**The 2004 Honduran National Mathematics Olympiad**

*Don Hooley — September 7*

We will view pictures of the Association of Bilingual Schools of Honduras 2004
National Mathematics Olympiad and the National Autonomous University of Honduras.
I will report briefly on the invited lectures at the Olympiad (one of which I gave)
and present several sample items from the exams.

**How to Win(?) at ****Quiddler**

*Darryl Nester — September 14*

The rules to Quiddler solitaire
are simple: You have 16 cards, in eight stacks of two cards each. Each card has a letter (or pair of letters).
From the eight top cards, make a word, and remove those cards. Repeat until all cards are gone, or no words
are possible. Your score is based on the letters used, minus the letters remaining, plus bonus
points for creating words with 5 or more letters.
When you are finished, you'll see how your score ranks among others who have played that day.

A few names show up consistently in the list of top scores, most of them impressive or intriguing "handles"
such as *sardonimous, Vinster, cc,* and *UK Lady.* And in the last several months, the
slightly-less-intriguing *Darryl from Ohio.* What skills do these Quiddler wizards possess? A colossal vocabulary?
Prodigious lexicographical intuition? Or, you know, just being, like, really good with words and stuff?
Perhaps all of these things ... but almost certainly, some of them have a computer doing all the grunt work
while they take all of the glory. We'll take a look at that grunt work, and the mathematics behind this word game.

**How to ****Play for a Billion**

*Darryl Nester — September 21*

Pepsi recently concluded its "Play for a Billion" contest with a primetime special to award a $1 million prize,
and reveal whether the prizewinner had won the titular BILLION DOLLAR prize (he did not).
The seven finalists were offered the opportunity to take home various cash prizes if they would
give up their chance at $1 million. No one took that option—so six went home with nothing.
Was that a good decision? We'll look at how to answer that question with probability and utility
theory.

**Least Squares Regression, Geometry, and Symmetry**

*Darryl Nester — September 28*

(Preview of talk to be given at Miami University Math and Statistics Conference)

Given a set of points {(*x*_{1},*y*_{1}),
(*x*_{2},*y*_{2}), ...
(*x _{n}*,

- What is the probability that, after
*n*bets, he has less than $*M*? - What happens to this probability as
*n*tends to ∞?

**Squares through four points**

*Don Hooley — October 26*

Is it possible to construct a square with sides going through four arbitrary points
in the plane? How might one do this? How many such squares exist? We will use Paul
Kunkel’s wonderful website and applets to help
consider answers to these questions and more.

**Earning Points on the Putnam Exam**

and **The 2004 Putnam Exam**

*Darryl Nester and Don Hooley — November 30 and December 7*

(part 1) We will look at a few problems about algebra, number sequences, area and geometry,
and probability in an attempt to identify strategies for earning points on the
annual William Lowell Putnam Mathematical Competition exam.

(part 2) Last Saturday, thousands of college students spent up to six hours
competing on the annual William Lowell Putnam exam. We'll see what we can make
of it in half an hour.

**A ****"Fish-Eye" view of the Plane**

*Darryl Nester — February 10*

Can you squeeze the whole Cartesian (*xy*) plane inside a circle?
(And if the answer is "yes"... how do you do it, and why would you want to?)
We’ll examine a view of geometry where
"objects in the mirror may be closer (or farther) than they appear."

- In basketball, what is the probability of making a basket for a shot taken from x feet away?
- What is the probability that a loan applicant will default, based on known information about that applicant’s credit history?
- What is the probability of a successful recovery from surgery, based on the patient’s condition (age, heart rate, BP, etc.)?

**The “Fish-Eye” Plane (Revisited)**

*Darryl Nester — March 17*

We’ll look again at different ways of squeezing the entire Cartesian (*xy*) plane
into a circle, including the mathematics involved with choosing the “best” function to
squeeze the plane, and the related idea of stereographic projection (see examples
here and
here).

