Junior Balkan mathematical olympiads

Michael Doob; Claude Laflamme; Société Mathématique Du Canada

Title......Page 1 Date-line......Page 2 Contents ......Page 3 Preface ......Page 5 Preface ......Page 9 Canadian Mathematical Olympiad Winners / Gagnants de l'Olympiade mathematique du Canada ......Page 13 Canadian Mathematical Olympiad Committee Chairs and Members / Presidents et membres du Comite de l'Olympiade mathematique du Canada ......Page 16 1969 (English) ......Page 19 1969 (francais) ......Page 25 1970 (English) ......Page 31 1970 (francais) ......Page 37 1971 (English) ......Page 43 1971 (francais) ......Page 49 1972 (English) ......Page 55 1972 (francais) ......Page 61 1973 (English) ......Page 67 1973 (francais) ......Page 71 1974 (English) ......Page 77 1974 (francais) ......Page 85 1975 (English) ......Page 93 1975 (francais) ......Page 101 1976 (English) ......Page 109 1976 (francais) ......Page 113 1977 (English) ......Page 119 1977 (francais) ......Page 125 1978 (English) ......Page 131 1978 (francais) ......Page 139 1979 (English) ......Page 147 1979 (francais) ......Page 151 1980 (English) ......Page 155 1980 (francais) ......Page 159 1981 (English) ......Page 163 1981 (francais) ......Page 165 1982 (English) ......Page 167 1982 (francais) ......Page 171 1983 (English) ......Page 175 1983 (francais) ......Page 177 1984 (English) ......Page 179 1984 (francais) ......Page 183 1985 (English) ......Page 187 1985 (francais) ......Page 191 1986 (English) ......Page 195 1986 (francais) ......Page 199 1987 (English) ......Page 203 1987 (francais)... Leer más…

Compiled And With Solutions By Samuel L. Greitzer

The International Olympiad has been held annually since 1959; the U.S. began participating in 1974, when the Sixteenth International Olympiad was held in Erfurt, G.D.R. In 1974 and 1975, the National Science Foundation funded a three week summer training session with Samuel L. Greitzer of Rutgers University and Murray Klamkin of the University of Alberta as the U.S. teams' coaches. Summer training sessions in 1976, 1977 were funded by grants from the Army Research Office and Office of Naval Research. To date the U.S. teams have consistently placed among the top three national scores: second in 1974(the USSR was first), third in 1975 (behind Hungary and the G.D.R) and 1976 (behind the USSR and Great Britain) and first in 1977. Members of U.S. team are selected from the 100 top scorers on the Annual High School Examinations (see NML vols. 5, 17, 25) by subsequent competition in the U.S. Mathematical Olympiad. In this volume the demonstrably effective coach and prime mover in planning the participation of the U.S.A. in the I.M.O., Samuel L. Greitzer, has compiled all the IMO problems from the First through the Nineteenth (1977) IMO and their solutions, some based on the contestants' papers. The problems ae solvable by methods accessible to secondary school students in most nations, but insight and ingenuity are often required. A chronological examination of the questions throws some light on the changes and trends in secondary school mathematics curricula. Leer más…

D. O. Shklarsky, N. N. Chentzov, I. M. Yaglom

Over 300 challenging problems in algebra, arithmetic, elementary number theory and trigonometry, selected from the archives of the Mathematical Olympiads held at Moscow University. Most presuppose only high school mathematics but some are of uncommon difficulty and will challenge any mathematician. Complete solutions to all problems. 27 black-and-white illustrations. 1962 edition. Leer más…

A M Yaglom; Basil Gordon; I M Yaglom

Over 170 challenging problems ranging from the relatively simple to the extremely difficult. Volume 1 contains 100 problems on probability theory and combinatorial analysis. Leer más…

