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Math Problems Notebook 2007 ed. [Mīkstie vāki]

  • Formāts: Paperback / softback, 236 pages, height x width: 235x155 mm, weight: 385 g, 21 Illustrations, black and white; XII, 236 p. 21 illus., 1 Paperback / softback
  • Izdošanas datums: 22-Aug-2007
  • Izdevniecība: Birkhauser Boston Inc
  • ISBN-10: 0817645462
  • ISBN-13: 9780817645465
Citas grāmatas par šo tēmu:
  • Mīkstie vāki
  • Cena: 46,91 €*
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  • Standarta cena: 55,19 €
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  • Formāts: Paperback / softback, 236 pages, height x width: 235x155 mm, weight: 385 g, 21 Illustrations, black and white; XII, 236 p. 21 illus., 1 Paperback / softback
  • Izdošanas datums: 22-Aug-2007
  • Izdevniecība: Birkhauser Boston Inc
  • ISBN-10: 0817645462
  • ISBN-13: 9780817645465
Citas grāmatas par šo tēmu:
The Math Problems Notebook is a collection of non-trivial, unconventional problems requiring deep insight and imagination nostalgic of those discussed at the Sunday Math Circles. These circles are comprised of college students who have a common passion for mathematics, and have become a place for disseminating beautiful mathematics at an elementary level. Following in the tradition of the math circles, the authors hope to inspire further enjoyment of mathematics with their collection of problems. Undergraduates and teachers of advanced mathematics, as will as the casual mathematician will mutually enjoy the collection.

The Math Problems Notebook is a collection of nontrivial, unconventional problems requiring deep insight and imagination reminiscent of those discussed at Sunday Math Circles. These circles have become a place for disseminating beautiful mathematics at an elementary level for college students who have a common passion for mathematics. The problems cover many topics, including number theory, algebra, combinatorics, geometry and analysis, of varying levels of difficulty. The presentation of each topic begins with simple exercises and follows with more difficult problems, challenging enough even for the experienced problem solver. The easier problems focus on basic methods and tools, while the more advanced problems develop problem-solving techniques, intuition and promote further research.Undergraduates and teachers of advanced mathematics, as well as the casual mathematician will mutually enjoy The Math Problems Notebook.

Recenzijas

Aus den Rezensionen:

Der vorliegende Band wendet sich an alle jene Personen, welche einerseits Freude am Lösen von Aufgaben aus unterschiedlichen mathematischen Bereichen haben und die andererseits das betreffende mathematische Umfeld kennenlernen möchten ... Im Anhang finden sich viele einschlägige Formeln und Aussagen. Dieses Buch ist auch deshalb sowohl Studierenden als auch Vortragenden sehr zu empfehlen, weil die unterschiedlichen Lösungsansätze nicht nur isoliert dargestellt, sondern untereinander verzahnt werden, sodass insgesamt ein Lehrbuch zu Problemlösungstechniken auf hohem Niveau vorliegt. (P. Paukowitsch, in: IMN Internationale Mathematische Nachrichten, April/2010, Issue 213, S. 43)

Preface vii
Part I Problems
1 Number Theory
3
2 Algebra and Combinatorics
11
2.1 Algebra
11
2.2 Algebraic Combinatorics
13
2.3 Geometric Combinatorics
18
3 Geometry
21
3.1 Synthetic Geometry
21
3.2 Combinatorial Geometry
23
3.3 Geometric Inequalities
27
4 Analysis
29
Part II Solutions and Comments to the Problems
5 Number Theory Solutions
37
6 Algebra and Combinatorics Solutions
85
6.1 Algebra
85
6.2 Algebraic Combinatorics
95
6.3 Geometric Combinatorics
120
7 Geometry Solutions
133
7.1 Synthetic Geometry
133
7.2 Combinatorial Geometry
142
7.3 Geometric Inequalities
175
8 Analysis Solutions
185
9 Glossary
217
9.1 Compendium of Triangle Basic Terminology and Formulas
217
9.1.1 Lengths in a Triangle
217
9.1.2 Important Points and Lines in a Triangle
218
9.1.3 Coordinates in a Triangle
219
9.2 Appendix: Pell's Equation
220
Index of Mathematical Results 225
Index of Mathematical Terms 227
Index of Topics and Methods 231