Mathematical Olympiad challenges
"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 for 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." "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."--Jacket
Problems and Exercises
1 online resource (xv, 260 pages) : illustrations
9781461221388, 1461221382
812613869
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.
Electronic reproduction, [Place of publication not identified], HathiTrust Digital Library, 2012