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For my own part, it was all about finding the right book. I enjoyed my degree in pure maths, and after finishing I really missed studying so I tried out dozens
by nimonian 6y ago
For my own part, it was all about finding the right book. I enjoyed my degree in pure maths, and after finishing I really missed studying so I tried out dozens of books. Eventually, I hit upon Calculus by Spivak. This book fundamentally changed me and I solved every problem in it fastidiously - it was just so well made, funny in parts, it had cliffhangers, and the problems were just amazing, linking together over chapters like characters in a novel. For the first time, I was solving problems just for fun and I was improving much faster than I did during my degree. I wrote all my solutions in LaTeX so I had an organised body of work to look back on and watch grow, adding to the satisfaction (I lose paper; pdf is better for me).
So my advice: find a great book, make notes and expand on what the author is saying with diagrams or additional lines of working, focus on solving problems, do it out of love.
- harperlee 6y agoSpivak was great, I remember it fondly from my university years. Is there any kind of crowdsourced "canonical" list of great books? Ideally something that does not bring 5 answers per question to the table. For example, what is the Spivak of discrete mathematics? Of statistics? What is Spivak for multivariate calculus?
- nimonian 6y agoI would love to know the answer to your question. On the one hand, it's too subjective to answer, one student's Spivak is another's Apostol; on the other hand, certain books just seem special in an almost objective way and rise above the scores of other books on the subject. There is this: https://mathblog.com/mathematics-books/ https://mathblog.com/mathematics-books/ which looks like a pretty well curated list
- he11ow 6y agoThis. For Algebra, look for Topics in Algebra by Herstein. It reads beautifully, and the problems at the end of each chapters are very good at solidifying the knowledge.
- hypersurface 6y agoThis is very nice to know as I have an ancient copy of this book to hand. Thanks!