 John Tolle
Lecturer
Ph.D., University of Kentucky
Office: Wean Hall 7209
Phone: (412) 268-3307
E-mail: tolle@andrew.cmu.edu
Teaching & Research Interests:
My dissertation (1996) was in an applied area of mathematics: Partial Differential Equations. The title was 'Location of Inhomogeneities in Elastic Media', and the work dealt with the mathematical modeling of testing materials for internal defects. The question was, If you perform response tests on the external surface of a material with known elastic properties, can you develop a profile of the material?s interior? If so, how complete/reliable is that profile? In particular, can you detect inclusions and determine their precise shapes and locations?
I joined the Mathematical Sciences Department in 1996. My main focus is undergraduate instruction and curriculum development. I also serve on the Small Undergraduate Research Grant selection committee, and in the summers teach a mathematics preparatory course for the Master of Science in Computational Finance program. I have also taught in, or directed research projects in, the Summer Undergraduate Applied Mathematics Institute.
I still love the enterprise of differential equations modeling, and co-wrote a paper with 2005 CMU alumna Francesca Reale on the subject of modeling a multi-species predator-prey ecosystem subject to external environmental effects. Our work involved extensive simulations using Matlab.
Other interests include the modeling of influence, power, and initiative in social choice theory. For example, in a weighted voting system wherein each party (not necessarily a political party) casts a bloc of votes rather than a single vote, how does one measure the relative "power" among the various parties? In 2001, Summer Institute students Jabari Harris and Christopher Carter Gay and I worked in this area and wrote up some results.
In 2003 I joined the Open Learning Initiative and began development of a fully-online, self-contained Differential and Integral Calculus course. This course will allow for self-directed study, free and open to any individual with internet access, who may enroll anonymously if desired.
And in my "copious spare time", I'm working on a text called 'Introduction to Applied Analysis'. Projected table of contents here: http://www.math.cmu.edu/~tolle/appliedanalysis.pdf. Chapters 0 through 11 are mostly complete (as of Fall 2005). The text is intended for graduate students outside of Mathematics departments (e.g., in physics, economics, engineering, finance) who need some of this advanced material but not at the level of rigor expected of Mathematics students.
|
