By the time you finish the final chapter on the "Axiom of Choice," you won’t be an expert. But you will be something rarer: a person who understands what pure mathematics is .
Furthermore, the lack of color graphics (the PDF is often grayscale scans of the B&W print edition) makes the diagrams for "Functions and Counting" look like hieroglyphics. You will hate the section on the Pigeonhole Principle until you realize it’s just common sense. A Concise Introduction to Pure Mathematics (PDF) is not a reference book. It is a tasting menu . It gives you one bite of logic, one bite of number theory, one bite of set theory, one bite of analysis, and one bite of combinatorics. a concise introduction to pure mathematics pdf
In the vast, intimidating ocean of academic textbooks, most volumes over 300 pages begin with a warning: "This text assumes a prior course in real analysis." By the time you finish the final chapter