Textbooks in Mathematical Sciences

Introduction · to Mathematical Structures and · Proofs

Authors: Gerstein, Larry

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  • ISBN 978-1-4684-6708-6
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About this book

This is a textbook for a one-term course whose goal is to ease the transition from lower-division calculus courses to upper-division courses in linear and abstract algebra, real and complex analysis, number theory, topology, combinatorics, and so on. Without such a "bridge" course, most upper­ division instructors feel the need to start their courses with the rudiments of logic, set theory, equivalence relations, and other basic mathematical raw materials before getting on with the subject at hand. Students who are new to higher mathematics are often startled to discover that mathematics is a subject of ideas, and not just formulaic rituals, and that they are now expected to understand and create mathematical proofs. Mastery of an assortment of technical tricks may have carried the students through calculus, but it is no longer a guarantee of academic success. Students need experience in working with abstract ideas at a nontrivial level if they are to achieve the sophisticated blend of knowledge, disci­ pline, and creativity that we call "mathematical maturity. " I don't believe that "theorem-proving" can be taught any more than "question-answering" can be taught. Nevertheless, I have found that it is possible to guide stu­ dents gently into the process of mathematical proof in such a way that they become comfortable with the experience and begin asking them­ selves questions that will lead them in the right direction.

Table of contents (6 chapters)

Buy this book

eBook $74.99
price for USA (gross)
  • ISBN 978-1-4684-6708-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $99.00
price for USA
  • ISBN 978-1-4684-6710-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Introduction · to Mathematical Structures and · Proofs
Authors
Series Title
Textbooks in Mathematical Sciences
Copyright
1996
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4684-6708-6
DOI
10.1007/978-1-4684-6708-6
Softcover ISBN
978-1-4684-6710-9
Series ISSN
1431-9381
Edition Number
1
Number of Pages
X, 350
Topics