Introduction to Mathematical Structures and Proofs

As a student moves from basic calculus courses into upper-division courses in linear and abstract algebra, real and complex analysis, number theory, topology, and so on, a "bridge" course can help ensure a smooth transition. Introduction to Mathematical Structures and Proofs is a textbook intended for such a course, or for self-study. This book introduces an array of fundamental mathematical structures. It also explores the delicate balance of intuition and rigor-and the flexible thinking-required to prove a nontrivial result. In short, this book seeks to enhance the mathematical maturity of the reader.

The new material in this second edition includes a section on graph theory, several new sections on number theory (including primitive roots, with an application to card-shuffling), and a brief introduction to the complex numbers (including a section on the arithmetic of the Gaussian integers). Solutions for even numbered exercises are available on springer. com forinstructors adopting the text for a course.

Preface to the Second Edition. - Preface to the First Edition. - 1. Logic. - 2. Sets. - 3. Functions. - 4. Finite and Infinite Sets. - 5. Combinatorics. - 6. Number Theory. - 7. Complex Numbers. - Hints and Partial Solutions to Selected Odd-Numbered Exercises. - Index.