Mathematical Olympiad challenges
著者
書誌事項
Mathematical Olympiad challenges
Birkhäuser, c2000
- : us : hbk
- : sz : hbk
- : us : pbk
- : sz : pbk
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内容説明・目次
- 巻冊次
-
: us : pbk ISBN 9780817641559
内容説明
Mathematical Olympiad Challenges is a rich collection of problems put together by two experienced and well-known professors and coaches of the U.S. International Mathematical Olympiad Team. Hundreds of beautiful, challenging, and instructive problems from algebra, geometry, trigonometry, combinatorics, and number theory were selected from numerous mathematical competitions and journals. An important feature of the work is the comprehensive background material provided with each grouping of problems. The problems are clustered by topic into self-contained sections with solutions provided separately. All sections start with an essay discussing basic facts and one or two representative examples. A list of carefully chosen problems follows and the reader is invited to take them on. Additionally, historical insights and asides are presented to stimulate further inquiry. The emphasis throughout is on encouraging readers to move away from routine exercises and memorized algorithms toward creative solutions to open-ended problems.
Aimed at motivated high school and beginning college students and instructors, this work can be used as a text for advanced problem- solving courses, for self-study, or as a resource for teachers and students training for mathematical competitions and for teacher professional development, seminars, and workshops.
目次
Foreword (by Mark Saul) * Preface * PART I: Problems * 1. Geometry and Trigonometry * 2. Algebra and Analysis * 3. Number Theory and Combinatorics * PART II: Solutions * 1. Geometry and Trigonometry * 2. Algebra and Analysis * 3. Number Theory and Combinatorics * Appendix: Definitions and Notation
- 巻冊次
-
: us : hbk ISBN 9780817641900
内容説明
Mathematical Olympiad Challenges is a rich collection of problems put together by two experienced and well-known professors and coaches of the U.S. International Mathematical Olympiad Team. Hundreds of beautiful, challenging, and instructive problems from algebra, geometry, trigonometry, combinatorics, and number theory were selected from numerous mathematical competitions and journals. An important feature of the work is the comprehensive background material provided with each grouping of problems. The problems are clustered by topic into self-contained sections with solutions provided separately. All sections start with an essay discussing basic facts and one or two representative examples. A list of carefully chosen problems follows and the reader is invited to take them on. Additionally, historical insights and asides are presented to stimulate further inquiry. The emphasis throughout is on encouraging readers to move away from routine exercises and memorized algorithms toward creative solutions to open-ended problems.
Aimed at motivated high school and beginning college students and instructors, this work can be used as a text for advanced problem- solving courses, for self-study, or as a resource for teachers and students training for mathematical competitions and for teacher professional development, seminars, and workshops.
目次
I Problems.- 1 Geometry and Trigonometry.- 1.1 A Property of Equilateral Triangles.- 1.2 Cyclic Quadrilaterals.- 1.3 Power of a Point.- 1.4 Dissections of Polygonal Surfaces.- 1.5 Regular Polygons.- 1.6 Geometric Constructions and Transformations.- 1.7 Problems with Physical Flavor.- 1.8 Tetrahedra Inscribed in Parallelepipeds.- 1.9 Telescopic Sums and Products in Trigonometry.- 1.10 Trigonometric Substitutions.- 2 Algebra and Analysis.- 2.1 No Square is Negative.- 2.2 Look at the Endpoints.- 2.3 Telescopic Sums and Products in Algebra.- 2.4 On an Algebraic Identity.- 2.5 Systems of Equations.- 2.6 Periodicity.- 2.7 The Abel Summation Formula.- 2.8 x + 1/x.- 2.9 Matrices.- 2.10 The Mean Value Theorem.- 3 Number Theory and Combinatorics.- 3.1 Arrange in Order.- 3.2 Squares and Cubes.- 3.3 Repunits.- 3.4 Digits of Numbers.- 3.5 Residues.- 3.6 Equations with Unknowns as Exponents.- 3.7 Numerical Functions.- 3.8 Invariants.- 3.9 Pell Equations.- 3.10 Prime Numbers and Binomial Coefficients.- II Solutions.- 1 Geometry and Trigonometry.- 1.1 A Property of Equilateral Triangles.- 1.2 Cyclic Quadrilaterals.- 1.3 Power of a Point.- 1.4 Dissections of Polygonal Surfaces.- 1.5 Regular Polygons.- 1.6 Geometric Constructions and Transformations.- 1.7 Problems with Physical Flavor.- 1.8 Tetrahedra Inscribed in Parallelepipeds.- 1.9 Telescopic Sums and Products in Trigonometry.- 1.10 Trigonometric Substitutions.- 2 Algebra and Analysis.- 2.1 No Square is Negative.- 2.2 Look at the Endpoints.- 2.3 Telescopic Sums and Products in Algebra.- 2.4 On an Algebraic Identity.- 2.5 Systems of Equations.- 2.6 Periodicity.- 2.7 The Abel Summation Formula.- 2.8 x + l/x.- 2.9 Matrices.- 2.10 The Mean Value Theorem.- 3 Number Theory and Combinatorics.- 3.1 Arrange in Order.- 3.2 Squares and Cubes.- 3.3 Repunits.- 3.4 Digits of Numbers.- 3.5 Residues.- 3.6 Equations with Unknowns as Exponents.- 3.7 Numerical Functions.- 3.8 Invariants.- 3.9 Pell Equations.- 3.10 Prime Numbers and Binomial Coefficients.- A Appendix A: Definitions and Notation.- A.1 Glossary of Terms.- A.2 Glossary of Notation.- About the Authors.
- 巻冊次
-
: sz : pbk ISBN 9783764341558
内容説明
This text offers a collection of problems written by two experienced teachers and coaches of the US International Mathematical Olympiad Team. Through essays, representative examples, and carefully chosen problems sets, readers are encouraged to move away from routine exercises and memorized algorithms toward creative solutions and problem-solving techniques.
- 巻冊次
-
: sz : hbk ISBN 9783764341909
内容説明
This text offers a collection of problems written by two experienced teachers and coaches of the US International Mathematical Olympiad Team. Through essays, representative examples, and carefully chosen problem sets, readers are encouraged to move away from routine exercises and memorized algorithms toward creative solutions and problem-solving techniques.
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