Edited By Titu Andreescu And Zuming Feng

This volume contains a large range of problems, with and without solutions, taken from 25 national and regional mathematics olympiads from around the world, and the problems are drawn from several years' contests. In many cases, more than one solution is given to a single problem in order to highlight different problem-solving strategies. The collection is intended as practice for students preparing for these competitions. Teachers and general readers looking for interesting problems will find also it very useful. Leer más…

Titu Andreescu; Zuming Feng; Mathematical Association Of America

Contained here are solutions to challenging problems from algebra, geometry, combinatorics and number theory featured in the earlier book, together with selected questions (without solutions) from national and regional Olympiads given during the year 2000. Intended for the serious student/problem solver, these books can help to improve performance in the Mathematical Olympiad competition. However, for those not entering the competition, there is much to challenge any mathematician, even those with advanced degrees. Different nations have different mathematical cultures, so you will find that some of the questions are extremely difficult and some rather easy. There are a wide variety of problems especially from those countries that have often done well in the IMO. Anyone interested in mathematical problem solving will encounter some beautiful mathematics in the pages of this book. If you are up to a real challenge, take some of these problems on! Leer más…

Titu Andreescu, Zuming Feng, George Lee Jr, Po-Ru Loh

This volume is a continuation of Mathematical Olympiads 1999-2000: Problems and Solutions From Around the World, republishing hundreds of mathematics problems and solutions from that book as well as selected problems (without solutions) from national and regional contests in 2001. The collection provides practice material for serious high-school level mathematicians who wish to prepare for the USA Math Olympiad (USAMO) and Team Selection Test (TST). The newly added 2001 problems were contributed by dozens of countries including Korea, Belarus, China, Poland, and Romania Leer más…

Kuczma Marcin E., Windischbacher Erich, Australian Mathematics Trust

This is a rich collection of problems from the national Olympiads of Austria and Poland, which both have exceptionally strong traditions. The particular interest in the problems selected is that all have at least two independent solutions, highlighting one of the beauties of mathematics. Leer más…

Compiled By G. Hájos, G. Neukomm, And J. Surányi Translated And Edited By Andy Liu

This book contains the problems and solutions of a famous Hungarian mathematics competition for high school students, from 1929 to 1943. The competition is the oldest in the world, and started in 1894. Two earlier volumes in this series contain the papers up to 1928, and further volumes are planned. The current edition adds a lot of background material which is helpful for solving the problems therein and beyond. Multiple solutions to each problem are exhibited, often with discussions of necessary background material or further remarks. This feature will increase the appeal of the book to experienced mathematicians as well as the beginners for whom it is primarily intended. Leer más…

Tutorials in Algebra, Number Theory, Combinatorics and Geometry Leer más…

Titu Andreescu; Zuming Feng; Mathematical Association Of America

The Mathematical Olympiad examinations, covering the USA Mathematical Olympiad (USAMO) and the International Mathematical Olympiad (IMO), have been published annually since 1976 by the MAA American Mathematics Competitions. This is the fourth volume in that series published by the MAA in its Problem Book series. The IMO is a world mathematics competition for high school students that takes place each year in a different country. Students from all over the world participate in this competition. The USAMO and the Team Selection Test are the last two stages of the process that lead to the selection of the team representing the USA in the IMO. Problems and solutions from both of these competitions for the year 2003 are included in this volume. These Olympiad style exams consist of several challenging essay-type problems. Although a correct and complete solution to an Olympiad problem often requires deep analysis and careful argument, the problems require no more than a solid background in high school mathematics coupled with a dose of mathematical ingenuity. There are helpful hints provided for each of the problems. These hints often help lead the student to a solution of the problem. Complete solutions to each of the problems is also included, and many of the problems are presented together with a collection of remarkable solutions developed by the examination committees, contestants and experts, during or after the contest. For each problem with... Leer más…

Arkadii M. Slinko

Arkadii Slinko, now at the University of Auckland, was one of the leading figures of the USSR Mathematical Olympiad Committee during the last years before democratisation. This book brings together the problems and solutions of the last four years of the All-Union Mathematics Olympiads. Not only are the problems and solutions highly expository but the book is worth reading alone for the fascinating history of mathematics competitions to be found in the introduction. Leer más…

