Lecture Notes on Mathematical Olympiad Courses

Lecture Notes on Mathematical Olympiad Courses
Author :
Publisher : World Scientific
Total Pages : 183
Release :
ISBN-10 : 9789814293563
ISBN-13 : 9814293563
Rating : 4/5 (63 Downloads)

Synopsis Lecture Notes on Mathematical Olympiad Courses by : Jiagu Xu

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 1: Operations on Rational Numbers (145k). Request Inspection Copy. Contents: .: Operations on Rational Numbers; Linear Equations of Single Variable; Multiplication Formulae; Absolute Value and Its Applications; Congruence of Triangles; Similarity of Triangles; Divisions of Polynomials; Solutions to Testing Questions; and other chapters. Readership: Mathematics students, school teachers, college lecturers, university professors; mathematics enthusiasts

A First Step To Mathematical Olympiad Problems

A First Step To Mathematical Olympiad Problems
Author :
Publisher : World Scientific Publishing Company
Total Pages : 292
Release :
ISBN-10 : 9789814365253
ISBN-13 : 9814365254
Rating : 4/5 (53 Downloads)

Synopsis A First Step To Mathematical Olympiad Problems by : Derek Allan Holton

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.

Problems of Number Theory in Mathematical Competitions

Problems of Number Theory in Mathematical Competitions
Author :
Publisher : World Scientific
Total Pages : 115
Release :
ISBN-10 : 9789814271141
ISBN-13 : 9814271144
Rating : 4/5 (41 Downloads)

Synopsis Problems of Number Theory in Mathematical Competitions by : Hong-Bing Yu

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.

Lecture Notes On Mathematical Olympiad Courses: For Senior Section - Volume 1

Lecture Notes On Mathematical Olympiad Courses: For Senior Section - Volume 1
Author :
Publisher : World Scientific Publishing Company
Total Pages : 261
Release :
ISBN-10 : 9789813100596
ISBN-13 : 9813100591
Rating : 4/5 (96 Downloads)

Synopsis Lecture Notes On Mathematical Olympiad Courses: For Senior Section - Volume 1 by : Jiagu Xu

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 beyond the usual syllabus, but introduces a variety of concepts and methods in modern mathematics as well.In each lecture, the concepts, theories and methods are taken as the core. The examples serve to explain and enrich their intentions and to indicate their applications. Besides, appropriate number of test questions is available for the readers' practice and testing purpose. Their detailed solutions are also conveniently provided.The examples are not very complicated so readers can easily understand. There are many real competition questions included which students can use to verify their abilities. These test questions originate from many countries all over the world. This book will serve as a useful textbook of mathematical Olympiad courses, a self-study lecture notes for students, or as a reference book for related teachers and researchers.

Lecture Notes On Mathematical Olympiad Courses: For Senior Section - Volume 2

Lecture Notes On Mathematical Olympiad Courses: For Senior Section - Volume 2
Author :
Publisher : World Scientific Publishing Company
Total Pages : 297
Release :
ISBN-10 : 9789813100589
ISBN-13 : 9813100583
Rating : 4/5 (89 Downloads)

Synopsis Lecture Notes On Mathematical Olympiad Courses: For Senior Section - Volume 2 by : Jiagu Xu

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 beyond the usual syllabus, but introduces a variety of concepts and methods in modern mathematics as well.In each lecture, the concepts, theories and methods are taken as the core. The examples serve to explain and enrich their intentions and to indicate their applications. Besides, appropriate number of test questions is available for the readers' practice and testing purpose. Their detailed solutions are also conveniently provided.The examples are not very complicated so readers can easily understand. There are many real competition questions included which students can use to verify their abilities. These test questions originate from many countries all over the world. This book will serve as a useful textbook of mathematical Olympiad courses, a self-study lecture notes for students, or as a reference book for related teachers and researchers.

