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An Invitation to Abstract Mathematics

  • Béla Bajnok

Part of the Undergraduate Texts in Mathematics book series (UTM)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. What’s Mathematics?

    1. Front Matter
      Pages 1-1
    2. Béla Bajnok
      Pages 3-10
    3. Béla Bajnok
      Pages 11-22
    4. Béla Bajnok
      Pages 23-31
    5. Béla Bajnok
      Pages 33-44
    6. Béla Bajnok
      Pages 45-54
    7. Béla Bajnok
      Pages 55-68
  3. How to Solve It?

    1. Front Matter
      Pages 69-69
    2. Béla Bajnok
      Pages 71-81
    3. Béla Bajnok
      Pages 83-94
    4. Béla Bajnok
      Pages 95-108
    5. Béla Bajnok
      Pages 109-123
    6. Béla Bajnok
      Pages 135-147
    7. Béla Bajnok
      Pages 149-160
    8. Béla Bajnok
      Pages 161-173
    9. Béla Bajnok
      Pages 175-187
    10. Béla Bajnok
      Pages 189-195
  4. Advanced Math for Beginners

    1. Front Matter
      Pages 197-197
    2. Béla Bajnok
      Pages 199-212
    3. Béla Bajnok
      Pages 213-227
    4. Béla Bajnok
      Pages 229-239
    5. Béla Bajnok
      Pages 241-257
    6. Béla Bajnok
      Pages 259-281
    7. Béla Bajnok
      Pages 283-310
    8. Béla Bajnok
      Pages 311-342
    9. Béla Bajnok
      Pages 343-380
  5. Back Matter
    Pages 381-406

About this book

Introduction

This undergraduate textbook is intended primarily for a transition course into higher mathematics, although it is written with a broader audience in mind.  The heart and soul of this book is problem solving, where each problem is carefully chosen to clarify a concept, demonstrate a technique, or to enthuse.  The exercises require relatively extensive arguments, creative approaches, or both, thus providing motivation for the reader.  With a unified approach to a diverse collection of topics, this text points out connections, similarities, and differences among subjects whenever possible.  This book shows students that mathematics is a vibrant and dynamic human enterprise by including historical perspectives and notes on the giants of mathematics, by mentioning current activity in the mathematical community, and by discussing many famous and less well-known questions that remain open for future mathematicians.

Ideally, this text should be used for a two semester course, where the first course has no prerequisites and the second is a more challenging course for math majors; yet, the flexible structure of the book allows it to be used in a variety of settings, including as a source of various independent-study and research projects.

Keywords

abstract mathematics bridge course cardinalities decision trees infinity logic mathematical proof mathematics milestones number systems prime number theorem pythagoream theorem set theory surreal numbers transition course

Authors and affiliations

  • Béla Bajnok
    • 1
  1. 1., Department of MathematicsGettysburg CollegeGettysburgUSA

Bibliographic information

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