XYZ Series 2010; 571 pp; hardcover Volume: 13 ISBN10: 0979926904 ISBN13: 9780979926907 List Price: US$69.95 Member Price: US$55.96 Order Code: XYZ/13
 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 wellwritten 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 CauchySchwarz ...
 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
