101 Problems in Algebra - MATHEMATICAL OLYMPIADS

101 PROBLEMS IN ALGEBRA

FROM THE TRAINING OF THE USA IMO TEAM

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AMT PUBLISHING

101 PROBLEMS IN ALGEBRA

FROM THE TRAINING OF THE USA 1MO TEAM

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Published by

AMT PUBLISHING

Australian Mathematics Trust

University of Canberra ACT 2601

AUSTRALIA

Copyright ?2001 AMT Publishing

Telephone: +61 2 6201 5137

AMTT Limited ACN 083 950 341

National Library of Australia Card Number and ISSN

Australian Mathematics Trust Enrichment Series ISSN 1326-0170

101 Problems in Algebra ISBN 1 876420 12 X

THE AUSTRALIAN MATHEMATICS TRUST

ENRICHMENT S E R I E S

EDITORIAL COMMITTEE

Chairman

Editor

GRAHAM H POLLARD, Canberra AUSTRALIA

PETER J TAYLOR, Canberra AUSTRALIA

WARREN J ATKINS, Canberra AUSTRALIA

ED J BARBEAU, Toronto CANADA

GEORGE BERZSENYI, Terra Haute USA

RON DUNKLEY, Waterloo CANADA

WALTER E MIENTKA, Lincoln USA

NIKOLAY KONSTANT1NOV, Moscow RUSSIA

ANDY Liu, Edmonton CANADA

JORDAN B TABOV, Sofia BULGARIA

JOHN WEBB, Cape Town SOUTH AFRICA

The books in this series are selected for their motivating, interesting

and stimulating sets of quality problems, with a lucid expository style

in their solutions. Typically, the problems have occurred in either

national or international contests at the secondary school level.

They are intended to be sufficiently detailed at an elementary level

for the mathematically inclined or interested to understand but, at

the same time, be interesting and sometimes challenging to the

undergraduate and the more advanced mathematician. It is believed

that these mathematics competition problems are a positive

influence on the learning and enrichment of mathematics.

THE AUSTRALIAN MATHEMATICS TRUST

ENRICHMENT

SERIES

BooKs IN THE SERIES

1

AUSTRALIAN MATHEMATICS COMPETITION BOOK 1 1978-1984

JD Edwards, DJ King Et PJ O'Halloran

2

MATHEMATICAL TOOLCHEST

AW Plank Et NH Williams

3

TOURNAMENT OF TOWNS QUESTIONS AND SOLUTIONS 1984-1989

PJ Taylor

4

AUSTRALIAN MATHEMATICS COMPETITION BOOK 2 1985-1991

PJ O'Halloran, G Pollard Et PJ Taylor

5

PROBLEM SOLVING VIA THE AMC

W Atkins

6

TOURNAMENT OF TOWNS QUESTIONS AND SOLUTIONS 1980-1984

PJ Taylor

7

TOURNAMENT OF TOWNS QUESTIONS AND SOLUTIONS 1989-1993

PJ Taylor

18

ASIAN PACIFIC MATHEMATICS OLYMPIADS 1989-2000

H Lausch Et C Bosch Giral

9

METHODS OF PROBLEM SOLVING BOOK 1

JB Tabov Ft PJ Taylor

10 CHALLENGE! 1991-1995

JB Henry, J Dowsey, AR Edwards, U Mottershead,

A Nakos Et G Vardaro

ii

1 12

USSR MATHEMATICAL OLYMPIADS 1989-1992

AM Slinko

AUSTRALIAN MATHEMATICAL OLYMPIADS 1979-1995

H Lausch Et PJ Taylor

13

CHINESE MATHEMATICS COMPETITIONS AND OLYMPIADS 1981-1993

A Liu

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