Mathematical Miniatures

Svetoslav Savchev, Titu Andreescu

224 pages, parution le 17/03/2003

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Résumé

Mathematical Miniatures is a collection of problems of arresting mathematical insight and ingenuity. The authors brought together material from mathematical competitions, books, research papers, discussions, and their own work. Such mathematical substance went far beyond the purposes of a traditional problem book. The most attractive results refused to fit into the rigid 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. This book is thus much more than a mathematical tool chest. It is an anthology of mathematical verse.

Contents

Preface
Warm-up Problem Set
1 A Telescoping Sum
2 Lagrange's Identity
3 Perfect Squares
4 Least 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 Holder'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 In-I Problem
44 The 2n + 1 Problem
45 The 3n Problem
Coffee Break 9
46 Pairwise Sums
47 Integer Progressions
48 Incomparable Sets
49 Morse's Sequence
50 A Favorite of Erdos
Instead of an Afterword
Glossary
About the Authors

Caractéristiques techniques

	PAPIER
Éditeur(s)	The Mathematical Association of America (MAA)
Auteur(s)	Svetoslav Savchev, Titu Andreescu
Parution	17/03/2003
Nb. de pages	224
Format	15 x 23
Couverture	Broché
Poids	330g
Intérieur	Noir et Blanc
EAN13	9780883856451
ISBN13	978-0-88385-645-1