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My initial goal was to understand mathematics well enough to have a some grasp of "Deep Learning" (2016) textbook by Goodfellow, Bengio, and Courville. I meant
by jeffhwang 4y ago
My initial goal was to understand mathematics well enough to have a some grasp of "Deep Learning" (2016) textbook by Goodfellow, Bengio, and Courville. I meant like 50-85% understanding of the math depending on the chapter. And being able to have reasonable understanding of deep learning papers being published in the 2012-2018 period. https://www.deeplearningbook.org https://www.deeplearningbook.org
1. Because my math was pretty rusty, I started with single-variable calculus. Good resources for this are Khan Academy including pre-calc prequisites all the way up to multivariable calc and linear algebra. I'm not sure which textbook on single-variable calc is good but there are many many to choose from.
2. For multivariable calc, I began with Lang's "Calculus of Several Variables". https://link.springer.com/book/10.1007/978-1-4612-1068-9 https://link.springer.com/book/10.1007/978-1-4612-1068-9
3. After Lang, I did a lot of the problems in the first half (differentiation only) of Baxandall and Liebeck's "Vector Calculus". This is truly an outstanding book; such clear exposition and excellent organization with many examples. It was a little more formal in it's presentation than I was used to. But this helped me learn to write decent and well-organized proofs. And when I got to item 6 below, Baxandall and Liebeck got me ready! https://store.doverpublications.com/0486466205.html https://store.doverpublications.com/0486466205.html
4. In parallel, I studied linear algebra. My two main intro books were Strang's "Introduction to Linear Algebra" (4th edition). https://math.mit.edu/~gs/linearalgebra/ https://math.mit.edu/~gs/linearalgebra/
But I found Strang (super popular among college students) was well-supplemented by Kuldeep Singh's "Linear Algebra Step-by-Step" https://global.oup.com/academic/product/linear-algebra-9780199654444 https://global.oup.com/academic/product/linear-algebra-97801...?
5. At this point, the Khan Academy videos on linear algebra were very helpful.
6. Now that I was ready, I started Axler's "Linear Algebra Done Right". It's more formal and abstract compared to 4 and 5 above. I love it though! It's taken me years and I'm still only part way through. It is one of my all-time favorite books--not just in math--but in any field. I'm a bit slow at this type of abstract / proof-based math but it's deeply deeply satisfying. https://linear.axler.net https://linear.axler.net
7. Recently, I started Jacobson's "Basic Algebra I". I'm only at the beginning of my journey into modern algebra but I really like it so far.https://www.maa.org/publications/maa-reviews/basic-algebra-i-0 https://www.maa.org/publications/maa-reviews/basic-algebra-i...
Hope this helps!