Mathematical Olympiad Series, vol.4.
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.
About Problem Solving
The Pigeonhole Principle
Elementary Graph Theory EKönigsberg, Euler, Hamilton, Planarity
Basic Number Theory EDivisibility, Fermats Little Theorem
Geometry of Elementary Shapes
Proof By Contradiction and Induction
Cartesian Geometry and Loci
A Discussion of Some IMO Level Problems
Readership: School students keen to learn more of mathematics and specifically mathematics related to the IMO; coaches and instructors of mathematical competitions.
300pp (approx.) Pub. date: Scheduled Summer 2009
ISBN 978-981-4273-86-2
ISBN 978-981-4273-87-9(pbk)
Mathematical Olympiad Series, vol.3.
In 1736, the mathematician Euler invented graph theory while solving the Konigsberg seven-bridge problem. Over 200 years later, graph theory remains the skeleton content of discrete mathematics, which serves as a theoretical basis for computer science and network information science. This book introduces some basic knowledge and the primary methods in graph theory by many interesting problems and games.
Contents:
Definition of Graph
Vertex Degrees
Turan Theorem
Tree
Euler Problem
Hamilton Problem
Planar Graph
Ramsey Problem
Tournament Graph
Readership: High-school mathematics students and teachers, coaches of mathematical olympiads, undergraduates and graduates in mathematics, non-experts interested in mathematical competitions.
100pp (approx.) Pub. date: Scheduled Summer 2009
ISBN 978-981-4271-12-7
Mathematical Olympiad Series, vol.2.
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.
Divisibility
Greatest Common Divisors and Least Common Multiples
Prime Numbers and Unique Factorization Theorem
Indeterminate Equations (I)
Selected Lectures on Competition Problems (I)
Congruence
Some Famous Theorems in Number Theory
Order and Its Application
Indeterminate Equations (II)
Selected Lectures on Competition Problems (II)
Readership: High-school mathematics students and teachers; coaches of mathematical olympiads, undergraduates and graduates in mathematics, non-experts interested in mathematical competitions.
100pp (approx.) Pub. date: Scheduled Summer 2009
ISBN 978-981-4271-14-1(pbk)
Mathematical Olympiad Series, vol.1.
This book focuses on combinatorial problems in mathematical competitions. It 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. Some enlightening and novel examples and exercises are well chosen in this book.
With this book, readers can explore, analyze and summarize the ideas and methods of solving combinatorial problems. Their mathematical culture and ability will be improved remarkably after reading this book.
Counting Principles and Counting Formulas
Pigeonhole Principles and Mean Value Principles
Generating Functions
Recurrence Sequence of Numbers
Classification and Method of Fractional Steps
Corresponding Method
Counting in Two Ways
Recurrence Method
Coloring Method and Evaluation Method
Proof by Contradiction and Extreme Principle
Locally Adjusted Method
Constructive Method
Combinatorial Counting Problems
Existence Problems and the Proof of Inequalities in Combinatorial Problems
Combinatorial Extremum Problems
Readership: Students and teachers of high school, coaches of mathematical olympiads, undergraduates and graduates in mathematics, non-experts interested in mathematical competitions.
250pp (approx.) Pub. date: Scheduled Summer 2009
ISBN 978-981-283-949-7(pbk)
This book is written for undergraduates who wish to learn some basic results in analytic number theory. It covers topics such as Bertrand's Postulate, the Prime Number Theorem and Dirichlet's Theorem of primes in arithmetic progression.
The materials in this book are based on A Hildebrand's 1991 lectures delivered at the University of Illinois at Urbana-Champaign and the author's course conducted at the National University of Singapore from 2001 to 2008.
Facts about Integers
Arithmetical Functions
Averages of Arithmetical Functions
Elementary Results on the Distribution of Primes
The Prime Number Theorem
Dirichlet Series
Primes in Arithmetic Progression
Readership: Final-year undergraduates and first-year graduates with basic knowledge of complex analysis and abstract algebra; academics.
200pp (approx.) Pub. date: Scheduled Summer 2009
ISBN 978-981-4271-35-6
ISBN 978-981-4271-36-3(pbk)