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	      Math190 - Spring 2024 - Tufts Univ</a>
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            <h1>Resources: References for the course
</h1>
            <article>
    <section class="header">
        Posted on 2024-01-07
        
            by George McNinch
        
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    <section>
        <h1 id="references-for-representations-of-finite-groups">References for <em>Representations of finite groups</em></h1>
<ul>
<li><p>These notes <span class="citation" data-cites="milnej.s.GroupTheory">(Milne, n.d.)</span> <a href="https://www.jmilne.org/math/CourseNotes/gt.html">Group Theory
Notes</a> are
available on-line; Chapter 7 contains a treatment of
representations of finite groups.</p></li>
<li><p><span class="citation" data-cites="jamesRepresentationsCharactersGroups2001">(James and Liebeck 2001)</span></p></li>
<li><p><span class="citation" data-cites="serreLinearRepresentationsFinite1977">(Serre 1977)</span></p></li>
<li><p>I hope to briefly discuss the Fast Fourier Transform, and I’ll
probably follow
<span class="citation" data-cites="ceccherini-silbersteinDiscreteHarmonicAnalysis2018">(Ceccherini-Silberstein, Scarabotti, and Tolli 2018)</span> for that discussion.</p></li>
</ul>
<h1 id="references-for-error-correcting-codes">References for <em>Error correcting codes</em></h1>
<ul>
<li><p><span class="citation" data-cites="huffmanFundamentalsErrorCorrectingCodes2003">(Huffman and Pless 2003)</span> is available
electronically at <a href="https://tischlibrary.tufts.edu/"><em>Tisch
Library</em></a></p></li>
<li><p><span class="citation" data-cites="ballCourseAlgebraicErrorCorrecting2020">(Ball 2020)</span></p></li>
<li><p>These notes of Spence <span class="citation" data-cites="spenceIntroductionAlgebraicCoding2002">(Spence 2002)</span> are
<a href="../course-assets/Spence--Supplementary-material-for-coding-Theory.pdf">available here</a></p></li>
<li><p><span class="citation" data-cites="tsfasmanAlgebraicGeometricCodes2007">(Tsfasman, Vlǎduţ, and Nogin 2007)</span></p></li>
</ul>
<h1 id="references-for-formalization-of-mathematics">References for <em>Formalization of mathematics</em></h1>
<p>For our discussion of <em>proof assistants</em> and formalization of math,
I’m going to use the <code>Lean</code> language; the <code>Lean</code> community web site
is here:
<a href="https://leanprover-community.github.io/">https://leanprover-community.github.io/</a>.</p>
<p>Learning resources for <code>Lean</code> may be <a href="https://leanprover-community.github.io/learn.html">found
here</a>. They
include the following:</p>
<ul>
<li><p><span class="citation" data-cites="avigadMathematicsLeanMathematics">(Avigad and Massot, n.d.)</span> <a href="https://leanprover-community.github.io/mathematics_in_lean/">Mathematics in Lean</a></p></li>
<li><p><span class="citation" data-cites="avigadTheoremProvingLean">(Avigad et al. 2024)</span> <a href="https://leanprover.github.io/theorem_proving_in_lean4/">Theorem Proving in Lean</a></p></li>
<li><p><span class="citation" data-cites="macbethMechanicsProof">(MacBeth, n.d.)</span> <a href="https://hrmacbeth.github.io/math2001/">The Mechanics of Proof</a></p></li>
</ul>
<h1 id="bibliography">Bibliography</h1>
<div class="refs">

