# Louis A. Talman, Ph.D.

## Emeritus Professor of Mathematics

Metropolitan State University of Denver

### Areas of Interest:

- Functional Analysis–Non-linear analysis; fixed point theory; differential equations; dynamical systems
- Role of Technology in Mathematics–Mathematica, Maple, etc

### Education:

- Ph. D. University of Kansas, 1975
- M.A. University of Kansas, 1973
- B.A. College of Wooster, 1966

### Selected Papers

- “Simpson’s Rule is Exact For Quintics,”
*American Mathematical Monthly*,**113**(2006), 144-155.**Abstract:**In this article, we use tools accessible to freshman calculus students to develop exact—though usually uncomputable—expressions for the error that results in replacing a definite integral with its midpoint rule, trapezoidal rule, or Simpson’s rule approximation. Among the tools we use is an extended version of the first mean value theorem for integrals. We obtain not only the classical estimates that appear in calculus books, but estimates for functions less smooth than the classical results require. We show, in particular, how to compute the exact error for a Simpson’s rule approximation to an integral of a quintic polynomial. - A Remarkable Concurrence: a short note in Portable Document Format (PDF). In May of 1999, Steve Sigur posted a note to the College Geometry Forum in which he mentioned a conjecture of Adam Bliss, who was then one of his students. A few days later, I put this proof up on this site (LaTeX and PDF being a much easier way to communicate the symbols than an ASCII post to a list-serve). In it I establish the main part of Bliss’ conjecture. I’d actually removed the link from this site until someone sent me a note (on March 5, 2001) saying that Floor van Lamoen had cited the note in his paper “Morley Related Triangles on the Nine-Point Circle” [
*Amer. Math. Monthly,*Vol. 107, 2000, pp 941–945], and asking how to get access. So I thought I probably ought to put it back. Here it is. Addenda: (1) I learned on July 21, 2001, that Bruce Shawyer had cited my proof in his note “Some Remarkable Concurrences” [*Forum Geometricorum,*Vol. 1, 2001, pp 69–74]. (2) More recently, Charles Thas cited this note in his paper “Projective Generalizations of Two Points of Concurrence on the Nine-Point Circle” [*Amer. Math. Monthly,*Vol. 110, 2003, pp 624–627]

This site is currently (05/22/2017) under construction to replace my old site. Much of my old stuff is accessible here, on the Department of Mathematical and Computer Science’s server. However, I don’t have easy access to that server now that I’m retired, so this will be my site for the foreseeable future.