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Transition to Higher Mathematics: Structure and Proof (Second Edition)

By Bob A Dumas and John E McCarthy


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.

Topics: Proofs, Mathematical arguments, Rigorous mathematics, Transition to Higher Mathematics, Real numbers, Logic, Set theory, OER, open education resources, Logic and Foundations, Mathematics, Other Mathematics
Publisher: Washington University Open Scholarship
Year: 2015
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