Mathematical miniatures / Svetoslav Savchev, Titu Andreescu.

Format:

Book

Author/Creator:

Savchev, Svetoslav.

Contributor:

Andreescu, Titu, 1956-

Mathematical Association of America, issuing body.

Series:

Anneli Lax New Mathematical Library

Anneli Lax new mathematical library ; v. 43

Anneli Lax New Mathematical Library, 2643-5586 ; v. 43

Language:

English

Subjects (All):

Mathematics--Problems, exercises, etc.

Mathematics.

Problem solving.

Physical Description:

1 online resource (xi, 223 pages) : digital, PDF file(s).

Edition:

1st ed.

Place of Publication:

Washington, D.C. : Mathematical Association of America, c2003.

Summary:

Mathematical Miniatures is a problem collection of arresting mathematical insight and ingenuity. The authors brought together materials from mathematical competitions, books, research papers, discussions, and their own work. Such mathematical substance went far beyond the purposes of a traditional problem-solving book. The most attractive results refused to fit into the schemes of an instruction manual meant to exemplify typical problem solving techniques. A broader interpretation of these problems had to be identified, and this book is the fruit of that effort. Savchev and Andreescu detach certain statements or groups of related statements into independent sections. Treating these gems separately, in self-contained essays, emphasizes the source of their natural charm---connections with genuine mathematical experience. The essays are of impressive diversity, enlivened by fresh and original ideas. They involve concepts not only useful but also beautiful and nonstandard, with lots of esthetic appeal. The book is thus not so much a mathematical toolchest: it is an anthology of mathematical verse.

Contents:

1. A telescoping sum

2. Lagrange's identity

3. Perfect squares

4. Lest common multiples

5. Trig substitutions

Coffee break 1

6. Popoviciu's theorem

7. Catalan's identity

8. Several inequalities

9. Vectors

10. Mathematical induction at work

Coffee break 2

11. A highly divisible determinant

12. Hermite's identity

13. Complete sequences

14. Three polynomials

15. More about induction

Coffee break 3

16. A classical identity

17. Multiplicative functions

18. The "arbitrary" Proizvolov

19. Hölder's inequality

20. Symmetry

Coffee break 4

21. He knows I know he knows

22. A special inequality

23. Two inductive constructions

24. Some old-fashioned geometry

25. Extremal arguments

Coffee break 5

26. The AMS inequality

27. Helly's theorem for one dimension

28. Two approaches

29. Radical axis

30. The pigeonhole principle

Coffee break 6

31. The three jug problem

32. Rectifying trajectories

33. Numerical systems

34. More on polynomials

35. Geometric transformations

Coffee break 7

36. The Game of life problem

37. Tetrahedra with a point in common

38. Should we count

39. Let's count now

40. Some elementary number theory

Coffee break 8

41. Euclid's game

42. Perfect powers

43. The 2n-1 problem

44. The 2n+1 problem

45. The 3n problem

Coffee break

46. Pairwise sums

47. Integer progressions

48. Incomparable sets

49. Morse's sequence

50. A favorite of Erdös.

Notes:

Title from publisher's bibliographic system (viewed on 02 Oct 2015).

Description based on print version record.

ISBN:

0-88385-957-2

OCLC:

923220141