Expeditions in Mathematics is a collection of some of the best talks from the Bay Area Mathematical Adventures (BAMA) program. Begun in 1998 to appeal to high school students, BAMA now attracts an enthusiastic following of the region’s teachers, parents, mathematics aficionados, and students.

The stellar collection of experts includes John Horton Conway, Don Saari, Bjorn Poonen, John Stillwell, Tom Banchoff, Francis Su, Steven Krantz, and David Bressoud—all fine mathematicians, renowned expositors, and well-known writers.

Catalogued under five mathematical headings, the topics include progress toward proving the twin primes conjecture; surprising mathematical paradoxes; facts about unnatural sequences of integers; applications of topology to questions in chemistry; ways of deciding when a tangle of string is actually a knot; how the medieval ranking of angels was related to the location of the planets, and by whom; the volume of a tetrahedron formed by a space rhombus; how the heavenly bodies seem to behave when viewed from the tropics and from the Southern Hemisphere; the latest techniques in cryptography; and determining preferences in voting.

Listing of all BAMA talks, 1998-2010

Table of Contents

Preface.
I. General.
II. Number Theory.
III. Geometry & Topology.
IV. Combinatorics & Graph Theory.
V. Applied Mathematics.
About the Authors.
Index

 

Excerpt (p. 129): Is it Knotted? by Joel Hass and Abigail Thompson

A knot can be thought of as a closed loop of string. We’ll say that two knots are the same if it is possible to wiggle one around, without cutting it, until it looks just like the other. In order to study knots, we first draw pictures of them called projections. In figure 1 we see a complicated picture of a knot, which we’ll name Q:

Is Q really knotted, or can it be moved around until it looks like the unknot that is drawn next to it? How can we tell?