Thursday Math Tea

A few weeks ago, as we gathered for tea and scones (thanks, Jeffrey!), one of the students came in with a problem posed in an education class, which we then attempted to solve. Here's the deal.

Take a square and put positive integers at each of the corners. (Choose numbers between 1 and 99.) Now at the midpoints of each side of the square, write down the absolute value of the difference of the two neighboring corners. Finally, join the midpoints to make a new square. Repeat.

In the problem posed to the education class, the final figure has seven squares (I think), one inside the other. This is a problem that is used in grade school classrooms, and the (stated) goal is to find numbers for the outermost square, so that the number zero never shows up anywhere in the final figure. (The actual goal is to get the students to practice their subtraction.)

Well, that sounded like an easy problem, so we set to it. After some deliberations we came up with a solution, then proceeded to ask lots of related questions. (A real mathematical spirit filled our students.) One thing the students there were able to prove, is that given enough concentric squares, any starting configuration eventually ends with all zeros.

Final note: We have a Thursday tea every week as long as classes meet that day. Tea starts at 3:00 pm in the Math Lab. Please feel free to join us if you are in the area.

Some Series Stuff (Part I)

Okay, this is something of an experiment.  I have translated a LaTeX file into HTML using tth (link on the official math links page on the UD site).  This should look okay if you are using a mozilla or firefox browser.  Otherwise you are taking your chances.

The idea of this post is to compute Taylor series for sines and cosines without using Calculus.

The rest of the post is after the jump.  (Click on the post title to get to the whole article and comments.)

The New Faculty Member

As I'm the newest member of the Mathematics Department, it's unlikely that anyone knows much about me. So, let me take this opportunity to tell you a little about myself.

I earned my Ph.D. in Mathematics in 1998 from The University of Texas at Austin, but I had earned my M.A. in Mathematics from 1990 to 1993 from Rice University where I became good friends with Dr. Paul Phillips, who was earning his Ph.D at the same time. My area of expertise is in topology (specifically, knot theory and geometric topology), but I have a passion for teaching mathematics. Since graduating I've taught at several small liberal arts college, beginning with Eureka College in Illinois, then Hampden-Sydney College in Virginia, and most recently Millsaps College in Mississippi. I've taught courses at all level -- from College Algebra and liberal arts mathematics courses, to advanced math courses for majors. The only courses I tend not to teach are statistics and applied math courses, but I'll likely teach most courses that require students to prove theorems.

Since leaving graduate school, however, my research interests have broadened in a surprising direction. Although I still research questions in topology, I have recently begun a very exciting research program in game theory. Specifically, I'm studying a game called The Lying Oracle Game, where an "oracle" tells you the outcome of a coin toss, but may lie at times. Your job is to determine when the oracle is lying. So far, I have one publication in topology and two in game theory, with another paper in topology in preparation. I'm looking for colleagues and students with whom to collaborate on the many variants of this fascinating problem!

Finally, I am a proud husband and father as well. My wife, Carolyn, is an ordained Minister of the Word and Sacrament in the Presbyterian Church (USA) and is seeking a call as a hospital chaplain in the Dallas area. My son, Allen, is beginning Kindergarten this year and will turn 6 in November, and my daughter Rebecca is 2 and will get her first haircut soon.

New Semester

Faculty Day was yesterday, Faculty Book Discussion (on Genome, by Matt Ridley) was today, and students are already beginning to move in.  The new academic year is upon us.


This year we welcome a new faculty member to the department, Dr. John Osoinach, and I hope to have a post up next week to (more formally) introduce him on the blog.

Gifts that Give

Just some quick photos of the plants I received from our graduating seniors. (Click on photos to see an embiggened image.)

Thanks again, Math Majors of 2009!

The top one is a tomato plant, and you might even be able to see some baby tomatoes on it. The bottom plant is a banana pepper plant from which I have already harvested two peppers.

Putnam 2008 Scores

The results are in.

Once again, we had a near record number of students (nine) take the Putnam Exam at the end of the Fall semester.

Congratulations to all nine for taking a significant chunk of time out of their day shortly before finals to cogitate deeply on math problems.

This year all of our students scored at least the mode (mode = 0 this year). There were 3627 contestants who took the exam this time, and a score of 0 earned a rank of 2771.5.

Two of our students beat the mode. One of them scored the median (median = 1 this year), joining only 172 other contestants to accomplish this feat. These students earned a rank of 1829. (An improvement of over 940 places above the mode.)

The other student beat both the median and the mode to rank 1660.5 along with 163 other contestants. (A further improvement of over 165 places above the median.)

Yea!

Math Majors Testing

Our math majors are taking their written comprehensive exams now. Wish them good skills.

Math Circles

Here is a great problem a friend of mine found at Math Circle Problem of the Week:

Click on the link and look up the problem from Sunday 12 January 2003.

Summary version: 100 prisoners, isolated from each other. Each day one is selected at random to enter a room with a single light bulb. They can flip the switch, leave it alone, or declare that all 100 prisoners have visited the room. A correct declaration sets all 100 prisoners free, and an incorrect declaration leads to a nastier resolution.

Assuming all 100 want to go free, what strategy can they decide on before the game starts? (They won't be isolated until the game has begun.)

Have fun!

Return to Classes

We are back.

What can I say? Things are busy. We are conducting a search for a new tenure-track position, and we have our full slate of classes to teach.

Drop by and say "hello," either in person or in the comments.