Introduction to Mathematical Structures and Proofs

Larry J. Gerstein

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English

Springer-Verlag New York Inc.
23 August 2016

Mathematical foundations; Mathematical logic; Discrete mathematics; Number theory

Series: Undergraduate Texts in Mathematics

"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."

By: Larry J. Gerstein
Imprint: Springer-Verlag New York Inc.
Country of Publication: United States
Edition: Softcover reprint of the original 2nd ed. 2012
Dimensions: Height: 254mm, Width: 178mm,
Weight: 787g
ISBN: 9781493951468
ISBN 10: 1493951467
Series: Undergraduate Texts in Mathematics
Pages: 401
Publication Date: 23 August 2016
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

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.

"Larry Gerstein's primary areas of research have been in quadratic forms and number theory and he has published extensively in these areas. The author's first edition of ""Introduction to Mathematical Structures and Proofs"" has sold to date (8/2/2010) over 6000 copies and has gone through 5 printings. Gerstein himself has a transition course at UC, Santa Barbara (Math 8-A transition to higher mathematics) from his book since its first publication date. The first edition also received 2 glowing reviews by Steve Krantz for the American Mathematical Monthly, and S. Gottwald for Zentralblatt."