teaching.bib

@misc{AMSEBooksMathematical,
  title = {{{AMS eBooks}}: {{Mathematical Surveys}} and {{Monographs}}},
  urldate = {2024-01-11},
  howpublished = {https://www.ams.org/books/surv/139/},
  file = {/home/george/Zotero/storage/HBT982W7/139.html}
}

@misc{avigadMathematicsLeanMathematics,
  title = {Mathematics in {{Lean}} --- {{Mathematics}} in {{Lean}} 0.1 Documentation},
  author = {Avigad, Jeremy and Massot, Patrick},
  urldate = {2024-01-11},
  howpublished = {https://leanprover-community.github.io/mathematics\_in\_lean/},
  file = {/home/george/Zotero/storage/ARI85SW7/mathematics_in_lean.html}
}

@misc{avigadTheoremProvingLean,
  title = {Theorem {{Proving}} in {{Lean}} 4},
  author = {Avigad, Jeremy and {de Moura}, Leondardo and Kong, Soonho and Ullrich, Sebastian},
  year = {2024},  
  urldate = {2024-01-11},
  howpublished = {https://leanprover.github.io/theorem\_proving\_in\_lean4/},
  file = {/home/george/Zotero/storage/N9RLELNU/theorem_proving_in_lean4.html}
}

@book{ballCourseAlgebraicErrorCorrecting2020,
  title = {A {{Course}} in {{Algebraic Error-Correcting Codes}}},
  author = {Ball, Simeon},
  year = {2020},
  series = {Compact {{Textbooks}} in {{Mathematics}}},
  publisher = {Springer International Publishing},
  address = {Cham},
  doi = {10.1007/978-3-030-41153-4},
  urldate = {2024-01-11},
  isbn = {978-3-030-41152-7 978-3-030-41153-4},
  langid = {english},
  keywords = {Algebraic error-correcting codes,Algebraic geometric codes,Block codes,Coding theory,Coding theory error correction,Cyclic code,Cyclic code error detection,Error-correcting codes,Expanders,Finite fields,LDPC codes,Linear code coding theory,Linear codes,Masters level error-correcting codes,MDS codes,p-adic codes,Reed-Muller codes,Reed-Muller error-correcting codes,Shannon-Hartley theorem,Shannon's theorem},
  file = {/home/george/Zotero/storage/9LT9CYTH/Ball - 2020 - A Course in Algebraic Error-Correcting Codes.pdf}
}

@book{beachyBlair,
  title = {Abstract Algebra, Fourth Edition},
  author = {Beachy, John A. and Blair, William D.},
  year = {2019},
  publisher = {Waveland Press Inc.}
}

@book{ceccherini-silbersteinDiscreteHarmonicAnalysis2018,
  title = {Discrete {{Harmonic Analysis}}: {{Representations}}, {{Number Theory}}, {{Expanders}}, and the {{Fourier Transform}}},
  shorttitle = {Discrete {{Harmonic Analysis}}},
  author = {{Ceccherini-Silberstein}, Tullio and Scarabotti, Fabio and Tolli, Filippo},
  year = {2018},
  series = {Cambridge {{Studies}} in {{Advanced Mathematics}}},
  publisher = {Cambridge University Press},
  address = {Cambridge},
  doi = {10.1017/9781316856383},
  urldate = {2024-01-11},
  abstract = {This self-contained book introduces readers to discrete harmonic analysis with an emphasis on the Discrete Fourier Transform and the Fast Fourier Transform on finite groups and finite fields, as well as their noncommutative versions. It also features applications to number theory, graph theory, and representation theory of finite groups. Beginning with elementary material on algebra and number theory, the book then delves into advanced topics from the frontiers of current research, including spectral analysis of the DFT, spectral graph theory and expanders, representation theory of finite groups and multiplicity-free triples, Tao's uncertainty principle for cyclic groups, harmonic analysis on GL(2,Fq), and applications of the Heisenberg group to DFT and FFT. With numerous examples, figures, and over 160 exercises to aid understanding, this book will be a valuable reference for graduate students and researchers in mathematics, engineering, and computer science.},
  isbn = {978-1-107-18233-2},
  file = {/home/george/Zotero/storage/UB5TXFAM/8B432BD3CC6E5E8B9E43A293E7D9E4F4.html}
}

