Leningrad Mathematics Olympiads 1987-1991

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

Leningrad Mathematics Olympiads 1987-1991

Authors

Dmitry Fomin and Alexey Kirichenko

Math Pro Press

P.O. Box 713

Westford, MA 01886-0021

1994; 197 pages

Paperback

Reviewer

Medhat H. Rahim

Lakehead University

Thunder Bay, Ontario, Canada

P7B SEl

The 197-page text, Leningrad Mathematics Olympiads 1987-1991, provides the problems and solutions of the five Leningrad Mathematics Olympiads competitions from 1987 through 1991. In addition, a short glossary of special terms, statistics for the number of contestants, the number of problems solved by contestants, and an index for the authors of the proposed problems are provided at the end of the text.

To fully appreciate this Leningrad Mathematics Olympiad text, one must examine it in view of its background and content.

Background

Since the 1930s, mathematicians at all levels of their profession, including highly and internationally recognized scholars in the field such as Kolmogorov (the father of the probability theory), established close connections between education and research, between university and high school, and between professor and teacher. They found the time and energy to write articles, give talks, and work with young children and adults at elementary and high school levels. But first, what is the Leningrad Mathematics Olympiad? And how is it organized?

The Leningrad Mathematics Olympiad, founded in 1934, is one of the most distinct events in the world of mathematics competitions. In particular, the Leningrad Mathematics Olympiad is a unique phenomenon in the mathematical world for two reasons: (a) nearly all of the problems proposed over the past 60 years were new and original, and (b) it is the only official competition in Russia (former Soviet Union), and perhaps the whole world, in which the final rounds of competition are held orally, that is, through a series of conversations between the competitors and jury members.

At the beginning and for the first several years, the Leningrad Olympiad was open only to students from the senior (tenth) grade. Then between 1938 and 1940, lower grades were included. The main objective was to encourage students to work for excellence in mathematics. The Leningrad Mathematics Olympiad event has a decisive impact on the Soviet Union as a whole, and, consequently, mathematics olympiads were organized throughout the country. As a result, by the 1960s mathematics and mathematics education in the Soviet Union had reached a high standard. In 1961 and 1967, the All-Russia Mathematical Olympiad and All-Union Mathematical Olympiad were created, respectively, and the building of the olympiad system throughout the country was completed. The system attracted many students to mathematics and many prominent mathematicians to contribute to the preparation and implementation of competitions.

In the 1980s, while the aura of mathematical competition was picking up strength everywhere in the Soviet Union, Leningrad teams prevailed both on the national and international levels. The Leningrad Mathematics Olympiad consists of four rounds: (a) School Round, for the top six grades (held in December and January); (b) Regional Round, for the winners of the previous round-competitors from 22 regions of the Leningrad city may participate (held in February); (c) All-City Round, also known as the Main Round, for the finalists of the previous round (held in February and March), an oral round lasting 3.5-4 hours; and (d) Final Round, an oral elimination round (held in March) lasting 5 hours.

Content

The Leningrad Mathematics Olympiad text covers only the proposed problems and their solutions for the Main Round and the Final Round of the competitions. The text is divided into three main sections: (a) Competition Problems for Grades 5-10; (b) Solutions for all problems; and (c) Appendixes for additional information covering first-prize winners for the years 1987-1991, statistics in the form of frequencies of the number of each problem solved in each grade and the total number of participants, a glossary containing explanations of technical terms and forms used in the text, and a list of the authors of the problems posed for the competitions.

While reading the text and trying many of the problems, I realized that the quality and challenge of the numerous proposed problems made this text an excellent resource for brainstorming. Students in preservice mathematics courses, as well as those in formal mathematics classes, will certainly enjoy the beauty, power, and challenge of the problem-solving exercises embedded in these competitions. The feeling of joy and happiness that overwhelmed me while reading this text is inexpressible in a few sentences. I decided to use many of the text's problems in my mathematics classes for the preservice junior/intermediate and intermediate/senior levels as part of my problem-solving activity-a focus among priorities outlined in the 1989 NCTM Standards. Mathematicians, mathematics educators, and teachers in middle and high schools who wish to enrich their students through problem-solving environments in algebra, mathematical analysis, combinatorics, geometry, number theory, recreational mathematics, and solid geometry will be interested in this resource text of thought-provoking problems.