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Field name	Details
Dewey Class	512.7
Title	Winning Solutions ([EBook] /) / by Edward Lozansky, Cecil Rousseau.
Author	Lozansky, Edward
Added Personal Name	Rousseau, Cecil author.
Other name(s)	SpringerLink (Online service)
Publication	New York, NY : : Springer New York, , 1996.
Physical Details	X, 260 p. : online resource.
Series	Problem books in mathematics 0941-3502
ISBN	9781461240341
Summary Note	Problem-solving competitions for mathematically talented sec ondary school students have burgeoned in recent years. The number of countries taking part in the International Mathematical Olympiad (IMO) has increased dramatically. In the United States, potential IMO team members are identified through the USA Mathematical Olympiad (USAMO), and most other participating countries use a similar selection procedure. Thus the number of such competitions has grown, and this growth has been accompanied by increased public interest in the accomplishments of mathematically talented young people. There is a significant gap between what most high school math ematics programs teach and what is expected of an IMO participant. This book is part of an effort to bridge that gap. It is written for students who have shown talent in mathematics but lack the back ground and experience necessary to solve olympiad-level problems. We try to provide some of that background and experience by point out useful theorems and techniques and by providing a suitable ing collection of examples and exercises. This book covers only a fraction of the topics normally rep resented in competitions such as the USAMO and IMO. Another volume would be necessary to cover geometry, and there are other v VI Preface special topics that need to be studied as part of preparation for olympiad-level competitions. At the end of the book we provide a list of resources for further study.:
Contents note	1 Numbers -- 1.1 The Natural Numbers -- 1.2 Mathematical Induction -- 1.3 Congruence -- 1.4 Rational and Irrational Numbers -- 1.5 Complex Numbers -- 1.6 Progressions and Sums -- 1.7 Diophantine Equations -- 1.8 Quadratic Reciprocity -- 2 Algebra -- 2.1 Basic Theorems and Techniques -- 2.2 Polynomial Equations -- 2.3 Algebraic Equations and Inequalities -- 2.4 The Classical Inequalities -- 3 Combinatorics -- 3.1 What is Combinatorics? -- 3.2 Basics of Counting -- 3.3 Recurrence Relations -- 3.4 Generating Functions -- 3.5 The Inclusion-Exclusion Principle -- 3.6 The Pigeonhole Principle -- 3.7 Combinatorial Averaging -- 3.8 Some Extremal Problems -- Hints and Answers for Selected Exercises -- General References -- List of Symbols.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-1-4612-4034-1
Links to Related Works	Subject References: Combinatorics . Mathematics . Number Theory . Authors: Lozansky, Edward . Rousseau, Cecil . Corporate Authors: SpringerLink (Online service) . Series: Problem books in mathematics . Classification: 512.7 .

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