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

I found Halmos' Naive Set Theory to be very helpful when first learning about proofs. Don't be offput by the title - the material is fundamental to any working mathematician. It is also quite short.

I suggest you start out with a course or book on formal logic in computer science. In particular doing proofs in intuitionistic logic. You can use a simple proof assistant to verify your proofs and it will help you really understand how proofs are done and how they are just a kind of programs in a special programming language called mathematics (given some assumptions). Proofs in higher level books are all informal, so you can’t do them programmatically in most cases, but it really helps with understanding how proofs works. After that, follow what subjects finds your fancy.

> what is the best resource to get started with studying college level mathematics?

> Basically I want to learn how to read and write proofs.

> The main goal is to understand and work through higher math books like analysis, combinatorics, graph theory, abstract algebra, etc.

I feel like these are three somewhat distinct goals, and may need distinct approaches.

If you only have HS geometry and algebra, you may want to fill in some additional foundational knowledge first. If the algebra is what we refer to in the US as "Algebra 1", then definitely do "Algebra 2" / "Precalculus" and preferably calculus as well. Someone else recommended Khan Academy, which is a great resource for this level. Calculus is not strictly required for most of the upper-level topics you mentioned, with the exception of analysis, for which it is a strong prerequisite.

For proofs, check out one of the dedicated "how to write proofs" books recommended by others. You can probably dive right into these, as they rarely require calculus or other prerequisites, as they focus mainly on simple proofs in geometry, number theory, set theory, combinatorics, and other fairly "entry level" topics.

A discrete math textbook is another good way to get started with proofs. These often cover basic topics in logic, set theory, and proof methods (induction, proof by contradiction, etc.). They also typically cover basic graph theory, combinatorics, and sometimes even basic abstract algebra (groups, rings, etc.), which will give you a head start on some of the advanced topics. Rosen's discrete math book is a good choice, widely used in courses at respectable universities.

Once you've covered that material, you should be good to go on the advanced topics you mentioned.

I like this guide

https://www.susanrigetti.com/math