Equations and Inequalities

Elementary Problems and Theorems in Algebra and Number Theory

  • Jiří Herman
  • Jaromír Šimša
  • Radan Kučera

Table of contents

  1. Front Matter
    Pages i-xi
  2. Jiří Herman, Jaromír Šimša, Radan Kučera
    Pages 1-87
  3. Jiří Herman, Jaromír Šimša, Radan Kučera
    Pages 89-171
  4. Jiří Herman, Jaromír Šimša, Radan Kučera
    Pages 173-282
  5. Jiří Herman, Jaromír Šimša, Radan Kučera
    Pages 283-336
  6. Back Matter
    Pages 337-344

About this book


This book is intended as a text for a problem-solving course at the first­ or second-year university level, as a text for enrichment classes for talented high-school students, or for mathematics competition training. It can also be used as a source of supplementary material for any course dealing with algebraic equations or inequalities, or to supplement a standard elementary number theory course. There are already many excellent books on the market that can be used for a problem-solving course. However, some are merely collections of prob­ lems from a variety of fields and lack cohesion. Others present problems according to topic, but provide little or no theoretical background. Most problem books have a limited number of rather challenging problems. While these problems tend to be quite beautiful, they can appear forbidding and discouraging to a beginning student, even with well-motivated and carefully written solutions. As a consequence, students may decide that problem solving is only for the few high performers in their class, and abandon this important part of their mathematical, and indeed overall, education.


algebra diophantine equation number theory prime number

Authors and affiliations

  • Jiří Herman
    • 1
  • Jaromír Šimša
    • 2
  • Radan Kučera
    • 3
  1. 1.Brno Grammar SchoolBrnoCzech Republic
  2. 2.Mathematical InstituteAcademy of Sciences of the Czech RepublicBrnoCzech Republic
  3. 3.Department of Mathematics Faculty of ScienceMasaryk UniversityBrnoCzech Republic

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag New York, Inc. 2000
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-7071-3
  • Online ISBN 978-1-4612-1270-6
  • Series Print ISSN 1613-5237
  • Buy this book on publisher's site