Introduction to Mathematical Structures and Proofs

By Larry J. Gerstein

Book Overview

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.

• Format: Hardcover
• Language: English
• ISBN: 1461442648
• ISBN13: 9781461442646
• Release Date: June 2012
• Publisher: Springer
• Length: 401 Pages
• Weight: 2.10 lbs.
• Dimensions: 0.9" x 7.0" x 10.0"

Customer Reviews

Good intro for beginning

Before this book, I was still wondering through a maze of nonsensical calculus textbooks and couldn't get myself out of that trap. I think this book is a good start for going further in math. This book is clearly written and makes me think clearly, relative to other too concise books. Now I know what's going on when proofs are present in books. It's worth a buy. Also, selected exericise solutions are just enough to get the hint on how to approach a problem and also are motivating enough to solve a problem on my own. This book would probably better as a textbook in a course taught by a good instructor, but self-study is probably possible. You get to peak inside for table of contents and few pages, so why not have a look?