Step 3: Get a book called Real Mathematical Analysis by Charles Pugh and you work through that and attempt as many problems as you can, with a view not to rush through it, but to expand your mind through each problem.
Step 4: Pick any of these books that interest you the most and do the same:
- Calculus by Spivak
- Algebra: Chapter 0 by Paolo Aluffi
- Linear Algebra Done Right by Axler
By then you should have enough mathematical maturity to know what to do next.
Step 2: Download the Book of Proof: http://www.people.vcu.edu/~rhammack/BookOfProof/ You read through it and do all the odd numbered exercises (the solutions are at the end of the book).
Step 3: Get a book called Real Mathematical Analysis by Charles Pugh and you work through that and attempt as many problems as you can, with a view not to rush through it, but to expand your mind through each problem.
Step 4: Pick any of these books that interest you the most and do the same:
- Calculus by Spivak
- Algebra: Chapter 0 by Paolo Aluffi
- Linear Algebra Done Right by Axler
By then you should have enough mathematical maturity to know what to do next.