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A major aspect of mathematical training and its benefit to society is the ability to use logic to solve problems. The American Mathematics Competitions have been given for more than fifty years to millions of students. This book considers the basic ideas behind the solutions to the majority of these problems, and presents examples and exercises from past exams to illustrate the concepts. Anyone preparing for the Mathematical Olympiads will find many useful ideas here, but people generally interested in logical problem solving should also find the problems and their solutions stimulating. The book can be used either for self-study or as topic-oriented material and samples of problems for practice exams. Useful reading for anyone who enjoys solving mathematical problems, and equally valuable for educators or parents who have children with mathematical interest and ability.
The New Mexico Mathematics Contest for high-school students has been held annually since 1966. Each November, thousands of middle- and high-school students from all over New Mexico converge to battle with elementary but tricky math problems. The 200 highest-scoring students meet for the second round the following February at the University of New Mexico in Albuquerque where they listen to a prominent mathematician give a keynote lecture, have lunch, and then get down to round two, an even more challenging set of mathematical mind-twisters. Liong-shin Hahn was charged with the task of creating a new set of problems each year for the New Mexico Mathematics Contest, 1990-1999. In this volume, Hahn has collected the 138 best problems to appear in these contests over the last decades. They range from the simple to the highly challenging--none are trivial. The solutions contain many clever analyses and often display uncommon ingenuity. His questions are always interesting and relevant to teenage contestants. Young people training for competitions will not only learn a great deal of useful mathematics from this book but, and this is much more important, they will take a step toward learning to love mathematics.
A compilation of 325 problems and solutions for high school students. A valuable resource for any mathematics teacher.
The Contest Problem Book VI contains 180 challenging problems from the six years of the American High School Mathematics Examinations (AHSME), 1989 through 1994, as well as a selection of other problems. A Problems Index classifies the 180 problems in the book into subject areas: algebra, complex numbers, discrete mathematics, number theory, statistics, and trigonometry.
This third volume of problems from the William Lowell Putnam Competition is unlike the previous two in that it places the problems in the context of important mathematical themes. The authors highlight connections to other problems, to the curriculum and to more advanced topics. The best problems contain kernels of sophisticated ideas related to important current research, and yet the problems are accessible to undergraduates. The solutions have been compiled from the American Mathematical Monthly, Mathematics Magazine and past competitors. Multiple solutions enhance the understanding of the audience, explaining techniques that have relevance to more than the problem at hand. In addition, the book contains suggestions for further reading, a hint to each problem, separate from the full solution and background information about the competition. The book will appeal to students, teachers, professors and indeed anyone interested in problem solving as a gateway to a deep understanding of mathematics.
The Putnam Competition has since 1928 been providing a challenge to gifted college mathematics students. This book, the second of the Putnam Competition volumes, contains problems with their solutions for the years 1965-1984. Additional solutions are presented for many of the problems. Included is an essay on recollections of the first Putnam Exam by Herbert Robbins, as well as appendices listing the winning teams and students from 1965 through 1984. This volume offers the problem solver an enticing sample of challenging problems and their solutions. In 1980, the MAA published the first William Lowell Putnam Mathematical Competition book, covering the contest from 1938 to 1964. In 2002 the third of the Putnam problem books appeared, covering the years 1985 through 2000. All three of these books belong on the bookshelf of students, teachers, and all interested in problem solving.
" ... offer[s] a challenging exploration of problem solving mathematics and preparation for programs such as MATHCOUNTS and the American Mathematics Competition."--Back cover