</div>
<div id="refs" class="references csl-bib-body hanging-indent" role="list">
<div id="ref-avigadTheoremProvingLean" class="csl-entry" role="listitem">
Avigad, Jeremy, Leondardo de Moura, Soonho Kong, and Sebastian Ullrich. 2024. <span>“Theorem <span>Proving</span> in <span>Lean</span> 4.”</span> https://leanprover.github.io/theorem_proving_in_lean4/.
</div>
<div id="ref-avigadMathematicsLeanMathematics" class="csl-entry" role="listitem">
Avigad, Jeremy, and Patrick Massot. n.d. <span>“Mathematics in <span>Lean</span> — <span>Mathematics</span> in <span>Lean</span> 0.1 Documentation.”</span> https://leanprover-community.github.io/mathematics_in_lean/. Accessed January 11, 2024.
</div>
<div id="ref-ballCourseAlgebraicErrorCorrecting2020" class="csl-entry" role="listitem">
Ball, Simeon. 2020. <em>A <span>Course</span> in <span>Algebraic Error-Correcting Codes</span></em>. Compact <span>Textbooks</span> in <span>Mathematics</span>. Cham: Springer International Publishing. <a href="https://doi.org/10.1007/978-3-030-41153-4">https://doi.org/10.1007/978-3-030-41153-4</a>.
</div>
<div id="ref-ceccherini-silbersteinDiscreteHarmonicAnalysis2018" class="csl-entry" role="listitem">
Ceccherini-Silberstein, Tullio, Fabio Scarabotti, and Filippo Tolli. 2018. <em>Discrete <span>Harmonic Analysis</span>: <span>Representations</span>, <span>Number Theory</span>, <span>Expanders</span>, and the <span>Fourier Transform</span></em>. Cambridge <span>Studies</span> in <span>Advanced Mathematics</span>. Cambridge: Cambridge University Press. <a href="https://doi.org/10.1017/9781316856383">https://doi.org/10.1017/9781316856383</a>.
</div>
<div id="ref-huffmanFundamentalsErrorCorrectingCodes2003" class="csl-entry" role="listitem">
Huffman, W. Cary, and Vera Pless. 2003. <em>Fundamentals of <span>Error-Correcting Codes</span></em>. Cambridge: Cambridge University Press. <a href="https://doi.org/10.1017/CBO9780511807077">https://doi.org/10.1017/CBO9780511807077</a>.
</div>
<div id="ref-jamesRepresentationsCharactersGroups2001" class="csl-entry" role="listitem">
James, Gordon, and Martin Liebeck. 2001. <em>Representations and <span>Characters</span> of <span>Groups</span></em>. 2nd ed. Cambridge: Cambridge University Press. <a href="https://doi.org/10.1017/CBO9780511814532">https://doi.org/10.1017/CBO9780511814532</a>.
</div>
<div id="ref-macbethMechanicsProof" class="csl-entry" role="listitem">
MacBeth, Heather. n.d. <span>“The <span>Mechanics</span> of <span>Proof</span>.”</span> https://hrmacbeth.github.io/math2001/. Accessed January 11, 2024.
</div>
<div id="ref-milnej.s.GroupTheory" class="csl-entry" role="listitem">
Milne, J. S. n.d. <span>“Group <span>Theory</span>.”</span> https://www.jmilne.org/math/CourseNotes/gt.html. Accessed January 11, 2024.
</div>
<div id="ref-serreLinearRepresentationsFinite1977" class="csl-entry" role="listitem">
Serre, Jean-Pierre. 1977. <em>Linear Representations of Finite Groups</em>. Springer-Verlag, New York-Heidelberg.
</div>
<div id="ref-spenceIntroductionAlgebraicCoding2002" class="csl-entry" role="listitem">
Spence, S. 2002. <span>“Introduction to <span>Algebraic Coding Theory</span>.”</span>
</div>
<div id="ref-tsfasmanAlgebraicGeometricCodes2007" class="csl-entry" role="listitem">
Tsfasman, Michael, Serge Vlǎduţ, and Dmitry Nogin. 2007. <em>Algebraic <span>Geometric Codes</span>: <span>Basic Notions</span></em>. Vol. 139. Mathematical <span>Surveys</span> and <span>Monographs</span>. American Mathematical Society. <a href="https://doi.org/10.1090/surv/139">https://doi.org/10.1090/surv/139</a>.
</div>
</div>
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