Description

This book is written for students who have taken calculus and want to learn what “real mathematics" is. We hope you will find the material engaging and interesting/ and that you will be encouraged to learn more advanced mathematics. This is the second edition of our text. It is intended for students who have taken a calculus course/ and are interested in learning what higher mathematics is all about. It can be used as a textbook for an "Introduction to Proofs" course/ or for self-study. Chapter 1: Preliminaries/ Chapter 2: Relations/ Chapter 3: Proofs/ Chapter 4: Principles of Induction/ Chapter 5: Limits/ Chapter 6: Cardinality/ Chapter 7: Divisibility/ Chapter 8: The Real Numbers/ Chapter 9: Complex Numbers. The last 4 chapters can also be used as independent introductions to four topics in mathematics: Cardinality; Divisibility; Real Numbers; Complex Numbers.