This helpful workbook-style "bridge" book introduces students to the foundations of advanced mathematics, spanning the gap between a practically oriented calculus sequence and subsequent courses in algebra and analysis with a more theoretical slant. Part 1 focuses on logic and number systems, providing the most basic tools, examples, and motivation for the manner, method, and concerns of higher mathematics. Part 2 covers sets, relations, functions, infinite sets, and mathematical proofs and reasoning. Author Dennis Sentilles also discusses the history and development of mathematics as well as the reasons behind axiom systems and their uses. He assumes no prior knowledge of proofs or logic, and he takes an intuitive approach that builds into a formal development. Advanced undergraduate students of mathematics and engineering will find this volume an excellent source of instruction, reinforcement, and review.

Preface

Part 1. Starting Points

Chapter 1. Logic, Language and Mathematics

Chapter 2. The Foundations of Mathematics

Part 2. The Strategic Attack in Mathematics

Chapter 3. A Formally Informal Theory of Sets

Chapter 4. Topology and Connected Sets

Chapter 5. Functions

Chapter 6. Counting the Infinite

Chapter 7. Equivalence Relations

Chapter 8. Continuity, Connectedness and Compactness

Appendix A

Index