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Probability and Expectation

Probability and Expectation Author Zun Shan
ISBN-10 9789813141513
Release 2016-07-14
Pages 208
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In China, lots of excellent students who are good at maths take an active part in various maths contests and the best six senior high school students will be selected to form the IMO National Team to compete in the International Mathematical Olympiad. In the past ten years China's IMO Team has achieved outstanding results — they have won the first place almost every year. The author is one of the senior coaches of China's IMO National Team, whose students have won many gold medals many times in IMO. This book is part of the Mathematical Olympiad Series which discusses several aspects related to maths contests, such as algebra, number theory, combinatorics, graph theory and geometry. This book will, in an interesting problem-solving way, explain what probability theory is: its concepts, methods and meanings; particularly, two important concepts — probability and mathematical expectation (briefly expectation) — are emphasized. It consists of 65 problems, appended by 107 exercises and their answers.



Solving Problems in Geometry

Solving Problems in Geometry Author Kim Hoo Hang
ISBN-10 9789814583763
Release 2017-05-19
Pages 356
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This new volume of the Mathematical Olympiad Series focuses on the topic of geometry. Basic and advanced theorems commonly seen in Mathematical Olympiad are introduced and illustrated with plenty of examples. Special techniques in solving various types of geometrical problems are also introduced, while the authors elaborate extensively on how to acquire an insight and develop strategies in tackling difficult geometrical problems. This book is suitable for any reader with elementary geometrical knowledge at the lower secondary level. Each chapter includes sufficient scaffolding and is comprehensive enough for the purpose of self-study. Readers who complete the chapters on the basic theorems and techniques would acquire a good foundation in geometry and may attempt to solve many geometrical problems in various mathematical competitions. Meanwhile, experienced contestants in Mathematical Olympiad competitions will find a large collection of problems pitched at competitions at the international level, with opportunities to practise and sharpen their problem-solving skills in geometry. Request Inspection Copy



Combinatorial Problems in Mathematical Competitions

Combinatorial Problems in Mathematical Competitions Author Yao Zhang
ISBN-10 9789812839497
Release 2011
Pages 289
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Annotation. This text provides basic knowledge on how to solve combinatorial problems in mathematical competitions, and also introduces important solutions to combinatorial problems and some typical problems with often-used solutions.



Lecture Notes on Mathematical Olympiad Courses

Lecture Notes on Mathematical Olympiad Courses Author Jiagu Xu
ISBN-10 9789814293570
Release 2010
Pages 376
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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. Errata(s). Errata. Sample Chapter(s). Lecture 16: Quadratic Surd Expressions and Their Operations (183k). Request Inspection Copy. Contents.: Volume 2: Congruence of Integers; Decimal Representation of Integers; Pigeonhole Principle; Linear Inequality and System of Linear Inequalities; Inequalities with Absolute Values; Geometric Inequalities; Solutions to Testing Questions; and other chapters. Readership: Mathematics students, school teachers, college lecturers, university professors; mathematics enthusiasts.



Selected Problems of the Vietnamese Mathematical Olympiad 1962 2009

Selected Problems of the Vietnamese Mathematical Olympiad  1962 2009 Author Hai Chau Le
ISBN-10 9789814289597
Release 2010
Pages 308
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Vietnam has actively organized the National Competition in Mathematics and since 1962, the Vietnamese Mathematical Olympiad (VMO). On the global stage, Vietnam has also competed in the International Mathematical Olympiad (IMO) since 1974 and constantly emerged as one of the top ten. To inspire and further challenge readers, we have gathered in this book selected problems of the VMO from 1962 to 2008. A number of Selection Test problems are also included to aid in the formation and training of a national team for IMO. The book is highly useful for high school students and teachers, coaches and instructors preparing for mathematical olympiads, as well as non-experts simply interested in having the edge over their opponents in mathematical competitions.



Mathematical Olympiad Treasures

Mathematical Olympiad Treasures Author Titu Andreescu
ISBN-10 0817682538
Release 2011-09-21
Pages 253
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Mathematical Olympiad Treasures aims at building a bridge between ordinary high school exercises and more sophisticated, intricate and abstract concepts in undergraduate mathematics. The book contains a stimulating collection of problems in the subjects of algebra, geometry, trigonometry, number theory and combinatorics. While it may be considered a sequel to "Mathematical Olympiad Challenges," the focus is on engaging a wider audience to apply techniques and strategies to real-world problems. Throughout the book students are encouraged to express their ideas, conjectures, and conclusions in writing. The goal is to help readers develop a host of new mathematical tools that will be useful beyond the classroom and in a number of disciplines.



