Mathematical Maturity Via Discrete Mathematics

Designed for a one-semester course for undergraduate majors in math, computer science, and computer engineering, this text helps students take the crucial step from consuming mathematics to producing mathematics. Author Vadim Ponomarenko employs the general concept of discrete mathematics to introduce the basic knowledge of proof techniques and their uses.
Like other beginning texts on methods of proof, this treatment offers definitions, theorems, and techniques. Unlike other books, it explains how to read, interpret, and use definitions, demonstrating not only general proof strategies — like proof of induction — but also the specific methods of thought for implementing these strategies. All techniques are built from scratch to provide an intellectually consistent whole. Each chapter contains several exercises, for which the author provides hints rather than solutions to encourage creative thinking.

This is the first book for Vadim Ponomarenko, a Professor of Mathematics at San Diego University. He is also the author of many published papers that may be consulted on his website.

Table of Contents:
Contents
Lists of Definitions
Foreword
1. Mathematical Definitions
2. Propositional Calculus
3. Semantics
4. Predicate Calculus
5. Proofs
6. Proof by Induction
7. Sequences and Recurrences
8. Set Theory I
9. Set Theory II
10. Relations
11. Equivalence Relations
12. Posets
13. Functions
Appendix: Details of Entry Point
Hints to Selected Exercises
Index