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Transition to Higher Mathematics: Structure and Proof - Second Edition

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Bob A Dumas, University of Washington - Seattle Campus

John E McCarthy, Washington University in St Louis

Copyright Year: 2015

ISBN 13: 9781941823033

Publisher: Open Scholarship

Language: English

Formats Available

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CC BY

Table of Contents

  • Chapter 0. Introduction
  • Chapter 1. Preliminaries
  • Chapter 2. Relations
  • Chapter 3. Proofs
  • Chapter 4. Principle of Induction
  • Chapter 5. Limits
  • Chapter 6. Cardinality
  • Chapter 7. Divisibility
  • Chapter 8. The Real Numbers
  • Chapter 9. Complex Numbers

About the Book

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.

About the Contributors

Authors

Bob A. Dumas, University of Washington - Seattle Campus

John E. McCarthy, Washington University in St Louis