Mathematical Olympiad in China (2007-2008)

Mathematical Olympiad in China (2007-2008)
Author :
Publisher : World Scientific
Total Pages : 221
Release :
ISBN-10 : 9789814261142
ISBN-13 : 9814261149
Rating : 4/5 (42 Downloads)

Synopsis Mathematical Olympiad in China (2007-2008) by : Bin Xiong

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 comprises a collection of original problems with solutions that China used to train their Olympiad team in the years from 2006 to 2008. Mathematical Olympiad problems with solutions for the years 2002?2006 appear in an earlier volume, Mathematical Olympiad in China.

Euclidean Geometry in Mathematical Olympiads

Euclidean Geometry in Mathematical Olympiads
Author :
Publisher : American Mathematical Soc.
Total Pages : 311
Release :
ISBN-10 : 9781470466206
ISBN-13 : 1470466201
Rating : 4/5 (06 Downloads)

Synopsis Euclidean Geometry in Mathematical Olympiads by : Evan Chen

This is a challenging problem-solving book in Euclidean geometry, assuming nothing of the reader other than a good deal of courage. Topics covered included cyclic quadrilaterals, power of a point, homothety, triangle centers; along the way the reader will meet such classical gems as the nine-point circle, the Simson line, the symmedian and the mixtilinear incircle, as well as the theorems of Euler, Ceva, Menelaus, and Pascal. Another part is dedicated to the use of complex numbers and barycentric coordinates, granting the reader both a traditional and computational viewpoint of the material. The final part consists of some more advanced topics, such as inversion in the plane, the cross ratio and projective transformations, and the theory of the complete quadrilateral. The exposition is friendly and relaxed, and accompanied by over 300 beautifully drawn figures. The emphasis of this book is placed squarely on the problems. Each chapter contains carefully chosen worked examples, which explain not only the solutions to the problems but also describe in close detail how one would invent the solution to begin with. The text contains a selection of 300 practice problems of varying difficulty from contests around the world, with extensive hints and selected solutions. This book is especially suitable for students preparing for national or international mathematical olympiads or for teachers looking for a text for an honor class.

Geometric Inequalities: In Mathematical Olympiad And Competitions

Geometric Inequalities: In Mathematical Olympiad And Competitions
Author :
Publisher : World Scientific Publishing Company
Total Pages : 145
Release :
ISBN-10 : 9789814696500
ISBN-13 : 9814696501
Rating : 4/5 (00 Downloads)

Synopsis Geometric Inequalities: In Mathematical Olympiad And Competitions by : Gangsong Leng

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.

Inequalities

Inequalities
Author :
Publisher : Springer Science & Business Media
Total Pages : 214
Release :
ISBN-10 : 9783034600507
ISBN-13 : 303460050X
Rating : 4/5 (07 Downloads)

Synopsis Inequalities by : Radmila Bulajich Manfrino

This book is intended for the Mathematical Olympiad students who wish to prepare for the study of inequalities, a topic now of frequent use at various levels of mathematical competitions. In this volume we present both classic inequalities and the more useful inequalities for confronting and solving optimization problems. An important part of this book deals with geometric inequalities and this fact makes a big difference with respect to most of the books that deal with this topic in the mathematical olympiad. The book has been organized in four chapters which have each of them a different character. Chapter 1 is dedicated to present basic inequalities. Most of them are numerical inequalities generally lacking any geometric meaning. However, where it is possible to provide a geometric interpretation, we include it as we go along. We emphasize the importance of some of these inequalities, such as the inequality between the arithmetic mean and the geometric mean, the Cauchy-Schwarz inequality, the rearrangementinequality, the Jensen inequality, the Muirhead theorem, among others. For all these, besides giving the proof, we present several examples that show how to use them in mathematical olympiad problems. We also emphasize how the substitution strategy is used to deduce several inequalities.

A Second Step to Mathematical Olympiad Problems

A Second Step to Mathematical Olympiad Problems
Author :
Publisher : World Scientific
Total Pages : 312
Release :
ISBN-10 : 9789814327879
ISBN-13 : 9814327875
Rating : 4/5 (79 Downloads)

Synopsis A Second Step to Mathematical Olympiad Problems by : Derek Allan Holton

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.