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Math Horizons - September 2005


Inversion Contest Winners
Results from the November 2004 Contest calling for Mathematical Inversions. See the winning entries by Jason Ermer, Daniel Chupin, Rheta Rubenstein, and Troy Siemers.
Liars and Truthtellers: Learning Logic from Raymond Smullyan
Robert L. Holliday
Brainteasers, mindbenders, riddles---how many mathematicians got their start realizing how much fun they had trying to solve logic puzzles? This article gives the reader a sampling of the wonderful Liar/Truthteller puzzles from the mind of Raymond Smullyan. "What do we conclude when a delusional person in a mental institution, hooked up to a lie detector is asked 'Are you Napolean?,' replies 'No!', and the lie detectors indicates he is lying!?"

Supplemental Material is now available.

What Good is Proof by Induction Anyway?
Catherine Abbott
Do you often think that proof by induction is a proof technique introduced to torture novice mathematicians? Perhaps you believe that the problems seem artificial and lack any application to real life? To the contrary, this article shows fascinating applications of induction to paper folding and finance.
Knowin' Induction
Lawrence Mark Lesser
A parody lyric to be sung to the tune of the Bob Dylan classic (and #2 hit for Peter, Paul, and Mary) "Blowin' in the Wind." 

NUMB3RS: The Intersection between Mathematics and Hollywood is Not Empty
Ron Buckmire
A conversation with Caltech Professor Gary Lorden, mathematical consultant to the CBS primetime crime drama Numb3rs.

Another Mathematician Looks at NUMB3RS
Adam N. Rosenberg
How a real-life mathematical sleuth solves the mystery. Industrial mathematician Adam Rosenberg talks about the reality of the CBS primetime crime drama Numb3rs.
The Evolution of Mathematical Certainty
Linda Becerra and Ron Barnes
The Greeks were the first to attempt a rational explanation of Nature and the nature of the universe. The crucial tool in their investigations was mathematical reasoning. They assumed that (1) all questions about Nature and the universe can be answered by reason; (2) all answers are knowable and can be discovered; and (3) all answers are compatible. This mathematical excursion demonstrates that these goals can never be fully realized. 
Mathematics and Oil: Do They Mix?
Sylvia Forman
You may have noticed that the price of oil is a hot topic recently. What is going on with the world's oil supply? How will it affect us? Soon we will be forced to deal with the issue of a declining oil supply. Hopefully using mathematics to look at this problem in a systematic way will alert people that this is an issue that needs to be addressed. 
Book Reviews
Aaron Magid and Elizabeth D. Russell
Reviews of Remarkable Mathematicians: From Euler to von Neuman by Ioan James and All the Mathematics You Missed [But Need to Know for Graudate School] by Thomas A. Garrity. 
Organizational Profile: Operations Research---The Science of Better
Barry List
Learn about Operations Research, the mathematics of doing things more efficiently, and the leading society for operation researchers INFORMS. 
It's Only Natural
Stan Wagon
An elementary, self-contained proof of Chebyshev's prime number theorem. 
REU Spotlight: Rice University Summer Institute of Statistics
Javier Rojo
A statistics/biostatistics research experience including tours of the Anderson Cancer Research Center and Johnson Space Center. 
The Virginia Tech Regional Math Contest
Peter A. Linnell
A mathematical contest to test your problem solving skills, pre-Putnam. Even if your university doesn't receive a letter of invitation, you are still welcome to participate. 
problem from a previous VTRMC and its solution are available.
Problem Section
Andy Liu
Self-answering Problem Contest
Chris Hill
Submit your entry (both question and answer!) by November 15, 2005.