A list of general resources you might find helpful. If you have any interesting links please email it to me!

Lower Level Math

Textbook PDFs can generally be found here if the university doesn’t have some form of subscription (e.g. through SpringerLink). Knowledge should be free!

Notes by Padraic Bartlett I used to learn how to write proofs.

Advice by John Lee on the ingredients of good mathematical writing.

A list of Putnam problems sorted by category. Could be useful for test preparation. He also has some recreational math on his website.

Upper Level Math

Many notes by Patrick Lei on various graduate courses at Columbia.

Compilation of the expository AMS “What Is…?” articles.

A listing of most virtual seminars in math and related subjects.

Advice by Jenia Tevelev on getting into math research. There are parts specific to UMass Amherst in there, but most of the advice is quite general and sound.

Advice in an article by some rather famous mathematicians on approaching research.