Introduction to Advanced Mathematics

Focused on "What Every Mathematician Needs to Know," this book focuses on the analytical tools necessary for thinking like a mathematician. It anticipates many of the questions readers might have, and develops the subject slowly and carefully, with each chapter containing a full exposition of topics, many examples, and practice problems to reinforce the concepts as they are introduced. "Find the Flaw" problems help readers learn to read proofs critically. Contains five core chapters on elementary logic, methods of proof, set theory, functions, and relations; and four chapters of examples, theorems, and projects. For those interested in abstract algebra or real analysis.