Skip to main content
SpringerLink
Log in
Birkhäuser
Book cover

Mathematical Olympiad Challenges

  • Textbook
  • © 2009

Overview

Authors:
  1. Titu Andreescu

    1. University of Texas at Dallas, School of Natural Sciences and Mathematics, Richardson, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Răzvan Gelca

    1. Department of Mathematics and Statistics, Texas Tech University, Lubbock, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • 404 beautiful, challenging, and instructive problems, all including solutions and discussion.
  • Organized by subject and difficulty to motivate students.
  • Covers topics in algebra, geometry, trigonometry, combinatorics, and number theory.
  • Provides historical insights and asides to stimulate further inquiry
  • Emphasizes creative solutions to open-ended problems

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 49.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 64.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (6 chapters)

  1. Front Matter

    Pages i-xvii
    Download chapter PDF

  3. Solutions

    1. Geometry and Trigonometry

      Pages 105-170

    2. Algebra and Analysis

      Pages 171-221

    3. Number Theory and Combinatorics

      Pages 223-276

  4. Back Matter

    Pages 277-283
    Download chapter PDF
Back to top

Keywords

About this book

Why Olympiads? Working mathematiciansoftentell us that results in the ?eld are achievedafter long experience and a deep familiarity with mathematical objects, that progress is made slowly and collectively, and that ?ashes of inspiration are mere punctuation in periods of sustained effort. TheOlympiadenvironment,incontrast,demandsarelativelybriefperiodofintense concentration,asksforquickinsightsonspeci?coccasions,andrequiresaconcentrated but isolated effort. Yet we have foundthat participantsin mathematicsOlympiadshave oftengoneontobecome?rst-classmathematiciansorscientistsandhaveattachedgreat signi?cance to their early Olympiad experiences. For many of these people, the Olympiad problem is an introduction, a glimpse into the world of mathematics not afforded by the usual classroom situation. A good Olympiad problem will capture in miniature the process of creating mathematics. It’s all there: the period of immersion in the situation, the quiet examination of possible approaches, the pursuit of various paths to solution. There is the fruitless dead end, as well as the path that ends abruptly but offers new perspectives, leading eventually to the discoveryof a better route. Perhapsmost obviously,grapplingwith a goodproblem provides practice in dealing with the frustration of working at material that refuses to yield. If the solver is lucky, there will be the moment of insight that heralds the start of a successful solution. Like a well-crafted work of ?ction, a good Olympiad problem tells a story of mathematical creativity that captures a good part of the real experience and leaves the participant wanting still more. And this book gives us more.

Reviews

From the 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

"The Olympiad book is easier to describe since the format of the Olympiad competition and the books it has spawned will be well known to most Gazette readers. … The authors have organised the material to reduce the pain … and to make the material a genuine learning experience for Olympian hopefuls and their teachers. … a valuable addition to the problem literature, and their organisational features are generally helpful rather than merely attempts to look different." (John Baylis, The Mathematical Gazette, July, 2004)

Authors and Affiliations

  • University of Texas at Dallas, School of Natural Sciences and Mathematics, Richardson, USA

    Titu Andreescu

  • Department of Mathematics and Statistics, Texas Tech University, Lubbock, USA

    Răzvan Gelca

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation