
Book DetailsAMS/MAA TextbooksVolume: 35; 2017; 161 pp
Reprinted edition available: TEXT/48
A TeXas Style Introduction to Proof is an IBL textbook designed for a onesemester 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 easygoing 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.

Table of Contents

Contents

Acknowledgements

Introduction

To the instructor

To the student

How to construct those proofs

Using LaTeX to write mathematics

Notation

The journey begins …

Symbolic logic

Statements

Compound statements and logical connectives

Proof via truth table

Implications

Quantifiers

Compound quantifiers

Proof methods

Variable names

Parity and divisibility

Negations

Proof methods

Mathematical induction

Geometric tilings

Induction versus deduction

Strong Induction

Set theory

Notation and definitions

Venn diagrams

General proofs with sets

Set operations

Deeper thinking

Set products

Power sets

Index sets and set operations

Spaciousness

Functions and relations

Relations

Partitions

Order relations

Functions

Throwing some math around

Counting

A (very) brief history of infinity

Finite sets

The Pigeonhole Principle

A foundation for infinity

Can we go beyond infinity?

Axiomatics

LSAT axiomatics

Charles Dodgson's axiomatic lookingglass

Shiny hidden people

Mathematical writing

Comments on Style

The Structure of a LaTeX Document

A sample LaTeX document

The Preamble

The Text

Formatting text

Typesetting mathematics

LaTeX codes for common mathematical symbols

Tables

Arrays with reasons

Making lists (Checking them twice is a good idea.)

An example of a homework assignment in LaTeX

TeX Source Code for the example

Bibliography

Index

About the Authors


Additional Material

Reviews

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 delightfulfull 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 proofwriting techniques so that the student createsand discovers the content. The book is wellwritten, the integration of LaTeX is unique, and the authors have a fantastic sense of humor.
Amanda Croll, Assistant Professor of Mathematics, Concordia University, Irvine

 Book Details
 Table of Contents
 Additional Material
 Reviews
Reprinted edition available: TEXT/48
A TeXas Style Introduction to Proof is an IBL textbook designed for a onesemester 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 easygoing 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.

Contents

Acknowledgements

Introduction

To the instructor

To the student

How to construct those proofs

Using LaTeX to write mathematics

Notation

The journey begins …

Symbolic logic

Statements

Compound statements and logical connectives

Proof via truth table

Implications

Quantifiers

Compound quantifiers

Proof methods

Variable names

Parity and divisibility

Negations

Proof methods

Mathematical induction

Geometric tilings

Induction versus deduction

Strong Induction

Set theory

Notation and definitions

Venn diagrams

General proofs with sets

Set operations

Deeper thinking

Set products

Power sets

Index sets and set operations

Spaciousness

Functions and relations

Relations

Partitions

Order relations

Functions

Throwing some math around

Counting

A (very) brief history of infinity

Finite sets

The Pigeonhole Principle

A foundation for infinity

Can we go beyond infinity?

Axiomatics

LSAT axiomatics

Charles Dodgson's axiomatic lookingglass

Shiny hidden people

Mathematical writing

Comments on Style

The Structure of a LaTeX Document

A sample LaTeX document

The Preamble

The Text

Formatting text

Typesetting mathematics

LaTeX codes for common mathematical symbols

Tables

Arrays with reasons

Making lists (Checking them twice is a good idea.)

An example of a homework assignment in LaTeX

TeX Source Code for the example

Bibliography

Index

About the Authors

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 delightfulfull 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 proofwriting techniques so that the student createsand discovers the content. The book is wellwritten, the integration of LaTeX is unique, and the authors have a fantastic sense of humor.
Amanda Croll, Assistant Professor of Mathematics, Concordia University, Irvine