Ask HN: Books or courses to understand college level mathematics?

1. “Vector Calculus” by Baxandall and Liebeck is excellent. Begins with a semi-formal review of single variable calculus before going onto a mix of linear algebra and multi variable calculus.

2. “Linear Algebra Done Right” by Axler is one of my favorite books in any field. Might be challenging to people completely new to proofs or linear algebra but starts with pretty simple foundations and builds up an excellent rigorous foundation. I enjoyed this way more than other intro LA books but needed to study more applied LA first to be able to read this. Another approach is to start with abstract algebra and then go into the Axler.

I self-studied both of these texts many years after college and had forgotten pretty much all my math except some high school stuff. Supplemented by YouTube videos, Khan Academy, I felt pretty confident and eventuallY fell in love with both of these texts.

Richard Hammack | Book of Proof (pdf book) - https://www.people.vcu.edu/~rhammack/BookOfProof/

Short book: Groups and their Graphs

Taylor Dupuy | Fundamentals of Mathematics (YouTube lecture course)

Silvanus P Thompson | Calculus Made Easy (html book) - https://calculusmadeeasy.org/ (This shouldn't be your only exposure to Calculus. It is more for building intuition.)

Gilbert Strang | Highlights of Calculus (YouTube lecture course)

Josh Starmer | StatQuest (Short various statistics videos) - https://www.youtube.com/c/joshstarmer/playlists

Bob Franzosa | Introduction to Topology (single public lecture) - https://www.youtube.com/watch?v=zsN_guq__Ac

Socratica | Abstract Algebra (short videos)

MIT Calculus Revisited (Single Variable Calculus): https://www.youtube.com/playlist?list=PL3B08AE665AB9002A

MIT Calculus Revisited (Multivariable Calculus): https://www.youtube.com/playlist?list=PL1C22D4DED943EF7B

MIT Calculus Revisited (Complex Variables, Differential Equations, Linear Algebra): https://www.youtube.com/playlist?list=PLD971E94905A70448

Matthew Macauley | Visual Group Theory, Differential Equations, Discrete Mathematical Structures, Advanced Linear Algebra, and Advanced Engineering Mathematics (YouTube lecture courses)

Open University (BBC) | Geometric Topology (YouTube lecture course)

Joel David Hamkins | Philosophy of Mathematics (YouTube lecture course)

Marco Taboga | Probability and Statistics & Matrix Algebra (html book, need calculus) - https://www.statlect.com/

On YouTube you can literally watch a good lecture course for just about any typical undergraduate course. You just need to know where to look. Also there are even some really good master's degree courses out there.

Of course the only way to really learn the mathematics deeply is to "learn by doing", aka problems and proofs.

Other than the usual big American universities another good source from India is NPTEL (https://nptel.ac.in/course.html).

For somewhat more entertaining short lectures try:

Grant Sanderson | 3Blue1Brown - https://www.youtube.com/c/3blue1brown

Brady Haran | Numberphile - https://www.youtube.com/c/numberphile/

Tai-Danae Bradley, Gabe Perez-Giz, and Kelsey Houston-Edwards | PBS Infinite Series - https://www.youtube.com/c/pbsinfiniteseries/

Raymond Flood (YouTube public lectures at Gresham College) | History of Mathematics

There are a ton of channels starting to pop up like Grant's 3B1B (I find like a new one every week). He had a contest recently so maybe look at some of the winners.

This is pretty useful if you get into higher mathematics:

Math Vault | The Definitive Glossary of Higher Mathematical Jargon - https://mathvault.ca/math-glossary/

Some books:

There is Eugenia Cheng's book: The Joy of Abstraction

See this list its pretty good: https://abakcus.com/30-best-math-books-to-learn-advanced-mat...

P.S. I created some Youtube lecture aggregation channels:

https://arisbe.carrd.co/#section03

Introduction to Mathematical Think by Dr. Keith Devlin on Coursera:

https://www.coursera.org/learn/mathematical-thinking