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As the millenium draws to a close, many people are busy creating and debating "top ten" lists -- greatest movies of all time, best fiction books of the decade, most successful musicians of the century, most significant inventions, and so on. One name which would appear on almost all such rankings of the top ten mathematicians of this century would be that of Paul Erdos.
Things were different in Budapest in 1983 when Gyuri Petruska and I first discussed the idea of St. Olaf undergraduates studying mathematics in Budapest: no internet, no e-mail, no fax machines (very few phone lines!), a Warsaw Pact, rent and heat at essentially no charge, and a world class opera absolutely anyone could afford. But some things were not so different: powerful and distinctive intellectual communities, a deeply rooted tradition of ferreting out and developing mathematical talent, colorful and effective institutions maintaining world class standards in the face of forbidding obstacles, a common opinion that soon all would be lost. I had spent several extended stays in Budapest doing research and by 1983, Petruska and I knew each other pretty well, but he really got my attention when out of the blue he asked "If there was a mathematics program in Hungary for St. Olaf students, would anyone come?"
We are two Saint Olaf students who attended the Budapest Semesters in Mathematics program in the fall of 1998. Here is a view of students' lives on the BSM program. We hope you enjoy following our character Brett around Budapest from Wednesday to Sunday, Szerda to Vasarnap.
Most students of mathematics know that the mathematician Charles Lutwidge Dodgson of Oxford University wrote Alice's Adventures in Wonderland under the pseudonym of Lewis Carroll. Yet very few of us, even the professional mathematicians, can discuss with any specificity what mathematics he investigated. What was the focus of his life's work? What were his mathematical tastes and enthusiasms? Where did this wonderful writer of children's fantasy constructed with a knowledge of formal logic choose to put his professional time? This past year, the centenary of his death, Oxford, Harvard, Princeton, the Pierpont-Morgan Library and others have staged exhibits to honor his life. An examination of his mathematical work provides an interesting glimpse of mathematical study in Victorian England, and tells us a bit about Dodgson too.
Here's a quiz for all of you prospective game show contestants out there. Can you answer these questions (or rather question these answers) in less than 5 seconds each?
a) The first chapter of this novel is titled "The Old Sea-Dog at the 'Admiral Benbow'"
b) This shark may have earned its name because the male hangs onto the female's fin with its teeth
c) The city of Polenque flourished from 600 to 900 during this North American civilization's Classic Era
When I teach mathematics, I try hard to encourage my students to participate in class. Many of them, however, are just too nervous to risk being wrong in front of me and their friends. So, sometimes, I tell the story of the mistake I made that was seen by millions. Back when I was a graduate student, I appeared on Jeopardy!, and in spite of my mathematical training, I failed to analyze the Final Jeopardy! round thoroughly enough. If you are familiar with the game, you may be wondering how this could happen. At first glance the rules seem simple. However, we shall see that even this simple game illustrates the paradoxes and pitfalls of game theory, the branch of mathematics devoted to the study of strategy in games.
If you're looking for something to help you while away those idle hours at the beach this summer, you might want to consider a math book. And while books like Halmos' Naive Set Theory and Spivak's Calculus on Manifolds are elegant little volumes that would make a different sort of fashion statement than would the latest in swimwear, they are, after all, textbooks, from which you might reasonably desire a break. Instead, try one of the many books of mathematical history, biography,puzzles, and appreciation. Here is a list of some good ones to get you started. Most of them are even in print. Happy reading.
T.B.W. Spencer, London, U.K. ABCD is an inscribed quadrilateral in a circle such that AB+BC=CD+DA. prove that AB+BC is less than or equal to sqrt(2) AC.
Proposed by E. M. Kaye, Vancouver, B.C. Determine an infinite family of relative prime integer triples (x,y,z) such that x+y+z exactly divides x^2+y^2+z^2.
Proposed by K. S. Murray. Determine the smallest radii of three congruent disks in order that they can cover a disk of radius r.
(To find out the answers to February's Final Exam, click here.)
How many digits of pi can you recite from memory? At this suggestion, the lucky among you will find a curiosity lodged in a remote corner of your brain, somewhere between Great-Aunt Tillie's birthday and your killer recipe for lemon bars. It's a sentence with the following property: write down the number of letters in each word, and you'll have written out the first few digits of pi. Chances are, it's the elegant "How i need a drink, alcoholic in nature, after the heavy lectures involving quantum mechanics," which is the only widely-recognized pi-mnemonic in the English language. It probably isn't:
Can I find a ratio, immutable, to descry?
There can exist constant qualities -- perfect roundness
For me the delicate star called pi
Speaks only for the splendid cry of heaven's soundness.
I'm still waiting for that one to catch on.