Overview
- 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
- Request lecturer material: sn.pub/lecturer-material
Part of the book series: Undergraduate Texts in Mathematics (UTM)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
About this book
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.
Similar content being viewed by others
Keywords
Table of contents (7 chapters)
-
Front Matter
-
Back Matter
Authors and Affiliations
About the author
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.
Bibliographic Information
Book Title: Introduction to Mathematical Structures and Proofs
Authors: Larry J. Gerstein
Series Title: Undergraduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-1-4614-4265-3
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media, LLC, part of Springer Nature 2012
Hardcover ISBN: 978-1-4614-4264-6Published: 06 June 2012
Softcover ISBN: 978-1-4939-5146-8Published: 23 August 2016
eBook ISBN: 978-1-4614-4265-3Published: 05 June 2012
Series ISSN: 0172-6056
Series E-ISSN: 2197-5604
Edition Number: 2
Number of Pages: XIII, 401
Topics: Mathematical Logic and Foundations, Number Theory, Combinatorics