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.