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© 2000

Mathematical Olympiad Challenges

Textbook

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Problems

    1. Front Matter
      Pages 1-1
    2. Titu Andreescu, Răzvan Gelca
      Pages 3-32
    3. Titu Andreescu, Răzvan Gelca
      Pages 33-58
    4. Titu Andreescu, Răzvan Gelca
      Pages 59-85
  3. Solutions

    1. Front Matter
      Pages 87-87
    2. Titu Andreescu, Răzvan Gelca
      Pages 89-150
    3. Titu Andreescu, Răzvan Gelca
      Pages 151-195
    4. Titu Andreescu, Răzvan Gelca
      Pages 197-249
  4. Back Matter
    Pages 251-260

About this book

Introduction

Mathematical Olympiad Challenges is a rich collection of problems put together by two experienced and well-known professors and coaches of the U.S. International Mathematical Olympiad Team. Hundreds of beautiful, challenging, and instructive problems from algebra, geometry, trigonometry, combinatorics, and number theory were selected from numerous mathematical competitions and journals. An important feature of the work is the comprehensive background material provided with each grouping of problems.

The problems are clustered by topic into self-contained sections with solutions provided separately. All sections start with an essay discussing basic facts and one or two representative examples. A list of carefully chosen problems follows and the reader is invited to take them on. Additionally, historical insights and asides are presented to stimulate further inquiry. The emphasis throughout is on encouraging readers to move away from routine exercises and memorized algorithms toward creative solutions to open-ended problems.

Aimed at motivated high school and beginning college students and instructors, this work can be used as a text for advanced problem- solving courses, for self-study, or as a resource for teachers and students training for mathematical competitions and for teacher professional development, seminars, and workshops.

Keywords

algebra geometry number theory binomial calculus combinatorics Invariant Mathematica matrices Prime prime number theorem transformation trigonometry variable

Authors and affiliations

  1. 1.American Mathematics CompetitionsUniversity of NebraskaLincolnUSA
  2. 2.Department of MathematicsUniversity of MichiganAnn ArborUSA

Bibliographic information

  • Book Title Mathematical Olympiad Challenges
  • Authors Titu Andreescu
    Razvan Gelca
  • DOI https://doi.org/10.1007/978-1-4612-2138-8
  • Copyright Information Birkhäuser Boston 2000
  • Publisher Name Birkhäuser Boston
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-8176-4190-0
  • Softcover ISBN 978-0-8176-4155-9
  • eBook ISBN 978-1-4612-2138-8
  • Edition Number 1
  • Number of Pages XVI, 260
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Mathematics, general
    Algebra
    Geometry
    Number Theory
  • Buy this book on publisher's site
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Reviews

"The authors are experienced problem solvers and coaches of mathematics teams. This expertise shows through and the result is a volume that would be a welcome addition to any mathematician's bookshelf."   —MAA Online

"This [book] is…much more than just another collection of interesting, challenging problems, but is instead organized specifically for learning. The book expertly weaves together related problems, so that insights gradually become techniques, tricks slowly become methods, and methods eventually evolve into mastery…. The book is aimed at motivated high school and beginning college students and instructors. It can be used as a text for advanced problem-solving courses, for self-study, or as a resource for teachers and students training for mathematical competitions, and for teacher professional development, seminars, and workshops.

I strongly recommend this book for anyone interested in creative problem-solving in mathematics…. It has already taken up a prized position in my personal library, and is bound to provide me with many hours of intellectual pleasure."   —The Mathematical Gazette