ARML-NYSML Contests 1989-1994 (Mathematics Competitions for High School Students)

School Science and Mathematics, Jan 1998 by Rahim, Medhat H

The American Regions Mathematics League of the United States of America was initiated in 1976. Within the last two decades, it has grown rather rapidly, passing through a transition from about 12 teams at the beginning to a nationwide competition of more than 100 teams from the United States and Canada at the present time.

The 189-page text, American Regions Mathematics League (ARML)-New York State Mathematics League (NYSML) Contests 1989-1994 (Mathematics Competitions for High School Students), provides the proposed problems and their solutions for the competition years 1989 to 1994 of the ARML and 1989 to 1992 of the NYSML. In addition, it contains tiebreaker problems (used to break ties among the individual top scores) and their solutions and an answer key for all problems. Appendixes containing statistics for the team and individual winners for both the ARML and NYSML, and a glossary for forms and symbols used, are also provided.

The text is well organized in a user-friendly format. It is clearly written, with a spice of challenges; I very much enjoyed reading the text and trying many of the problems. The solutions provided are chosen for their instructional value rather than for simply being the shortest ones. The inclusion of the relay questions adds a touch of fun and gaming to the competitions. High school mathematics teachers, mathematics educators, and mathematicians alike will find this text to be an excellent resource for providing problem-solving activities in their classes.

The text comprises five parts: ARML Problems 1989-1994; NYS ML Problems 1989-1992, Tiebreakers Problems for ARML and NYSML competitions from 1983 through 1994, Solutions for the ARML and NYSML problems, and Answer Key for all of the problems. In contrast to the Leningrad Mathematics Olympiads, which are open to students in Grades 10 and below, the ARML and NYSML are open to high school students.

For both the ARML and NYSML, the problems fall into four categories: Power Questions, Team Questions, Individual Questions, and Relay Questions. The power problems are quite challenging and form a focus on a single mathematical theme such as Pythagorean polygons, Diophantine equations, and sums of consecutive integers. In fact, the authors of the text have received much feedback stating that some of the power problems have served as the basis of classroom enrichment, research papers, and Westinghouse Science Talent Search projects.

The ARML and NYSML competitions are among the most exciting and thought-provoking mathematical events in the world at the high school level. The problems in this text provide interesting as well as significant mathematical ideas for the new generation to experience, enjoy, and employ in the process of building their mathematical knowledge. It is rare indeed, anywhere in the world, to find such selflessly devoted people who give generously of their time and energy to increase mathematical knowledge and to provide for the future. The value of these mathematical competitions is not only in promoting mathematics and discovering new eminent mathematicians but also in promoting interest in the advancement of knowledge in mathematics.

Editor's Note: S. Wali Abdi's postal address is The University of Memphis, Department of Instruction and Curriculum Leadership, 401 A Ball Hall, Memphis, TN 38152,and e-mail address is abdi.wali@coe.memphis.edu.

Authors

Lawrence Zimmerman and Gilbert Kessler

Math Pro Press

P.O. Box 713

Westford, MA 01886-0021

1995; 189 pages Paperback

Reviewer

Medhat H. Rahim

Lakehead University

Thunder Bay, Ontario, Canada P7B SE1