Ivars Peterson has made presentations at schools, colleges, professional meetings, banquets, and many other venues before diverse audiences, ranging from students and classroom teachers to NASA engineers and math enthusiasts.
Möbius Madness
Since its discovery in the 19th century, the astonishing one-sided, one-edged Möbius strip has confounded and fascinated generations of people, inspiring stories, magic tricks, patents, artworks, cartoons, playground equipment, and much else. Learn more than you ever thought possible about how a mathematical object conquered the modern world. Bibliography.
The Jungles of Randomness
From slot machines and amusement park rides to dice games and shuffled cards, chance and chaos pervade everyday life. Sorting through the various meanings of randomness and distinguishing between what we can and cannot know with certainty proves to be no simple matter. Inside information on how slot machines work, the perils of believing random number generators, and the questionable fairness of dice, tossed coins, and shuffled cards illustrate how tricky randomness can be. Bibliography.
Geometreks
Few people expect to encounter mathematics on a visit to an art gallery or even a walk down a city street (or across campus). When we explore the world around us with mathematics in mind, however, we see the many ways in which mathematics can manifest itself, in streetscapes, sculptures, paintings, architectural structures, and more. This illustrated presentation offers illuminating glimpses of mathematics, from Euclidean geometry and normal distributions to Riemann sums and Möbius strips, as seen in a variety of structures and artworks in Washington, D.C., Philadelphia, Toronto, Ottawa, New Orleans, and many other locales. Bibliography.
Newton's Clock: Chaos in the Solar System
With astronomical questions inspiring new mathematics, the remarkable insights of Johannes Kepler, Isaac Newton, and Henri Poincaré paved the way to celestial mechanics and modern notions of chaotic dynamics. The result is a new picture of a solar system less placid and predictable that its venerable clockwork image would suggest. Bibliography.
A Journey into Mathematical Art
From Fibonacci numbers and the digits of pi to tetrahedra, fractals, and Möbius strips, mathematics has inspired a wide variety of artists. Many people are familiar with the work of M. C. Escher and aware of the intertwining of math and art during the Renaissance, but the realm of mathematical art is far wider and more diverse than most people realize. An illustrated survey of contemporary math-related art illuminates these rich interactions. Bibliography.
By the Numbers
This illustrated trek ventures into the realm of numbers, as revealed in mathematics, science, literature, and art. It offers glimpses of the enduring appeal of integers, primes, partitions, pi, Fibonacci numbers and the golden ratio, hailstone numbers, Pascal's triangle, and other quirky and fascinating denizens of numeropolis. Bibliography.
Soap Bubbles in Math, Science, and Art
Artworks dating back to the invention of soap illustrate the wonder of soap bubbles and soap films. Soap bubbles have inspired not only art but also important developments in mathematics and science. Get a fresh perspective on minimal surfaces and their role in art, mathematics, science, and engineering. Bibliography.
MythMath
Ponder the number of Eskimo words for snow, the tragic fate of lemmings, the golden ratio's mysterious pervasiveness, and other myths of the modern media age. How do such stories become widely accepted "truths"? Get the scoop on the Nobel prize for mathematics, bumblebee modeling, Galois' last hours, young Gauss' quick calculation, and more. Bibliography.
How Math Becomes News
Several case studies illustrate how significant or crowd-pleasing developments in mathematics can gain media attention, in print, online, and elsewhere. Learn how public relations efforts to publicize mathematics can garner public attention. Get a glimpse of how and why major journals, such as Science and Nature, control much of science coverage in the media.
Pancake Sorting, Prefix Reversals, and DNA Rearrangements
The seemingly simple problem of sorting a stack of differently sized pancakes has become a staple of theoretical computer science and led to insights into the evolution of species. First proposed many years ago in The American Mathematical Monthly, the problem attracted the attention of noted mathematicians and computer scientists. It now plays an important role in the realm of molecular biology for making sense of DNA rearrangements. Bibliography.
Knotty Tales: From Vortex Atoms to DNA Tangles
The unexpected discovery more than two decades ago of several new ways to distinguish mathematical knots precipitated a surge of interest in knot theory. Today, intriguing links between knots and physics and illuminating biological applications testify to the new importance of a mathematical pursuit that began in the 19th century with the search for a new atomic theory. Bibliography.
Workshop: Communicating Mathematics (3 hours)
The importance of communicating mathematics clearly and effectively is evident in the many ways in which mathematicians must write, whether to produce technical reports, expository articles, book reviews, essays, referee's reports, grant proposals, research papers, evaluations, or slides for oral presentations. With a focus on exposition, this workshop offers tips for improving writing skills, from grammar and usage to organization and manuscript or slide preparation. It also provides insights into how news media cover mathematics and science and suggests how participants can contribute to the public understanding of mathematics. Bibliography.
Workshop for Middle School Teachers: Adventures in the MathZone (3 hours)
Explore the many-sided wonders of the Möbius strip, perform fold-and-cut magic, ponder the vagaries of dice, venture into higher dimensions, play with soap bubbles, untangle knots, and more in this hands-on workshop introducing concepts in contemporary mathematics to middle school teachers and students.
Math Treks: Bringing Real-World Math into the Classroom
When we explore the world around us with mathematics in mind, a walk down a city street, a visit to an amusement park or art gallery, a news report, or even a song on an MP3 player can offer telling glimpses of mathematical ideas. Look for the twists and turns of knots and Möbius strips, the chaos of a Tilt-A-Whirl, the digits of pi, unusual dice, startling geometric symmetries, and much more in this illustrated presentation. Bibliography.
