>>13803359Don't listen to this
>>13803372 guy.
I am going to assume you have at least a early high school familiarity with basic algebra, geometry, maybe even some pre-calculus and calculus. And when you say math you mean math and not applied math.
Start with a book on logic and proofs. Often recommended is a book titled "How to Prove it". This should get you familiarized with basic notions in mathematics such as logic, sets, numbers, proofs.
Then move on to a book on abstract algebra, often recommended is "A First Course in Abstract Algebra". This well get you more familiarized with abstraction, which is at the heart of math, and all the basic results in group theory.
You can, either concurrently or afterwards, move on to an introductory real analysis text. There are many good options, I liked Tao's Analysis, as well as Carother's Real Analysis. These might be a bit advanced (often meant for honors undergraduates or beginning graduates), so you may have to some research on what the best beginning texts on the subject are. Real Analysis is the study of the structure of the real numbers, which includes real series, real sequences, real-valued functions. You will also learn about general metric spaces, and some basic topology.
Then pick up Munkres' book and study Topology. Topology is more or less the study of abstract "spaces/structures" under continuous deformations (famous tea cup to doughnut and vice versa). Here one is not interested in notions of distance, angles, size, length, but more general concepts such as connectedness and compactness.
Afterwards, you can jump into many topics. Depending on what interests you. Complex Analysis, Number Theory, Automata Theory, Algebraic Topology, Graph Theory etc. You'd be ready.
When I listed all the books, I recommend doing all the problems the author recommends (often has some notation to indicate particularly important exercises), and a bit more (think all the odd numbers or all the prime numbers and 1.
