October10, 2000 Volume 29, No. 5

St. Olaf Mathematics Department 

Math  Mess

October10, 2000 Volume 29, No. 5

This Week’s Colloquium
Wavelets are creating a common link between mathematicians, physicists and electrical engineers. Although wavelet analysis will never completely replace Fourier analysis, wavelets have replaced the discrete Fourier transform in fingerprint analysis, and is closing the gap in movie analysis. One of the advantages of wavelets is that they are highly localized and regularly scaled. Wavelets form an orthonormal basis for L2 by translations and dialation of a single function with vanishing moments.  Since most images are locally constant or linear, except near edges, wavelets can take advantage of this and compress an image, providing the necessary details as needed.

This Week’s Speaker
Gerry Naughton recieved his Ph.D. from the University of Minnesota in 1999.  His area of specialization is symmetric orthogonal wavelets and image analysis.  Gerry is currently holding a faculty position at Augsburg College.  He and and his wife Carrie recently had their first child. Their son Edward was born this past June.

Book Review
Brett Werner (’03) takes a look at: The Man Who Loved Only Numbers, written by Paul Hoffman:

On a list of eccentrics in recent history, Paul Erdos, the Hungarian number theorist, couldn’t be far from the top, and Paul Hoffman couldn’t have written a more interesting tale of his life and activities. Using anecdotes and first-hand accounts, Hoffman describes the Supreme Fascist, the Erdos Number idea, and Erdos’ struggle to look at numbers from many different perspectives. Not only does Hoffman give insight into the life of Erdos, but also into the lives of his friends and acquaintances.  Anyone going to Budapest this interim or for a semester must read this book. For a more traditional biography of Erdos, check out My Brain is Open by Bruce Schechter. The library has Paul Hoffman’s book or you can check out: www.paulerdos.com for a website about Erdos.

Fun Math Stuff
The Centre de Recerca Matmematica in Barcelona is sponsoring a world-wide on-line mathematics contest on October 17.  You can check out the details and enter the competition at www.mq2000.org/.

Paul Pearson ’01 has found some interesting math related web sites.  Check out the Mandelbrot fractal slide show:
www.znw.com/homepage/mandelbrot/man1.htm
Common mathematics errors:
http://math.vanderbilt.edu/~schectex/commerrs/
A movie of pi:
http://www.pithemovie.com/
A daily changing site of math history:
www-history.mcs.stand.ac.uk/history/Day_files/Now.html

Announcements
There is now room for two additional students on the Budapest Interim. They will have to share a room so they probably should be of the same gender.  If you are interested talk to Cliff Corzatt immediately.

For information on a Research Experience for Undergraduates in biostats, visit www.stat. ohio-state.edu/ or talk to Mike Kahn.

Last Week’s Solutions
Last week’s problem appears in: “How To Solve It: Modern Heuristics” by Z. Michalewicz and D.B. Fogel. The short version of the problem is that you are to determine the ages of three children given the following hints:  1) The product of their ages is 36. 2) The sum of the ages is the number of windows in a building. 3) The oldest child has blue eyes.

Lars Peterson’s (’01) solution: There are 8 possible three-number combinations without repetition to satisfy the first hint.  The second hint suggests that the mathematician is aware of how any windows exist in the building next to them. However, the fact that the mathematician needs another hint implies that there is more than one possible three-number sum, out of the 8 possible combinations, that equals the fixed number of windows in the building, namely (1,6,6) and (2,2,9) which both sum to 13. Furthermore, the third hint implies that there exists an oldest son, which eliminates the (1,6,6) possibility, in which case there exists two oldest sons as opposed to one.  Hence, the ages of the three sons are 2, 2, and 9 respectively. The color of the oldest son’s eyes is interesting, and happens to be the color of my own, but is irrelevant in this case.

*Also solved by Paul Fjelstad, Jonathon Kuiper, Jonathon Von Stroh, John Edmundson and Michael Zahniser.

Problem of the Week
A T-tetramino is a set of 4 unit cubes arranged in the shape of a capital  letter T. Prove that if T-tetraminos cover the area of an m by n rectangle without overlapping then the product mn is a multiple of 8.

To subscribe to the Math Mess, please contact Donna Brakke at brakke@stolaf.edu.

Editor-in-Chief: Jill Dietz
Associate Editor: Jennifer Beilfuss
Problems Editor: Cliff Corzatt
Czar: Donna Brakke
mathmess@stolaf.edu