A First Step to Mathematical Olympiad Problems

A First Step to Mathematical Olympiad Problems Author Derek Holton
ISBN-10 9789814365253
Release 2009-07-30
Pages 292
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See also A SECOND STEP TO MATHEMATICAL OLYMPIAD PROBLEMS The International Mathematical Olympiad (IMO) is an annual international mathematics competition held for pre-collegiate students. It is also the oldest of the international science olympiads, and competition for places is particularly fierce. This book is an amalgamation of the first 8 of 15 booklets originally produced to guide students intending to contend for placement on their country's IMO team. The material contained in this book provides an introduction to the main mathematical topics covered in the IMO, which are: Combinatorics, Geometry and Number Theory. In addition, there is a special emphasis on how to approach unseen questions in Mathematics, and model the writing of proofs. Full answers are given to all questions. Though A First Step to Mathematical Olympiad Problems is written from the perspective of a mathematician, it is written in a way that makes it easily comprehensible to adolescents. This book is also a must-read for coaches and instructors of mathematical competitions.



Methods and Techniques for Proving Inequalities

Methods and Techniques for Proving Inequalities Author Yong Su
ISBN-10 9789814696470
Release 2015-10-06
Pages 228
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In China, lots of excellent maths students take an active interest in various maths contests and the best six senior high school students will be selected to form the IMO National Team to compete in the International Mathematical Olympiad. In the past ten years China's IMO Team has achieved outstanding results — they won the first place almost every year. The authors are coaches of China's IMO National Team, whose students have won many gold medals many times in IMO. This book is part of the Mathematical Olympiad Series which discusses several aspects related to maths contests, such as algebra, number theory, combinatorics, graph theory and geometry. The book explains many basic techniques for proving inequalities such as direct comparison, method of magnifying and reducing, substitution method, construction method, and so on.



Mathematical Olympiad In China 2009 2010 Problems And Solutions

Mathematical Olympiad In China  2009 2010   Problems And Solutions Author Xiong Bin
ISBN-10 9789814397438
Release 2013-02-20
Pages 204
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The International Mathematical Olympiad (IMO) is a competition for high school students. China has taken part in the IMO 21 times since 1985 and has won the top ranking for countries 14 times, with a multitude of golds for individual students. The six students China has sent every year were selected from 20 to 30 students among approximately 130 students who took part in the annual China Mathematical Competition during the winter months. This volume of comprises a collection of original problems with solutions that China used to train their Olympiad team in the years from 2009 to 2010. Mathematical Olympiad problems with solutions for the years 2002-2008 appear in an earlier volume, Mathematical Olympiad in China.



Geometric Inequalities

Geometric Inequalities Author Gangsong Leng
ISBN-10 9789814696500
Release 2015-10-21
Pages 144
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In China, lots of excellent maths students take an active interest in various maths contests and the best six senior high school students will be selected to form the IMO National Team to compete in the International Mathematical Olympiad. In the past ten years China's IMO Team has achieved outstanding results — they won the first place almost every year. The author is one of the coaches of China's IMO National Team, whose students have won many gold medals many times in IMO. This book is part of the Mathematical Olympiad Series which discusses several aspects related to maths contests, such as algebra, number theory, combinatorics, graph theory and geometry. The book elaborates on Geometric Inequality problems such as inequality for the inscribed quadrilateral, the area inequality for special polygons, linear geometric inequalities, etc.



Combinatorial Extremization

Combinatorial Extremization Author Yuefeng Feng
ISBN-10 9789814723183
Release 2016-02-17
Pages 232
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In China, lots of excellent students who are good at maths takes an active part in various maths contests and the best six senior high school students will be selected to form the IMO National Team to compete in the International Mathematical Olympiad. In the past ten years China's IMO Team has achieved outstanding results — they have won the first place almost every year. The author is one of the coaches of China's IMO National Team, whose students have won many gold medals many times in IMO. This book is part of the Mathematical Olympiad Series which discusses several aspects related to maths contests, such as algebra, number theory, combinatorics, graph theory and geometry. The book elaborates on methods of discrete extremization, such as inequality control, repeated extremum, partial adjustment, exploiting symmetry, polishing transform, space estimates, etc.



