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Mathematical Olympiad Treasures / by Titu Andreescu, Bogdan Enescu
Mitwirkende(r): Resource type: Ressourcentyp: Buch (Online)Buch (Online)Sprache: Englisch Reihen: SpringerLink BücherVerlag: Boston : Springer Science+Business Media, LLC, 2012Beschreibung: Online-Ressource (VIII, 253p. 93 illus, digital)ISBN:- 9780817682538
- 511.6
- QA164-167.2
Inhalte:
Zusammenfassung: I Problems -- 1 Algebra -- 2 Geometry and Trigonometry -- 3 Number Theory and Combinatorics -- II Solutions -- 4 Algebra -- 5 Geometry and Trigonometry -- 6 Number Theory and Combinatorics.Zusammenfassung: "I took great pleasure in reading Mathematical Olympiad Treasures, by Titu Andreescu and Bogdan Enescu. This book is the fruit of the prodigious activity of two well-known creators of mathematics problems in various mathematical journals.... In all the chapters, the reader can find numerous challenging problems. All featured solutions are interesting, given in increasing level of difficulty; some of them are real gems that will give great satisfaction to any math lover attempting to solve the problems—or even extend them. I believe strongly that Mathematical Olympiad Treasures will reveal the beauty of mathematics to all students, teachers, and all math lovers." —MAA Online (Review of the First Edition) "...this is one of a long recent series of challenging secondary math books, coauthored by Dr. Titu Andreescu and published by Birkhäuser, a series that has definitely enriched the literature on secondary mathematics—a credit to the coauthor and to the wisdom of the editor." —Zentralblatt MATH (Review of the First Edition) This second edition of Mathematical Olympiad Treasures contains a stimulating collection of problems in geometry and trigonometry, algebra, number theory, and combinatorics. It encourages readers to think creatively about techniques and strategies for solving real-world problems, with new sections, revisions, and many more Olympiad-like problems at various levels of difficulty. The problems are clustered by topic into three self-contained chapters. The book begins with elementary facts, followed by carefully selected problems and detailed, step-by-step solutions, which then lead to more complicated, challenging problems and their solutions. Reflecting the vast experience of two professors and Mathematical Olympiad coaches, the text will be invaluable to teachers, students, and puzzle enthusiasts. The advanced reader is challenged to find alternative solutions and extensions of the proposed problems.PPN: PPN: 1651082162Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SXMS | ZDB-2-SMA
""Mathematical Olympiad Treasures""; ""Preface""; ""Contents""; ""Part I: Problems""; ""Chapter 1: Algebra""; ""1.1 An Algebraic Identity""; ""1.2 Cauchy-Schwarz Revisited""; ""1.3 Easy Ways Through Absolute Values""; ""1.4 Parameters""; ""1.5 Take the Conjugate!""; ""1.6 Inequalities with Convex Functions""; ""1.7 Induction at Work""; ""1.8 Roots and Coefficients""; ""1.9 The Rearrangements Inequality""; ""Chapter 2: Geometry and Trigonometry""; ""2.1 Geometric Inequalities""; ""2.2 An Interesting Locus""; ""2.3 Cyclic Quads""; ""2.4 Equiangular Polygons""
""2.5 More on Equilateral Triangles""""2.6 The ""Carpets"" Theorem""; ""2.7 Quadrilaterals with an Inscribed Circle""; ""2.8 Dr. Trig Learns Complex Numbers""; ""Chapter 3: Number Theory and Combinatorics""; ""3.1 Arrays of Numbers""; ""3.2 Functions Defined on Sets of Points""; ""3.3 Count Twice!""; ""3.4 Sequences of Integers""; ""3.5 Equations with Infinitely Many Solutions""; ""3.6 Equations with No Solutions""; ""3.7 Powers of 2""; ""3.8 Progressions""; ""3.9 The Marriage Lemma""; ""Part II: Solutions""; ""Chapter 4: Algebra""; ""4.1 An Algebraic Identity""
""4.2 Cauchy-Schwarz Revisited""""4.3 Easy Ways Through Absolute Values""; ""4.4 Parameters""; ""4.5 Take the Conjugate!""; ""4.6 Inequalities with Convex Functions""; ""4.7 Induction at Work""; ""4.8 Roots and Coefficients""; ""4.9 The Rearrangements Inequality""; ""Chapter 5: Geometry and Trigonometry""; ""5.1 Geometric Inequalities""; ""5.2 An Interesting Locus""; ""5.3 Cyclic Quads""; ""5.4 Equiangular Polygons""; ""5.5 More on Equilateral Triangles""; ""5.6 The ""Carpets"" Theorem""; ""5.7 Quadrilaterals with an Inscribed Circle""; ""5.8 Dr. Trig Learns Complex Numbers""
""Chapter 6: Number Theory and Combinatorics""""6.1 Arrays of Numbers""; ""6.2 Functions Defined on Sets of Points""; ""6.3 Count Twice!""; ""6.4 Sequences of Integers""; ""6.5 Equations with Infinitely Many Solutions""; ""6.6 Equations with No Solutions""; ""6.7 Powers of 2""; ""6.8 Progressions""; ""6.9 The Marriage Lemma""; ""Glossary""; ""Index of Notations""; ""Index to the Problems""
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