Reddit mentions of The Probability Tutoring Book: An Intuitive Course for Engineers and Scientists (and Everyone Else!)

Usual hierarchy of what comes after what is simply artificial. They like to teach Linear Algebra before Abstract Algebra, but it doesn't mean that it is all there's to Linear Algebra especially because Linear Algebra is a part of Abstract Algebra.

Example,

Linear Algebra for freshmen: some books that talk about manipulating matrices at length.

Linear Algebra for 2nd/3rd year undergrads: Linear Algebra Done Right by Axler

Linear Algebra for grad students(aka overkill): Advanced Linear Algebra by Roman

Basically, math is all interconnected and it doesn't matter where exactly you enter it.

Coming in cold might be a bit of a shocker, so studying up on foundational stuff before plunging into modern math is probably great.

Books you might like:

Discrete Mathematics with Applications by Susanna Epp

Learning to Reason: An Introduction to Logic, Sets, and Relations by Nancy Rodgers

Building Proofs: A Practical Guide by Oliveira/Stewart

Book Of Proof by Hammack

Mathematical Proofs: A Transition to Advanced Mathematics by Chartrand et al

How to Prove It: A Structured Approach by Velleman

The Nuts and Bolts of Proofs by Antonella Cupillary

How To Think About Analysis by Alcock

Principles and Techniques in Combinatorics by Khee-Meng Koh , Chuan Chong Chen

The Probability Tutoring Book: An Intuitive Course for Engineers and Scientists (and Everyone Else!) by Carol Ash

Problems and Proofs in Numbers and Algebra by Millman et al

Theorems, Corollaries, Lemmas, and Methods of Proof by Rossi

Mathematical Concepts by Jost - can't wait to start reading this

Proof Patterns by Joshi

...and about a billion other books like that I can't remember right now.

Good Luck.