@article{diaconisGeneralizationSpectralAnalysis1989,
  title = {A {{Generalization}} of {{Spectral Analysis}} with {{Application}} to {{Ranked Data}}},
  author = {Diaconis, Persi},
  year = {1989},
  journal = {The Annals of Statistics},
  volume = {17},
  number = {3},
  eprint = {2241705},
  eprinttype = {jstor},
  pages = {949--979},
  publisher = {Institute of Mathematical Statistics},
  issn = {0090-5364},
  urldate = {2024-02-06},
  abstract = {An analog of the spectral analysis of time series is developed for data in general spaces. This is applied to data from an election in which 5738 people rank ordered five candidates. Group theoretic considerations offer an analysis of variance like decomposition which seems natural and fruitful. A variety of inferential tools are suggested. The spectral ideas are then extended to general homogeneous spaces such as the sphere.}
}

@book{fitzpatrickAdvancedCalculus2009,
  title = {Advanced {{Calculus}}},
  author = {Fitzpatrick, Patrick},
  year = {2009},
  publisher = {American Mathematical Soc.},
  abstract = {"Advanced Calculus is intended as a text for courses that furnish the backbone of the student's undergraduate education in mathematical analysis. The goal is to rigorously present the fundamental concepts within the context of illuminating examples and stimulating exercises. This book is self-contained and starts with the creation of basic tools using the completeness axiom. The continuity, differentiability, integrability, and power series representation properties of functions of a single variable are established. The next few chapters describe the topological and metric properties of Euclidean space. These are the basis of a rigorous treatment of differential calculus (including the Implicit Function Theorem and Lagrange Multipliers) for mappings between Euclidean spaces and integration for functions of several real variables."--pub. desc.},
  googlebooks = {4hhFXPdTXwoC},
  isbn = {978-0-8218-4791-6},
  langid = {english},
  keywords = {Mathematics / Calculus}
}

@book{goldschmidtAlgebraicFunctionsProjective2003,
  title = {Algebraic Functions and Projective Curves},
  author = {Goldschmidt, David M.},
  year = {2003},
  series = {Graduate {{Texts}} in {{Mathematics}}},
  volume = {215},
  publisher = {Springer-Verlag, New York},
  doi = {10.1007/b97844},
  mrnumber = {1934359 (2003j:14001)}
}

@book{gutermanNitecki,
  title = {Differential Equations: {{A}} First Course},
  author = {Nitecki, Zbigniew and Guterman, Martin},
  year = {1992},
  publisher = {Saunders}
}

@book{huffmanFundamentalsErrorCorrectingCodes2003,
  title = {Fundamentals of {{Error-Correcting Codes}}},
  author = {Huffman, W. Cary and Pless, Vera},
  year = {2003},
  publisher = {Cambridge University Press},
  address = {Cambridge},
  doi = {10.1017/CBO9780511807077},
  urldate = {2024-01-11},
  abstract = {Fundamentals of Error Correcting Codes is an in-depth introduction to coding theory from both an engineering and mathematical viewpoint. As well as covering classical topics, there is much coverage of techniques which could only be found in specialist journals and book publications. Numerous exercises and examples and an accessible writing style make this a lucid and effective introduction to coding theory for advanced undergraduate and graduate students, researchers and engineers, whether approaching the subject from a mathematical, engineering or computer science background.},
  isbn = {978-0-521-13170-4},
  file = {/home/george/Zotero/storage/P8SMV9UU/BF3AFDFB539C3C023BBD9DCBA4CDA761.html}
}

@book{jamesRepresentationsCharactersGroups2001,
  title = {Representations and {{Characters}} of {{Groups}}},
  author = {James, Gordon and Liebeck, Martin},
  year = {2001},
  edition = {2},
  publisher = {Cambridge University Press},
  address = {Cambridge},
  doi = {10.1017/CBO9780511814532},
  urldate = {2024-01-11},
  abstract = {This book provides a modern introduction to the representation theory of finite groups. Now in its second edition, the authors have revised the text and added much new material. The theory is developed in terms of modules, since this is appropriate for more advanced work, but considerable emphasis is placed upon constructing characters. Included here are the character tables of all groups of order less than 32, and all simple groups of order less than 1000. Applications covered include Burnside's paqb theorem, the use of character theory in studying subgroup structure and permutation groups, and how to use representation theory to investigate molecular vibration. Each chapter features a variety of exercises, with full solutions provided at the end of the book. This will be ideal as a course text in representation theory, and in view of the applications, will be of interest to chemists and physicists as well as mathematicians.},
  isbn = {978-0-521-81205-4},
  file = {/home/george/Zotero/storage/MSX477JT/James and Liebeck - 2001 - Representations and Characters of Groups.pdf;/home/george/Zotero/storage/5LKJ4FZ8/9F525E6ACAC7FFADFDBDECE98C115F40.html}
}

