# Transition to Higher Mathematics: Structure and Proof - Second Edition

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

## Conditions of Use

Attribution

CC BY

## Reviews

The text covers the areas and ideas of the subject appropriately. It also provides an index and appendices. The table of contents is organized and easy to use to navigate between the topics. The inclusion of more hints or solutions to some... read more

The text covers the areas and ideas of the subject appropriately. It also provides an index and appendices. The table of contents is organized and easy to use to navigate between the topics. The inclusion of more hints or solutions to some exercises would be helpful to both students and instructors. The text should include more examples to help clarify concepts for students.

The content seems mostly accurate. There is an adequate number of examples and justifications in the proofs of statements.

The content is presented in a traditional way. The text is written in such a way that necessary updates will be straightforward to implement.

The language in the text is clear. There are some transitional explanation paragraphs, which aid in student understanding of mathematics in the text.

The text is consistent in writing and terminology.

Each chapter of the book includes several subsections, which makes the content easier to understand.

The topics in the text are presented in a logical manner. The table of contents should be made clickable for ease of use.

The text and images are displayed in a clear and orderly manner.

I found no grammatical errors.

There is no inclusion of any culturally relevant pieces, which is consistent with introductory proof textbooks. More examples related to applications of the content could have been included to make the content more culturally relevant.

## 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

## Ancillary Material

## 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