Good reads
This is a collection of math-related books and articles that I enjoyed reading. I do not recommend text books on algebra or group theory, since in these cases I prefer my own lectures notes.
Books
- O. Forster, Analysis 1, 13. Auflage, Springer Spektrum, 2023 (most concise German text)
- K. Fritzsche, Grundkurs Funktionentheorie, 3. Auflage, Springer Spektrum 2024 (very linear reading)
- A. Leutbecher, Zahlentheorie, Springer, 1996 (extremely carefully written, serious use of traditional German language)
- G. Navarro, Characters and blocks of finite groups, CUP, 1998 (down to earth approach, best intro to Brauer's theory)
- T. Petsinis, The French mathematician, Walker & Co, 1998 (a novel based on Galois' life)
- K. Ono, A. D. Aczel, My Search for Ramanujan, Springer, 2016 (Ono compares his emigrant life to Ramanujan's)
- S. G. Krantz, Mathematical Apocrypha (redux), AMS, 2002 (2006) (faithful mathematical anecdotes)
- P. R. Halmos, I want to be a mathematician, Springer, 1985 (confidential details of the AMS in the last century, sometimes a bit long-winded)
- S. Budiansky, Journey to the Edge of Reason: The life of Kurt Gödel, Norton & Company, 2021 (Gödel's intense personality provides plenty of entertainment)
Articles
- P. R. Halmos, How to write mathematics, l’Enseignement Mathématique 16 (1970), 123–152, pdf
- P. R. Halmos, How to talk mathematics, Notices of the AMS (1974) 21, 155–158, pdf
- P. G. Casazza, A mathematician's survival guide, pdf
- W. P. Thurston, On proof and progress in mathematics, Bull. AMS 30 (1994), 161–177, pdf
- G.-C. Rota, Ten lessons I wish I had been taught, Notices Amer. Math. Soc. 44 (1997), 22–25, pdf
- D. E. Knuth, Two notes on notation, Amer. Math. Monthly 99 (1992), 403-422, pdf
- J.-P. Serre, How to write mathematics badly, talk, YouTube
\[|g_1H_1\cup\ldots\cup g_nH_n|\le \frac{2^n-1}{2^n}|G|\]