Solow D. The Keys to Advanced Mathematics...1995

Textbook in PDF format

This book simplifies the process of learning such courses as discrete math, linear algebra, abstract algebra, and real analysis by explaining the following concepts:
- Closed-form Solutions: solutions obtained from the problem data by a simple rule or formula.
- Numerical Methods: solutions obtained from the problem data by performing a sequence of computations.
- Unification: the process of combining two or more problems into a single problem whose solution provides the solution to all of the original problems.
- Generalization: the process of creating, from an original problem, a new problem with a solution procedure that solves not only the original problem, but many other different problems as well.
- Abstraction: the process of learning to think in terms of general objects rather than specific items.
- Axiomatic Systems: an approach to studying the broad class of problems created by abstraction.
And that's not all.
You also learn these skills:
- Doing mathematical proofs.
- Identifying similarities and differences.
- Translating visual images to symbolic form.
- Understanding definitions