The Alberta High School Math Competitions 1957 2006

The Alberta High School Math Competitions 1957 2006 Author Chiang-Fung Andrew Liu
ISBN-10 0883858304
Release 2008
Pages 283
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Although there were some older contests in the Maritime region and in Lower and Upper Canada, the Alberta High School Mathematics Competition was the first and oldest in Canada to be run on a provincial scale. Started in 1957, the competition recently celebrated its fiftieth anniversary. These fifty years can be broken down to three periods, Ancient (1957--1966), Medieval (1967--1983) and Modern (1984--2006), with very distinctive flavors which reflect what was taught in the schools of the day. The first two periods are primarily of historical interest. During the Modern period, the talented problem committee was led by the world renown problemist Murray Klamkin, and composed many innovative and challenging problems. In this book you will find all the problems and answers for the first fifty years of the competition, up to 2005/2006 – and full solutions are provided to those from the Modern period, often supplemented with multiple solutions or additional commentaries. Taken together, this unique collection of problems represent an interesting and valuable resource for students today preparing for these types of mathematics contests. The Alberta High School Mathematics Competitions 1957 - 2006 : A Canadian Problem Book is published by the Mathematical Association of America (MAA) in collaboration with the Canadian Mathematical Society (CMS). It is the second volume in The Canadian Collection.



A Second Step to Mathematical Olympiad Problems

A Second Step to Mathematical Olympiad Problems Author Derek Allan Holton
ISBN-10 9789814327879
Release 2011
Pages 299
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The International Mathematical Olympiad (IMO) is an annual international mathematics competition held for pre-collegiate students. It is also the oldest of the international science olympiads, and competition for places is particularly fierce. This book is an amalgamation of the booklets originally produced to guide students intending to contend for placement on their country's IMO team. See also A First Step to Mathematical Olympiad Problems which was published in 2009. The material contained in this book provides an introduction to the main mathematical topics covered in the IMO, which are: Combinatorics, Geometry and Number Theory. In addition, there is a special emphasis on how to approach unseen questions in Mathematics, and model the writing of proofs. Full answers are given to all questions. Though A Second Step to Mathematical Olympiad Problems is written from the perspective of a mathematician, it is written in a way that makes it easily comprehensible to adolescents. This book is also a must-read for coaches and instructors of mathematical competitions.



104 Number Theory Problems

104 Number Theory Problems Author Titu Andreescu
ISBN-10 0817645616
Release 2007-04-05
Pages 204
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This challenging problem book by renowned US Olympiad coaches, mathematics teachers, and researchers develops a multitude of problem-solving skills needed to excel in mathematical contests and in mathematical research in number theory. Offering inspiration and intellectual delight, the problems throughout the book encourage students to express their ideas in writing to explain how they conceive problems, what conjectures they make, and what conclusions they reach. Applying specific techniques and strategies, readers will acquire a solid understanding of the fundamental concepts and ideas of number theory.



Five Hundred Mathematical Challenges

Five Hundred Mathematical Challenges Author Edward J. Barbeau
ISBN-10 0883855194
Release 1995-01-01
Pages 227
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Contains 500 problems ranging over a wide spectrum of mathematics and of levels of difficulty.



Problems of Number Theory in Mathematical Competitions

Problems of Number Theory in Mathematical Competitions Author Hong-Bing Yu
ISBN-10 9789814271141
Release 2010
Pages 106
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Number theory is an important research field of mathematics. In mathematical competitions, problems of elementary number theory occur frequently. These problems use little knowledge and have many variations. They are flexible and diverse. In this book, the author introduces some basic concepts and methods in elementary number theory via problems in mathematical competitions. Readers are encouraged to try to solve the problems by themselves before they read the given solutions of examples. Only in this way can they truly appreciate the tricks of problem-solving.



Mathematical Bridges

Mathematical Bridges Author Titu Andreescu
ISBN-10 9780817646295
Release 2017-02-27
Pages 309
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Building bridges between classical results and contemporary nonstandard problems, this highly relevant work embraces important topics in analysis and algebra from a problem-solving perspective. The book is structured to assist the reader in formulating and proving conjectures, as well as devising solutions to important mathematical problems by making connections between various concepts and ideas from different areas of mathematics. Instructors and motivated mathematics students from high school juniors to college seniors will find the work a useful resource in calculus, linear and abstract algebra, analysis and differential equations. Students with an interest in mathematics competitions must have this book in their personal libraries.