Resources: References for the course

Posted on 2024-01-07 by George McNinch

References for Representations of finite groups

  • These notes (Milne, n.d.) Group Theory Notes are available on-line; Chapter 7 contains a treatment of representations of finite groups.

  • (James and Liebeck 2001)

  • (Serre 1977)

  • I hope to briefly discuss the Fast Fourier Transform, and I’ll probably follow (Ceccherini-Silberstein, Scarabotti, and Tolli 2018) for that discussion.

References for Error correcting codes

  • (Huffman and Pless 2003) is available electronically at Tisch Library

  • (Ball 2020)

  • These notes of Spence (Spence 2002) are available here

  • (Tsfasman, Vlǎduţ, and Nogin 2007)

References for Formalization of mathematics

For our discussion of proof assistants and formalization of math, I’m going to use the Lean language; the Lean community web site is here: https://leanprover-community.github.io/.

Learning resources for Lean may be found here. They include the following:

Bibliography

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