Best books or courses to self study undergrad math subjects?

Question

For someone out of touch in mathematics and done undergrad in electrical engineering and currently working as a programmer I want to relearn/learn mathematica again. I have done calculus in the past and some matrix algebra and probability in college. But I remember those topics very foggily.I want to learn undergrad math properly again. Books or courses are my friend in this journey.I ask you all HNers who have had similar experiences or have suggestions please suggest a path I should follow.P.S.: Being an electrical engineering grad I know boolean logic and all. But have never formally learned or written mathematical proofs. I want to learn that too.

akasakahakada · Accepted Answer

If you want thickness:https://www.cis.upenn.edu/~jean/gbooks/geomath.htmlIf you want proofs:https://cseweb.ucsd.edu/~gill/CILASite/If you want dictionary:https://press.princeton.edu/books/hardcover/9780691118802/th...If you want usefullness:any mathematical physics book will do

mindcrime · Answer

I won't recommend any specific books, as I don't consider myself enough of a maths expert to have any standing to do so. But what I will suggest is to give the Youtube channel "The Math Sorcerer"[1] a look. He does a LOT of book reviews, talks a lot about self-study, and most of his book reviews include a pretty big focus on which books are or are not really good for self-study.[1]: https://www.youtube.com/@TheMathSorcerer

scrum-treats · Answer

I really like MIT's Open Courseware offerings (available on youtube).
From HN, @optbuild shared some math-stuff, e.g.,
- Fourier Transform (https://news.ycombinator.com/item?id=35858725)
- Mathematical Problem Solving (https://news.ycombinator.com/item?id=35858763)
So did @rito (https://news.ycombinator.com/submitted?id=rito).
I am also a fan of Complexity Explorer (which @rito shared). Can't say enough great things about Santa Fe Institute.

uptownfunk · Answer

Chartrand - mathematical proofs (if you don’t have background with proofs)
Then-
Baby Rudin - analysis (first 8 chapters is good)
Dummit Foote - algebra (as much as you can read, groups, rings, fields, even more if you can)
Needham - complex analysis
Friedberg - linear algebra
After that you can go in many directions
Many other interesting courses
Number theory
Representation theory
Probability -> stochastic processes
Statistics

tiberious726 · Answer

Spivak and Apostol are the two classic intro texts. Apostol is used more in programs that eventually get into physics, while Spivak is used more as a lead-in to analysis.In my youth, I once wrote a paper just on how Apostol's proof of the fundamental theorem of calculus was more beautiful than Spivak's, and that they were both way better my school's textbook, rofl. In my old age, I recognize that Spivak teaches you incredibly powerful and useful tools in its kinda obtuse approaches to things

jimkoen · Answer

Springer literally has a book series called "Undergraduate texts in mathematics". The quality varies from book to book, but overall I would highly recommend taking a look.

markus_zhang · Answer

Back in university the honor students use Rudin to learn real analysis. My university is a peasant comparing to MIT/Berk but I guess it says something.

creamyhorror · Answer

A very similar Ask HN post title asking for books and courses for college math was posted less than a day before your post. Why do requests for math courses come up so often?

warrenm · Answer

see also this question asked a couple hours before you asked yours: https://news.ycombinator.com/item?id=35854717