Undergraduate Texts in Mathematics

Introduction to Mathematical Structures and Proofs

Authors: Gerstein, Larry

  • 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
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eBook $44.99
price for USA (gross)
  • ISBN 978-1-4614-4265-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $59.95
price for USA
  • ISBN 978-1-4614-4264-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $59.95
price for USA
  • ISBN 978-1-4939-5146-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
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About this Textbook

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.

About the authors

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.

Table of contents (7 chapters)

Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-1-4614-4265-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $59.95
price for USA
  • ISBN 978-1-4614-4264-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $59.95
price for USA
  • ISBN 978-1-4939-5146-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Introduction to Mathematical Structures and Proofs
Authors
Series Title
Undergraduate Texts in Mathematics
Copyright
2012
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media, LLC
eBook ISBN
978-1-4614-4265-3
DOI
10.1007/978-1-4614-4265-3
Hardcover ISBN
978-1-4614-4264-6
Softcover ISBN
978-1-4939-5146-8
Series ISSN
0172-6056
Edition Number
2
Number of Pages
XIII, 401
Topics