Write Your Own Proofs in Set Theory and Discrete Mathematics

Written by a pair of math teachers and based on their classroom notes and experiences, this introductory treatment of theory, proof techniques, and related concepts is designed for undergraduate courses. No knowledge of calculus is assumed, making it a useful text for students at many levels. The focus is on teaching students to prove theorems and write mathematical proofs so that others can read them.
Since proving theorems takes lots of practice, this text is designed to provide plenty of exercises. The authors break the theorems into pieces and walk readers through examples, encouraging them to use mathematical notation and write proofs themselves. Topics include propositional logic, set notation, basic set theory proofs, relations, functions, induction, countability, and some combinatorics, including a small amount of probability. The text is ideal for courses in discrete mathematics or logic and set theory, and its accessibility makes the book equally suitable for classes in mathematics for liberal arts students or courses geared toward proof writing in mathematics.

Novelist and mathematician Amy Babich resides in Austin, Texas.
Laura Person is a Professor of Mathematics at SUNY Potsdam, a liberal arts university in northern New York.

Foreword A--This Book and How to Use It.
Foreword B--Words and Numbers: Mathematics, Writing, and the Two Cultures
Foreword C--Mathematical Proof as a Form of Writing
Foreword D--Amazing Secrets of Professional Mathematicians Revealed!
1. Basic Logic
2. Proving Theorems About Sets
3. Cartesian Products and Relations
4. Functions
5. Induction, Power Sets, and Cardinality
6. Introduction to Combinatorics
7. Derangements and Other Entertainments
Afterword A--A Few Words on the History of Set Theory
Afterword B--A Little Bit About Limits
Afterword C--Why No Answers in the Back of this Book
Afterword D--What Next?  Concise Synopses of Selected College Mathematics Courses
Dr. Spencer's Mantra for the Relief of Anxiety that Accompanies Attempts to Create and Write Proofs
Bibliography
Index
List of Symbols