Introduction To Mathematical Structures And Proofs

Introduction To Mathematical Structures And Proofs
2nd Edition
2012

From the Back Cover
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).


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Chapters
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01 - Logic
02 - Sets
03 - Functions
04 - Finite And Infinite Sets
05 - Combinatorics
06 - Number Theory
07 - Complex Numbers