* "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.
Rezensionen / Stimmen
Aus den Rezensionen: "! Das vorliegende Buch ! liefert einen didaktischen Leitfaden zum Einstieg in die fur Olympiade-Beispiele charakteristische Denkweise. Nichtsdestotrotz besitzt das Werk einen klar strukturierten Aufbau, der das Erarbeiten des dargebotenen Stoffes enorm erleichtert. Zu Beginn eines jeden Kapitels wird anhand einiger exemplarischer Problemstellungen die zugrundeliegende Idee erlautert ! Die Herkunftsgebiete der Beispiele erstrecken sich uber alle Sparten der Mathematik ! Aufgrund all dieser Punkte ist das Buch fur Leiter eines Olympiade-Kurses an Gymnasien ! gleichwie fur andere an der Thematik interessierte Leser warmstens zu empfehlen." (O. Pfeiffer, in: Internationale Mathematische Nachrichten, 2005, Vol. 59, Issue 198, S. 20)
Sprache
Verlagsort
Zielgruppe
Für Beruf und Forschung
Lower undergraduate
Produkt-Hinweis
Illustrationen
48 s/w Abbildungen
48 black & white illustrations, biography
Maße
Höhe: 23.5 cm
Breite: 15.5 cm
Dicke: 13 mm
Gewicht
ISBN-13
978-0-8176-4305-8 (9780817643058)
DOI
10.1007/978-1-4612-2052-7
Schweitzer Klassifikation
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.
