Ask HN: Serious mathematics books that can replace a good teacher?

How to solve it by Polya.

George Polya's "How to solve it" taught me how to think better, in engineering, mathematics & problem solving.

Spivak's Calculus

Spivak - Calculus

Spivak's Calculus!

baby Rudin ("Principles of Mathematical Analysis") can be very good for a first course

Baby Rudin (Principles of Mathematical Analysis, Walter Rudin)

W. Rudin's, as I recall, third edition, Principles of Mathematical Analysis.

Agree, Rudin is excellent as a second course on real analysis, but as a first one it is absolutely terrible.

Came here to say Rudin.

I recently saw Sheldon Axler's Linear Algebra Done Right recommended here, and have been working through it.

Loved that book !

Complex Analysis: Visual Complex Analysis

I liked that book.

an introduction book on calculus from 1910

Probability Theory: The Logic of Science by E. T. Jaynes.

2a. Naive Set Theory - Halmos

Understanding Analysis by Stephen Abbott

https://www.amazon.com/Understanding-Analysis-Undergraduate-...

Papa Rudin (Real and Complex Analysis, Walter Rudin)

the first half of Rudin's Real and Complex Analysis.

1a. How to Prove It: A Structured Approach

https://www.amazon.com/How-Prove-Structured-Daniel-Velleman-...

I'm a big fan of Herstein's exposition.

For basic abstract algebra Herstein, Topics in Algebra should usually be enough and is well written.

I also really liked Herstein on algebra