse_in=4020&schd_in=">Intro To Number Theory (4c)</a>
</span>
<ul class="prof-list">
<li>Gina Irene Kucinski</li>
</ul>
<span class="course-capacity">
Seats Taken: 32/30
</span>
</div>
</td>
<td colspan="2" class="term summer not-offered">
</td>
<td class="term fall not-offered">
</td>
</tr>
<tr>
<th class="year">2016</th>
<td class="term spring not-offered">
</td>
<td colspan="2" class="term summer not-offered">
</td>
<td class="term fall not-offered">
</td>
</tr>
<tr>
<th class="year">2015</th>
<td class="term spring offered">
<div class="view-container detail-view-container">
<span class="term-course-info">
<a href="https://sis.rpi.edu/rss/bwckctlg.p_disp_listcrse?term_in=201501&subj_in=MATH&crse_in=4020&schd_in=">Intro To Number Theory (4c)</a>
</span>
<ul class="prof-list">
<li>Bruce Piper</li>
</ul>
<span class="course-capacity">
Seats Taken: 40/45
</span>
</div>
</td>
<td colspan="2" class="term summer not-offered">
</td>
<td class="term fall not-offered">
</td>
</tr>
<tr>
<th class="year">2014</th>
<td class="term spring not-offered">
</td>
<td colspan="2" class="term summer not-offered">
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<td class="term fall not-offered">
</td>
</tr>
<tr>
<th class="year">2013</th>
<td class="term spring offered">
<div class="view-container detail-view-container">
<span class="term-course-info">
<a href="https://sis.rpi.edu/rss/bwckctlg.p_disp_listcrse?term_in=201301&subj_in=MATH&crse_in=4020&schd_in=">Intro To Number Theory (4c)</a>
</span>
<ul class="prof-list">
<li>Bruce Piper</li>
</ul>
<span class="course-capacity">
Seats Taken: 47/45
</span>
</div>
</td>
<td colspan="2" class="term summer not-offered">
</td>
<td class="term fall not-offered">
</td>
</tr>
<tr>
<th class="year">2012</th>
<td class="term spring not-offered">
</td>
<td colspan="2" class="term summer not-offered">
</td>
<td class="term fall not-offered">
</td>
</tr>
<tr>
<th class="year">2011</th>
<td class="term spring offered">
<div class="view-container detail-view-container">
<span class="term-course-info">
<a href="https://sis.rpi.edu/rss/bwckctlg.p_disp_listcrse?term_in=201101&subj_in=MATH&crse_in=4020&schd_in=">Intro To Number Theory (4c)</a>
</span>
<ul class="prof-list">
<li>Bruce Piper</li>
</ul>
<span class="course-capacity">
Seats Taken: 36/42
</span>
</div>
</td>
<td colspan="2" class="term summer not-offered">
</td>
<td class="term fall not-offered">
</td>
</tr>
<tr>
<th class="year">2010</th>
<td class="term spring not-offered">
</td>
<td colspan="2" class="term summer not-offered">
</td>
<td class="term fall not-offered">
</td>
</tr>
<tr>
<th class="year">2009</th>
<td class="term spring offered">
<div class="view-container detail-view-container">
<span class="term-course-info">
<a href="https://sis.rpi.edu/rss/bwckctlg.p_disp_listcrse?term_in=200901&subj_in=MATH&crse_in=4020&schd_in=">Intro To Number Theory (4c)</a>
</span>
<ul class="prof-list">
<li>Bruce Piper</li>
</ul>
<span class="course-capacity">
Seats Taken: 39/40
</span>
</div>
</td>
<td colspan="2" class="term summer not-offered">
</td>
<td class="term fall not-offered">
</td>
</tr>
<tr>
<th class="year">2008</th>
<td class="term spring not-offered">
</td>
<td colspan="2" class="term summer not-offered">
</td>
<td class="term fall not-offered">
</td>
</tr>
<tr>
<th class="year">2007</th>
<td class="term spring offered">
<div class="view-container detail-view-container">
