After years of divorce with mathematics I decided to come back to it. I studied computer science, so had quite a lot of maths in university, but though passing the exams, I didn't feel I fully grasped it. Now I'd like to come back to this material and go through it in detail to really understand it.
My reasons are:
- For fun
- I plan to also study some university physics
- It'll surely sharpen some of the skills used at my work as a programmer
I was recommended to start with linear algebra and calculus. I'm planning to study both of them more or less concurrently.
I want to self-study and am deciding what books to use for that. I like to dig deep into things and relly understand theory behind them, so probably I'd like books with more theoretical approach. But I wouldn't like to totally skip any real-world applications of those things, so ideally the book would also cover some of that. I'd also like something challenging and rigorous.
Recommended positions
I've done some research and see people recommending those positions:
Calculus:
- "Calculus" by Michael Spivak
- "Calculus" by Tom Apostol (2 volumes)
Linear algebra:
- "Linear Algebra" by by Stephen H. Friedberg, Lawrence E. Spence,, Arnold J. Insel
- "Linear Algebra" by Kenneth Hoffman
- "Linear Algebra Done Right" by Sheldon Axler
- "Linear Algebra" by Georgi E. Shilov
Questions
- I've read Tom Apostol's book covers some linear algebra. Does it mean that I would be able to skip linear algebra book at all and learn both just doing his "Calculus"?
- Spivak's "Calculus" covers only single-variable. If I choose to follow his book, what would be good choice of a book for multi-variable calculus?
- Which of those books on linear algebra cover both theory and applications? Or maybe it'd be wise to complete one more theoretical and then read about applications alone in another text?