@misc{macbethMechanicsProof,
  title = {The {{Mechanics}} of {{Proof}}},
  author = {MacBeth, Heather},
  urldate = {2024-01-11},
  howpublished = {https://hrmacbeth.github.io/math2001/},
  file = {/home/george/Zotero/storage/242D64VA/math2001.html}
}

@misc{milnej.s.GroupTheory,
  title = {Group {{Theory}}},
  author = {Milne, J.S.},
  urldate = {2024-01-11},
  howpublished = {https://www.jmilne.org/math/CourseNotes/gt.html},
  file = {/home/george/Zotero/storage/PP4XTZFM/gt.html}
}

@misc{rijkeIntroductionHomotopyType,
  title = {Introduction to {{Homotopy Type Theory}}},
  author = {Rijke, Egbert},
  year = {2024},
  urldate = {2024-04-10},
  howpublished = {https://arxiv.org/abs/2212.11082},
  file = {/home/george/Zotero/storage/4ZB4EEUB/2212.html}
}

@book{rosenNumberTheoryFunction2002,
  title = {Number Theory in Function Fields},
  author = {Rosen, Michael},
  year = {2002},
  series = {Graduate {{Texts}} in {{Mathematics}}},
  volume = {210},
  publisher = {Springer-Verlag, New York},
  doi = {10.1007/978-1-4757-6046-0},
  mrnumber = {1876657 (2003d:11171)}
}

@book{serreLinearRepresentationsFinite1977,
  title = {Linear Representations of Finite Groups},
  author = {Serre, Jean-Pierre},
  year = {1977},
  publisher = {Springer-Verlag, New York-Heidelberg},
  mrnumber = {0450380 (56 \#8675)}
}

@book{serreRationalPointsCurves2020,
  title = {Rational Points on Curves over Finite Fields},
  author = {Serre, Jean-Pierre},
  editor = {Bassa, Alp and Lorenzo Garc{\'i}a, Elisa and Ritzenthaler, Christophe and Schoof, Ren{\'e}},
  year = {2020},
  series = {Documents {{Math{\'e}matiques}} ({{Paris}}) [{{Mathematical Documents}} ({{Paris}})]},
  volume = {18},
  publisher = {Soci{\'e}t{\'e} Math{\'e}matique de France, Paris},
  isbn = {978-2-85629-923-4},
  mrnumber = {4242817},
  file = {/home/george/Zotero/storage/8FRKDR75/article.html}
}

@misc{spenceIntroductionAlgebraicCoding2002,
  title = {Introduction to {{Algebraic Coding Theory}}},
  author = {Spence, S.},
  year = {2002},
  urldate = {2024-01-11},
  abstract = {4 Ideals and cyclic codes 19 4.1 Ideals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 4.2 Cyclic codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 4.3 Group of a code . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 4.4 Minimal polynomials . . . . . . . . . . . . . . . . . . . . . . . . . 31 4.5 BCH and Reed-Solomon codes . . . . . . . . . . . . . . . . . . . 33 4.6 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39},
  file = {/home/george/Zotero/storage/A3MMWVL9/Spence - 2002 - Introduction to Algebraic Coding Theory.pdf}
}

@book{tsfasmanAlgebraicGeometricCodes2007,
  title = {Algebraic {{Geometric Codes}}: {{Basic Notions}}},
  shorttitle = {Algebraic {{Geometric Codes}}},
  author = {Tsfasman, Michael and Vl{\v a}du{\c t}, Serge and Nogin, Dmitry},
  year = {2007},
  month = sep,
  series = {Mathematical {{Surveys}} and {{Monographs}}},
  volume = {139},
  publisher = {American Mathematical Society},
  issn = {0076-5376, 2331-7159},
  doi = {10.1090/surv/139},
  urldate = {2024-01-11},
  abstract = {Advancing research. Creating connections.},
  isbn = {978-0-8218-4306-2 978-0-8218-7520-9 978-1-4704-1366-8},
  langid = {english}
}