Mathematical Olympiad Treasures - Brossura

Andreescu, Titu; Enescu, Bogdan

Brossura

ISBN 10: 0817643052 ISBN 13: 9780817643058

Casa editrice: Birkhauser, 2010

Riassunto

* "Mathematical Olympiad Treasures" aims at building a bridge between ordinary high school exercises and more sophisticated, intricate and abstract concepts and problems in undergraduate mathematics.

* The book contains a stimulating collection of problems in the subjects of algebra, geometry and trigonometry, number theory and combinatorics.

* The problems are clustered by topic into self-contained sections, that begin with elementary facts, followed by a number of carefully selected problems and an extensive discussion of their solutions.

* Should benefit undergraduate students, advanced high school students, instructors, and coaches.

* "Treasures" is similar in structure to "Challenges", but with more emphasis on unconventional examples, essay answers, and creative thinking.

Su questo libro

Recensione:

"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....

Treasures is organized in six chapters. The first three deal with problems from algebra, geometry and trigonometry, number theory and combinatorics. Chapters 4, 5 and 6 give the solutions to problems presented in the first three chapters. 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

"...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

Contenuti:

I Problems.- 1 Algebra.- 1.1 An Algebraic Identity.- 1.2 Cauchy-Schwartz 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.- 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.- 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.- II Solutions.- 4 Algebra.- 4.1 An Algebraic Identity.- 4.2 Cauchy-Schwartz 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 coef cients.- 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 ìcarpetsî theorem.- 5.7 Quadrilaterals with an inscribed circle.- 5.8 Dr. Trig learns complex numbers.- 6 Number Theory and Combinatorics.- 6.1 Arrays of numbers.- 6.2 Functions de ned on sets of points.- 6.3 Count twice!.- 6.4 Sequences of integers.- 6.5 Equations with in nitely many solutions.- 6.6 Equations with no solutions.- 6.7 Powers of 2.- 6.8 Progressions.- Index of notations.- Index to the problems.

Su questa edizione

• Editore: Birkhauser
• Data di pubblicazione: 2010
• ISBN 10: 0817643052
• ISBN 13: 9780817643058
• Rilegatura: Copertina flessibile
• Numero edizione: 1
• Numero di pagine: 300