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An Outline of Set Theory

  • James M. Henle

Part of the Problem Books in Mathematics book series (PBM)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Introduction

    1. James M. Henle
      Pages 1-4
  3. Projects

    1. Front Matter
      Pages 5-5
    2. James M. Henle
      Pages 7-13
    3. James M. Henle
      Pages 15-19
    4. James M. Henle
      Pages 21-22
    5. James M. Henle
      Pages 23-24
    6. James M. Henle
      Pages 25-26
    7. James M. Henle
      Pages 27-32
    8. James M. Henle
      Pages 33-36
    9. James M. Henle
      Pages 37-40
    10. James M. Henle
      Pages 41-44
    11. James M. Henle
      Pages 45-48
  4. Suggestions

    1. Front Matter
      Pages 49-49
    2. James M. Henle
      Pages 51-53
    3. James M. Henle
      Pages 55-56
    4. James M. Henle
      Pages 57-58
    5. James M. Henle
      Pages 59-61
    6. James M. Henle
      Pages 63-66
    7. James M. Henle
      Pages 67-70
    8. James M. Henle
      Pages 71-79
    9. James M. Henle
      Pages 81-83
    10. James M. Henle
      Pages 85-89
    11. James M. Henle
      Pages 91-93
  5. Solutions

    1. Front Matter
      Pages 95-95
    2. James M. Henle
      Pages 97-99
    3. James M. Henle
      Pages 101-104
    4. James M. Henle
      Pages 105-108
    5. James M. Henle
      Pages 109-114
    6. James M. Henle
      Pages 115-117
    7. James M. Henle
      Pages 119-121
    8. James M. Henle
      Pages 123-127
    9. James M. Henle
      Pages 129-132
    10. James M. Henle
      Pages 133-135
    11. James M. Henle
      Pages 137-139
  6. Back Matter
    Pages 141-145

About this book

Introduction

This book is designed for use in a one semester problem-oriented course in undergraduate set theory. The combination of level and format is somewhat unusual and deserves an explanation. Normally, problem courses are offered to graduate students or selected undergraduates. I have found, however, that the experience is equally valuable to ordinary mathematics majors. I use a recent modification of R. L. Moore's famous method developed in recent years by D. W. Cohen [1]. Briefly, in this new approach, projects are assigned to groups of students each week. With all the necessary assistance from the instructor, the groups complete their projects, carefully write a short paper for their classmates, and then, in the single weekly class meeting, lecture on their results. While the em­ phasis is on the student, the instructor is available at every stage to assure success in the research, to explain and critique mathematical prose, and to coach the groups in clear mathematical presentation. The subject matter of set theory is peculiarly appropriate to this style of course. For much of the book the objects of study are familiar and while the theorems are significant and often deep, it is the methods and ideas that are most important. The necessity of rea­ soning about numbers and sets forces students to come to grips with the nature of proof, logic, and mathematics. In their research they experience the same dilemmas and uncertainties that faced the pio­ neers.

Keywords

Finite calculus cardinals mathematics ordinal set theory theorem

Authors and affiliations

  • James M. Henle
    • 1
  1. 1.Department of MathematicsSmith CollegeNorthamptonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4613-8680-3
  • Copyright Information Springer-Verlag New York 1986
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-96368-6
  • Online ISBN 978-1-4613-8680-3
  • Series Print ISSN 0941-3502
  • Buy this book on publisher's site
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