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Introduction · to Mathematical Structures and · Proofs

  • Larry J. Gerstein

Part of the Textbooks in Mathematical Sciences book series (TIMS)

Table of contents

  1. Front Matter
    Pages i-x
  2. Larry J. Gerstein
    Pages 1-37
  3. Larry J. Gerstein
    Pages 39-115
  4. Larry J. Gerstein
    Pages 117-150
  5. Larry J. Gerstein
    Pages 151-203
  6. Larry J. Gerstein
    Pages 205-280
  7. Larry J. Gerstein
    Pages 281-327
  8. Back Matter
    Pages 329-350

About this book

Introduction

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.

Keywords

Permutation algebra calculus mathematics number theory

Authors and affiliations

  • Larry J. Gerstein
    • 1
  1. 1.University of CaliforniaSanta BarbaraUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4684-6708-6
  • Copyright Information Springer Science+Business Media New York 1996
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4684-6710-9
  • Online ISBN 978-1-4684-6708-6
  • Series Print ISSN 1431-9381
  • Buy this book on publisher's site