A Problem Seminar

  • Donald J. Newman

Part of the Problem Books in Mathematics book series (volume 2)

Table of contents

  1. Front Matter
    Pages I-VII
  2. Donald J. Newman
    Pages 1-1
  3. Donald J. Newman
    Pages 3-28
  4. Donald J. Newman
    Pages 29-40
  5. Donald J. Newman
    Pages 41-113

About this book

Introduction

There was once a bumper sticker that read, "Remember the good old days when air was clean and sex was dirty?" Indeed, some of us are old enough to remember not only those good old days, but even the days when Math was/un(!), not the ponderous THEOREM, PROOF, THEOREM, PROOF, . . . , but the whimsical, "I've got a good prob­ lem. " Why did the mood change? What misguided educational philoso­ phy transformed graduate mathematics from a passionate activity to a form of passive scholarship? In less sentimental terms, why have the graduate schools dropped the Problem Seminar? We therefore offer "A Problem Seminar" to those students who haven't enjoyed the fun and games of problem solving. CONTENTS Preface v Format I Problems 3 Estimation Theory 11 Generating Functions 17 Limits of Integrals 19 Expectations 21 Prime Factors 23 Category Arguments 25 Convexity 27 Hints 29 Solutions 41 FORMAT This book has three parts: first, the list of problems, briefly punctuated by some descriptive pages; second, a list of hints, which are merely meant as words to the (very) wise; and third, the (almost) complete solutions. Thus, the problems can be viewed on any of three levels: as somewhat difficult challenges (without the hints), as more routine problems (with the hints), or as a textbook on "how to solve it" (when the solutions are read). Of course it is our hope that the book can be enjoyed on any of these three levels.

Keywords

Mathematik /Aufgabensammlung Problem-solving function mathematics proof theorem

Authors and affiliations

  • Donald J. Newman
    • 1
  1. 1.Department of MathematicsTemple UniversityPhiladelphiaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4613-8214-0
  • Copyright Information Springer-Verlag New York Inc. 1982
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-90765-9
  • Online ISBN 978-1-4613-8214-0
  • Series Print ISSN 0171-1873
  • About this book