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Dr. Elisha Peterson

Assistant Professor/Davies Fellow
United States Military Academy

Office: Thayer 252
Phone: 845-938-5649

Currently teaching MA153 (advanced multivariable calculus), MA493D (topology), and overseeing MA498/499 (the honors research program).

About

Mathlets

APPLET OF THE WEEK: the Lorenz differential equations

Teaching

Students

  • James Lee '09 (Math): trace diagrams, linear algebra, and invariant theory
  • Lucas Gebhart '09 (OR): cooperation in pursuit and evasion games
  • Daniel Ball '08 (Math): Cooperative Linear Pursuit
  • Steven Morse '08 (Honors Math): Diagramming Linear Algebra: Some Results and Trivial Proofs (PDF)
  • Andrew Plucker '08 (Honors Math): Pursuit and Evasion Modeling: the Effect of Leading (DOC)

Technology

Java Applets

  1. PEG: an applet for pursuit-evasion games; see the linear version.
  2. Blaise: function plotter, vector field plotter, a cool space-filling curves applet, and lots more!
  3. A long time ago at Harvey Mudd, I worked on the Fair Division Calculator, which was featured in Science Magazine.
I use and highly recommend NetBeans for programming in Java.

Talks & Papers on Teaching with Technology

  1. "Using a Wiki to Enhance Cooperative Learning in a Real Analysis Course", PRIMUS, to appear early 2009.
  2. "Dynamic Mathematics and Pursuit-Evasion Games" PDF Slides and PPTX Slides and Applets Page, USMA Department of Mathematics Center for Faculty Development (Colloquium), 20-Nov-08.
  3. "Online Collaboration with a Wiki in Real Analysis" PPT Slides, session on Creative Uses of Emerging Technologies for Mathematics Teaching, MathFest 2008, 1-Aug-08.
  4. "Creating a Dynamic Cobwebbing Demonstration with Geogebra" online tutorial, Jul-08.
  5. "Visualizing Lagrange Multipliers: a Discovery Approach to Constrained Optimization" PDF Slides and Demo Page, MAA session on Demos and Strategies with Technology that Enhance Teaching and Learning Mathematics, JMM 2008, 7-Jan-2008.

Research

Trace Diagrams Research Page
Pursuit-evasion games Applet

Interests

  • Trace Diagrams (spin networks) and applications to linear algebra, invariant theory, moduli spaces, character varieties, and geometric structures
  • Game theory and multi-agent systems, particularly the mathematics of cooperation int he context of pursuit-evasion games
  • Graph theory and its applications; Sperner's Lemma; fair division
  • Technology and visual aesthetics in the communication and teaching of mathematics

Selected Papers & Preprints (complete list)

  1. "Computing SL(2,C) Central Functions with Spin Networks" with Sean Lawton (in preparation).
  2. "Cooperation in Social Networks: Communication, Trust, and Selflessness" PDF with Chris Arney, Proceedings of the 2008 Army Science Conference (chosen Best Paper in the Advanced Modeling and Simulation Category and 3rd Best Paper Overall).
  3. "Spin networks and SL(2,C)-character varieties" PDF with Sean Lawton (arXiv: math.QA/0511271), to appear in The Handbook of Teichmuller Theory, Vol. II, 2008.
  4. "Trace Diagrams, Representations, and Low-Dimensional Topology" PDF, PhD Thesis at the University of Maryland, 2006.
  5. "A Polytopal Generalization of Sperner's Lemma" with Francis Su & Jesus deLoera, Journal of Combinatorial Theory Series A, 2002.
  6. "Combinatorial Proofs of Generalizations of Sperner's Lemma" PDF, undergraduate thesis at Harvey Mudd College, 2000.

