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Macmillan Higher Education

Introduction to Mathematical Structures and Proofs (2nd Edition)

Author(s):
Publisher:

Springer

Pages: 401
Further Actions:

Recommend to library

AVAILABLE FORMATS

Paperback - 9781493951468

23 August 2016

$59.95

In stock

Ebook - 9781461442653

05 June 2012

$44.99

In stock

Hardcover - 9781461442646

08 June 2012

$59.95

In stock

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....

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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 for instructors adopting the text for a course.

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Solutions manual for even numbered exercises is available on springer.com for instructors adopting the text for a course

Discusses the multifaceted process of mathematical proof by thoughtful oscillation between what is known and what is to be demonstrated

Presents more than one proof for many results, for instance for the fact that there are infinitely many prime numbers

Shows how the processes of counting and comparing the sizes of finite sets are based in function theory, and how the ideas can be extended to infinite sets via Cantor's theorems

Contains a wide assortment of exercises, ranging from routine checks of a student's grasp of definitions through problems requiring more sophisticated mastery of fundamental ideas

Demonstrates the dual importance of intuition and rigor in the development of mathematical ideas

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.

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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.

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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.

Show Less

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