<span class="term-course-info">
<a href="https://sis.rpi.edu/rss/bwckctlg.p_disp_listcrse?term_in=200701&subj_in=MATH&crse_in=4020&schd_in=">Intro To Number Theory (4c)</a>
</span>
<ul class="prof-list">
<li>Bruce Piper</li>
</ul>
<span class="course-capacity">
Seats Taken: 22/30
</span>
</div>
</td>
<td colspan="2" class="term summer not-offered">
</td>
<td class="term fall not-offered">
</td>
</tr>
<tr>
<th class="year">2006</th>
<td class="term spring not-offered">
</td>
<td colspan="2" class="term summer not-offered">
</td>
<td class="term fall not-offered">
</td>
</tr>
<tr>
<th class="year">2005</th>
<td class="term spring offered">
<div class="view-container detail-view-container">
<span class="term-course-info">
<a href="https://sis.rpi.edu/rss/bwckctlg.p_disp_listcrse?term_in=200501&subj_in=MATH&crse_in=4020&schd_in=">Intro To Number Theory (4c)</a>
</span>
<ul class="prof-list">
<li>Bruce Piper</li>
</ul>
<span class="course-capacity">
Seats Taken: 36/45
</span>
</div>
</td>
<td colspan="2" class="term summer not-offered">
</td>
<td class="term fall not-offered">
</td>
</tr>
<tr>
<th class="year">2004</th>
<td class="term spring not-offered">
</td>
<td colspan="2" class="term summer not-offered">
</td>
<td class="term fall not-offered">
</td>
</tr>
<tr>
<th class="year">2003</th>
<td class="term spring offered">
<div class="view-container detail-view-container">
<span class="term-course-info">
<a href="https://sis.rpi.edu/rss/bwckctlg.p_disp_listcrse?term_in=200301&subj_in=MATH&crse_in=4020&schd_in=">Intro To Number Theory (4c)</a>
</span>
<ul class="prof-list">
<li>Bruce Piper</li>
</ul>
<span class="course-capacity">
Seats Taken: 40/45
</span>
</div>
</td>
<td colspan="2" class="term summer not-offered">
</td>
<td class="term fall not-offered">
</td>
</tr>
<tr>
<th class="year">2002</th>
<td class="term spring not-offered">
</td>
<td colspan="2" class="term summer not-offered">
</td>
<td class="term fall not-offered">
</td>
</tr>
<tr>
<th class="year">2001</th>
<td class="term spring offered">
<div class="view-container detail-view-container">
<span class="term-course-info">
<a href="https://sis.rpi.edu/rss/bwckctlg.p_disp_listcrse?term_in=200101&subj_in=MATH&crse_in=4020&schd_in=">Intro To Number Theory (4c)</a>
</span>
<ul class="prof-list">
<li>Jason Thomas Blackford</li>
</ul>
<span class="course-capacity">
Seats Taken: 29/40
</span>
</div>
</td>
<td colspan="2" class="term summer not-offered">
</td>
<td class="term fall not-offered">
</td>
</tr>
<tr>
<th class="year">2000</th>
<td class="term spring not-offered">
</td>
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</td>
</tr>
<tr>
<th class="year">1999</th>
<td class="term spring offered">
<div class="view-container detail-view-container">
<span class="term-course-info">
<a href="https://sis.rpi.edu/rss/bwckctlg.p_disp_listcrse?term_in=199901&subj_in=MATH&crse_in=4020&schd_in=">Intro To Number Theory (4c)</a>
</span>
<ul class="prof-list">
<li>Bruce Piper</li>
</ul>
<span class="course-capacity">
Seats Taken: 27/35
</span>
</div>
</td>
<td colspan="2" class="term summer not-offered">
</td>
<td class="term fall not-offered">
</td>
</tr>
<tr>
<th class="year">1998</th>
<td class="term spring unscheduled">
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</td>
</tr>
</tbody>
</table>
</div>
</div>
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