Mathematical Adventures For Students and Amateurs

by HAYES, DAVID F.; Shubin, Tatiana; Alexanderson, Gerald L.; Ross, Peter

• ISBN13: 9780883855485
• ISBN10: 0883855488
• Format: Paperback
• Copyright: 2004-05-01
• Publisher: Mathematical Assn of Amer

Summary

This is a partial record of the Bay Area Math Adventures (BAMA), a lecture series for high school students (and incidentally their teachers, parents, and other interested adults) hosted by San Jose State and Santa Clara Universities in the San Francisco Bay Area. These lectures are aimed primarily at talented high school students and as a result, the mathematics in some cases is far from what one would expect to see in talks at this level. There are serious mathematical issues addressed here. The authors are distinguished mathematicians; some are bright newcomers while others have been well known in mathematical circles for decades. We hope that this book will capture some of the magic of these talks that have filled auditoriums at the host schools almost monthly for several years. Join the students in sharing these mathematical adventures.

Table of Contents

Preface	v
Introduction	ix
I. General	1	(48)
1 Prime Numbers and the Search for Extraterrestrial Intelligence,
Carl Pomerance	3	(4)
2 Space Shuttle Geometry,
Helen Moore	7	(10)
3 Mathematicians versus the Silicon Age: Who Wins?,
Sheldon Axler	17	(10)
4 Breaking Driver's License Codes,
Joseph A. Gallian	27	(14)
5 Jumping Frogs and Powers of Two,
Paul Zeitz	41	(8)
II. Number Theory	49	(32)
6 Triangles, Squares, Oranges and Cuboids,
Peter Stevenhagen	51	(14)
7 When Is an Integer the Product of Two and of Three Consecutive Integers?
Edward F. Schaefer	65	(8)
8 Right Triangles and Elliptic Curves,
Karl Rubin	73	(8)
III. Combinatorics and Probability	81	(74)
9 Proofs that Really Count: The Magic of Fibonacci Numbers and More,
Arthur T. Benjamin & Jennifer J. Quinn	83	(16)
10 Juggling Patterns, Passing, and Posets,
Joe Buhler & Ron Graham	99	(18)
11 Platonic Divisions of Space,
Jean Pedersen	117	(18)
12 Probability by Surprise,
Susan Holmes	135	(20)
IV. Geometry and Topology	155	(62)
13 The Rule of False Position,
Don Chakerian	157	(12)
14 Geometric Puzzles and Constructions-Six Classical Geometry Theorems,
Zvezdelina Stankova	169	(16)
15 Cusps,
Dmitry Fuchs	185	(16)
16 Triangles and Curvature,
Richard Scott	201	(16)
V. Applications and History	217	(64)
17 Archimedes and his Floating Paraboloids,
Sherman Stein	219	(14)
18 Mathematical Mapping from Mercator to the Millennium,
Robert Osserman	233	(26)
19 Alice in Numberland: an informal dramatic presentation in 8 fits,
Robin Wilson	259	(22)
Biographical Notes	281	(6)
Index	287