**Exploring Interactivate**

**GIMPS: The Great Internet Mersenne Prime Search**

*Mike Bumbaugh — October 2*

GIMPS uses the power of many computers linked through the Internet to do the massive computing
required to check if very large numbers are prime. Specifically, GIMPS attempts to identify
*Mersenne primes*, primes of the form 2^{P}–1, where *P* is a prime.
The first seven of these are 3, 7, 31, 127, 8191, 131071, and 524287.
To date, the effort has identified five—the five largest primes known.
Two years ago, a GIMPS contributor was credited with identifying the 39th Mersenne prime, with over 4 million
digits.
For more information about GIMPS, visit mersenne.org.
More Mersenne primes can be seen here.

**A Report from a Mathematics Alumnus (and Bluffton College Lifetime Service
Award Recipient)**

*Dr. Isaac Riak — October 16*

Wondering what you can do with a mathematics major? Dr. Isaac Riak graduated from Bluffton
in 1971 with a mathematics degree, and went on to teach mathematics in Jamaica for
several years. Since then, his career path has turned towards economics, specifically
the area of international development. At the Alumni Awards Banquet last weekend, he and
his wife, Dr. Pauline Riak, received the Lifetime Service Award for their work. At this
week's Math Seminar, he will tell us a bit about his journey from Bluffton College
to his current home in Nairobi, Kenya.

- learned how to square numbers in my head,
- learned how to create magic squares "on the fly,"
- saw some nifty tricks with
*Excel*, - ate far too much Halloween candy, and
- made some general observations about the changing state of technology.

**Modelling with ****STELLA
and Madonna**

*Steve Harnish — November 13*

If this title isn't enough to pique your interest, then let's try simulations
of dynamical systems:

- Population Dynamics
- Pharmacology Simulations
- Newton's Law of Cooling/Heating
- Coupled Harmonic Oscillators, and
- A question posed by a Calculus 1 student to model the cooling of a computer's CPU

**Recursion Excursion**

*Mike Bumbaugh — November 20 and December 4*

We will look at Italian rabbits that never die and hop down the bunny trail to
an efficient method for finding Mersenne primes.
Also, we will examine a very simple problem that elementary kids could have
fun with, but the proof eluded mathematicians for many years: Ulam's Conjecture.
Much of the discussion should be accessible to a broad audience.

**Three (of the many) Faces of Gamma**

*Steve Harnish — January 27 & February 10*

What should be the next entries in these lists?

- List A: 1, 2, 6, 24, 120, ...
- List B: 120, 24, 6, 2, 1, ...
- List C: 16!, 8!, 4!, 2!, 1!, ...
- List D: 120x
^{3}, 30x^{4}, 6x^{5}, x^{6}, ...

**Three sticks**

*Darryl Nester — February 3*

You have three sticks, of length *x*, *y*, and *z*, all attached at
one end to a point *P*. The sticks can rotate freely about point *P*.
You want to arrange them so that the other (unattached) ends lie at the vertices of a right triangle.
(1) When is this possible? (2) Of those triangles formed in this way, which one has the largest possible area?
You can explore this further with the applet here.
*(This is a restatement of problem #11057 from the January 2004 issue of American Mathematical Monthly.)*

**Recursion Excursion (conclusion)**

*Mike Bumbaugh — February 17*

We'll explore visual demonstrations of recursion with the
Koch snowflake
(and variations on that idea). You can see another interesting view of recursion
here (Shockwave animation).

**Coin Flips, Random Walks, and Standing Waves ... Matrices to the Rescue**

*Steve Harnish — March 9, 18, & 23*

Several talks on a mathematical model for solid-state physics (both in Math Seminar and in
the Thursday Math Physics Discussion).

**Slide Rules**

*Duane Bollenbacher — March 30 & April 6*

Slide rules will be provided for your use. We will discuss its history,
its role in the classroom, and its overnight demise. Old-timers (like
Professor Harnish) will wax nostalgic; youngsters (like Professor Nester)
will be in solemn wonder. We even have music for you!!