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Problems from the Book
Titu Andreescu, University of Texas at Dallas, Richardson, TX, and Gabriel Dospinescu, Ecole Normale Supérieure de Lyon, France
A publication of XYZ Press.
cover
XYZ Series
2010; 571 pp; hardcover
Volume: 13
ISBN-10: 0-9799269-0-4
ISBN-13: 978-0-9799269-0-7
List Price: US$69.95
Member Price: US$55.96
Order Code: XYZ/13
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The authors provide a combination of enthusiasm and experience, which will delight any reader. In this volume, they present innumerable beautiful results, intriguing problems, and ingenious solutions. The problems range from elementary gems to deep truths. A truly delightful and highly instructive book, this will prepare the engaged reader not only for any mathematics competition they may enter but also for a lifetime of mathematical enjoyment. This book is a must for the bookshelves of both aspiring and seasoned mathematicians.

A publication of XYZ Press. Distributed in North America by the American Mathematical Society.

Readership

High school students interested in mathematics competition preparation, as well as seasoned mathematicians.

Reviews

"This is an exceptionally well-written book. The material is arranged in small chapters, with brief theory in the beginning of each chapter followed by a set of exceptionally difficult problems with solutions. These solutions are elegant, innovative and beautiful. You learn a lot from the solutions. In every page, you will discover one or more clever steps/tricks that will make you wonder "How come I could not think of that?" If you are preparing for Mathematics Olympiads, working through this book will boost your confidence 100 fold. If you are a math enthusiast, you will enjoy the material - most of it is "Mathematical poetry." Grab it before it gets sold out!"

-- Dr. S. Muralidharan

Table of Contents

  • Some useful substitutions
  • Always Cauchy-Schwarz ...
  • Look at the exponent
  • Primes and squares
  • T2's lemma
  • Some classical problems in extremal graph theory
  • Complex combinatorics
  • Formal series revisited
  • A brief introduction to algebraic number theory
  • Arithmetic properties of polynomials
  • Lagrange interpolation formula
  • Higher algebra in combinatorics
  • Geometry and numbers
  • The smaller, the better
  • Density and regular distribution
  • The digit sum of a positive integer
  • At the border of analysis and number theory
  • Quadratic reciprocity
  • Solving elementary inequalities using integrals
  • Pigeonhole principle revisited
  • Some useful irreducibility criteria
  • Cycles, paths, and other ways
  • Some special applications of polynomials
  • Bibliography
  • Index
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