# A TeXas Style Introduction to Proof

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*Ron Taylor; Patrick X. Rault*

MAA Press: An Imprint of the American Mathematical Society

Reprinted edition available: TEXT/48

A TeXas Style Introduction to Proof is
an IBL textbook designed for a one-semester course on proofs (the
“bridge course”) that also introduces TeX as a tool
students can use to communicate their work. As befitting
“textless” text, the book is, as one reviewer
characterized it, “minimal.” Written in an easy-going
style, the exposition is just enough to support the activities, and it
is clear, concise, and effective. The book is well organized and
contains ample carefully selected exercises that are varied,
interesting, and probing, without being discouragingly
difficult.

#### Reviews & Endorsements

A lovely little book for beginning mathematics majors and other students encountering proofs for the first time. Students should find the text appealing, and it contains many good exercises that a professor can build a course around. … Overall, a most satisfying book for a beginning class in mathematical proofs.

-- Curt Bennett, Professor of Mathematics at Loyola Marymount University and 2010 Haimo Award Winner

A TeXas Style Introduction to Proof by Ron Taylor and Patrick X. Rault is truly delightful-full of humanizing charm that softens the hard edge of mathematical rigor. It is gentle, lively, clear, and warm. … From this book, students and their instructors will find many proofs of the joy of mathematics.

-- Michael Starbird, University Distinguished Teaching Professor ofMathematics at The University of Texas at Austin and 2007 Haimo Award Winner

Taylor and Rault skillfully guide students through basic proof-writing techniques so that the student createsand discovers the content. The book is well-written, the integration of LaTeX is unique, and the authors have a fantastic sense of humor.

-- Amanda Croll, Assistant Professor of Mathematics, Concordia University, Irvine

# Table of Contents

## A TeXas Style Introduction to Proof

- Contents ix10
- Acknowledgements xiii14
- Introduction 117
- Symbolic logic 1531
- Proof methods 3551
- Mathematical induction 4965
- Set theory 6379
- Functions and relations 87103
- Counting 109125
- Axiomatics 123139
- Mathematical writing 131147
- Comments on Style 133149
- The Structure of a LaTeX Document 135151
- A sample LaTeX document 136152
- The Preamble 136152
- The Text 138154
- Formatting text 139155
- Typesetting mathematics 140156
- LaTeX codes for common mathematical symbols 141157
- Tables 145161
- Arrays with reasons 146162
- Making lists (Checking them twice is a good idea.) 148164
- An example of a homework assignment in LaTeX 149165
- TeX Source Code for the example 149165

- Bibliography 151167
- Index 155171
- About the Authors 161177