Compiled And With Solutions By Murray S. Klamkin

People delight in working on problems "because they are there," for the sheer pleasure of meeting a challenge. This is a book full of such delights. In it, Murray S. Klamkin brings together 75 original USA Mathematical Olympiad (USAMO) problems for yearss 1972-1986, with many improvements, extensions, related exercises, open problems, referneces and solutions, often showing alternative approaches. The problems are coded by subject, and solutions are arranged by subject, e.g., algebra, number theory, solid geometry, etc., as an aid to those interested in a particular field. Included is a Glossary of frequently used terms and theorems and a comprehensive bibliography with items numbered and referred to in brackets in the text. This a collection of problemsand solutions of arresting ingenuit, all accessible to secondary school students. The USAMO has been taken annually by about 150 of the nation's best high school mathematics students. This exam helps to find and encourage high school students with superior mathematical talent and creativity and is the culmination of a three-tiered competition that begins with the American High School Mathematics Examination (AHSME) taken by over 400, 000 students. The eight winners of the USAMO are canidates for the US team in the International Mathematical Olympiad. Schools are encouraged to join this large and important enterprise. See page x of the preface for further information. this book includes a list of all of the top... Leer más…

Xu, Jiagu

Olympiad mathematics is not a collection of techniques of solving mathematical problems but a system for advancing mathematical education. This book is based on the lecture notes of the mathematical Olympiad training courses conducted by the author in Singapore. Its scope and depth not only covers and exceeds the usual syllabus, but introduces a variety concepts and methods in modern mathematics. In each lecture, the concepts, theories and methods are taken as the core. The examples are served to explain and enrich their intension and to indicate their applications. Besides, appropriate number of test questions is available for reader's practice and testing purpose. Their detailed solutions are also conveniently provided. The examples are not very complicated so that readers can easily understand. There are many real competition questions included which students can use to verify their abilities. These test questions are from many countries, e.g. China, Russia, USA, Singapore, etc. In particular, the reader can find many questions from China, if he is interested in understanding mathematical Olympiad in China. This book serves as a useful textbook of mathematical Olympiad courses, or as a reference book for related teachers and researchers. Operations on Rational Numbers Linear Equations of Single Variable Multiplication Formulae Absolute Value and Its Applications Congruence of Triangles Similarity of Triangles Divisions of... Leer más…

Andy Liu

This book is a continuation of the earlier volume (1981-1993) and covers the years 1993 to 2001.China has an outstanding record in the International Mathematical Olympiad, and the book contains the problems which were used to identify the team candidates and select the Chinese teams. The problems are meticulously constructed, many with distinctive flavour. They come in all levels of difficulty, from the relatively basic to the most challenging. Leer más…

Xu, Jiagu

Olympiad mathematics is not a collection of techniques of solving mathematical problems but a system for advancing mathematical education. This book is based on the lecture notes of the mathematical Olympiad training courses conducted by the author in Singapore. Its scope and depth not only covers and exceeds the usual syllabus, but introduces a variety concepts and methods in modern mathematics. In each lecture, the concepts, theories and methods are taken as the core. The examples are served to explain and enrich their intension and to indicate their applications. Besides, appropriate number of test questions is available for reader's practice and testing purpose. Their detailed solutions are also conveniently provided. The examples are not very complicated so that readers can easily understand. There are many real competition questions included which students can use to verify their abilities. These test questions are from many countries, e.g. China, Russia, USA, Singapore, etc. In particular, the reader can find many questions from China, if he is interested in understanding mathematical Olympiad in China. This book serves as a useful textbook of mathematical Olympiad courses, or as a reference book for related teachers and researchers. Congruence of Integers Decimal Representation of Integers Pigeonhole Principle Linear Inequality and System of Linear Inequalities Inequalities with Absolute Values Geometric Inequalities ... Leer más…