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A TeXas Style Introduction to Proof

MAA Press: An Imprint of the American Mathematical Society
Now available in new edition: TEXT/48
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A TeXas Style Introduction to Proof
MAA Press: An Imprint of the American Mathematical Society
Now available in new edition: TEXT/48
• Book Details

AMS/MAA Textbooks
Volume: 352017; 161 pp

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.

• 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 looking-glass
• Shiny hidden people
• Mathematical writing
• 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

• 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 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
• Requests

Review Copy – for publishers of book reviews
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Accessibility – to request an alternate format of an AMS title
Volume: 352017; 161 pp

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.

• 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 looking-glass
• Shiny hidden people
• Mathematical writing
• 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
• 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
Review Copy – for publishers of book reviews
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Accessibility – to request an alternate format of an AMS title
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