Recent Talks on Trace Diagrams

  1. "Signed Graph Coloring, the Art of Linear Algebra, and a Theorem of Jacobi" PDF Slides, MathFest 2008, 31-Jul-08.
  2. "The Character Variety's New Clothes" PDF Slides, AMS Session on Algebra and Number Theory, JMM 2008, 7-Jan-08.
  3. "The Art of Linear Algebra" PDF Slides and PDF Handout, USMA Math Department Research Seminar, 5-Dec-07.
  4. "Trace Diagrams, Spin Networks, and Spaces of Graphs" PDF Slides and "Diagrammatic Central Functions" PDF Slides, talks at the 7th KAIST Geometric Topology Fair in Gyeongju, Korea, 10-Jul-07.
  5. "Trace Diagrams, Surfaces, and Character Varieties" PDF Slides, colloquium at Kansas State University, 15-Apr-07.
  6. "Trace Diagrams, Surfaces, and Low-Dimensional Topology" PDF Slides, PhD Defense, 25-Apr-06.

Recent Talks on Cooperation & Pursuit-Evasion

  1. "Communication in Social Networks: Communication, Trust, and Selflessness" PPTX, Army Science Conference, Modeling and Simulation Track, 2-Dec-08.
  2. "The Mathematics of Altruism and Selfish Cooperation" PPTX, ARL-USMA Technical Symposium, 23-Oct-08.
  3. "Altruism and Selfish Cooperation in Social Networks" PPTX, USMA Network Science Workshop, 16-Oct-08.
  4. "Cooperating Teams in Pursuit-Evasion Games" PPT, ARL-USMA Technical Symposium, 30-Oct-07.
  5. "Social Network Optimization and Synergy in Cooperative Systems: Trust & Selflessness" PPT, USMA Network Science Workshop, 23-Oct-07.
I use LaTeX for typesetting, including the MikTeX package, TeXnicCenter or WinEdt for editing/compiling, Beamer for slides, and PGF/TiKZ for figures.

Biography

Elisha Peterson was born in Oregon on September 11, 1980. After a brief sojourn in Haiti, his family settled in a small California town named Oakhurst 13 miles outside Yosemite National Park. He graduated from Yosemite High School in 1996, and was accepted to Harvey Mudd College in Claremont, CA, where students sing songs about slide rules and unicycle while juggling. He couldn't use a slide rule, unicycle, or juggle, but did memorize 314 digits of pi to make sure he fit in. He also ran Division III cross country and track for the combined Claremont McKenna/Harvey Mudd team. During the summer, he spent one year doing research in Combinatorics and Fair Division, and the next two in the Director's Summer Program at the [censored] [censored] Agency. His only memory from this time is one very brilliant flash of light, although he discovered after returning from [cens ored...] that he could juggle. He was selected as a Rhodes Scholar on a December night his senior year at Harvey Mudd and consumed his first beverage at a cross country party later that night. He matriculated in September 2000 to Oxford University. There he ran with the oldest and muddiest cross country club in the world, spent his early mornings rowing on the Thames for Magdalen College, traveled in Europe, and theoretically worked on research involving knot theory, surgery, and hyperbolic volume. In 2002 he returned to Maryland and married Jennifer, a classmate from Harvey Mudd College. The wedding did not take place in the Camp Mabry chapel in Austin as planned, one small consequence of an event that occurred on his 21st birthday. In August 2002 he began his doctoral studies at the University of Maryland. He found a mathematician scratching his head over some doodles on a chalkboard one day, and decided it would be fun to write equations using pictures so mathematicians wouldn't recognize them. Those doodles became his PhD thesis, which was formally called "Trace Diagrams, Representations, and Low-Dimensional Topology". As was pointed out in his thesis defense, the only low-dimensional topology in his thesis is the drawing of a pair of pants on the front cover. After successfully typesetting and defending his PhD thesis in April of 2006, he joined the Math Department at the United States Military Academy. He was thrilled in January 2007 to become the father of Micah Andrew Peterson. The little guy can't tell directions very well, but he seems anxious to digest calculus and does function continuously.



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