Christian G J Roettger Office 463 Carver Phone 294-8164 |

Amongst other things, I am interested in

- Asymptotic counting problems
- Discrete dynamical systems
- Kloosterman sums and uniform distribution
- Diophantine approximation
- Representations of finite groups
- Finite fields, Galois rings

**Rashomon - Reconstructing Reality**
from inexact measurements

Joint work with H Hofmann, D Cook.

MAA section meeting, Graceland University, Lamoni, IA, Oct 3, 2015

Here are
slides.

The art installation 'Rashomon' was displayed on the Iowa State University campus during summer 2015. It consists of 15 identical, abstract sculptures. Artist Chuck Ginnever posed the challenge whether it is possible to display the sculptures so that no two of them are in the same position (modulo translation/rotation). We investigated the related question of reconstructing such a sculpture from (ordinary tape-measure) inexact measurements. Mathematics involved are the Cayley-Menger determinant, and the gradient method / Steepest Descent. We'll explain the mathematics with some simple examples and then show the results of our reconstruction. We will only assume elementary linear algebra (matrix - vector multiplication, determinants).

**Visual Hypothesis Testing - Lineups and Probability**

MAA section meeting, Clarke University, Dubuque, IA, Oct 14, 2014

Police use lineups involving one suspect and several 'dummies' to get evidence that a witness can identify the suspect. In an abstract sense, we can form a hypothesis about 'suspect' data and test it in this way: literally have people looking at a lineup of plots with the task of identifying the data plot among the dummies. Repetition with several observers makes this approach surprisingly powerful. It also has potential when comparing the efficiency of different visual representations of the same data. Disclaimer: do not expect analysis of actual police lineups. But we will try out the method on the audience! This is joint work with Heike Hofmann, Di Cook, Phil Dixon, and Andreas Buja. I have investigated the underlying probability distributions. This meant evaluating some multiple integrals, and revising all the tricks from Calculus II.

Math 166: Calculus II (recitations only)

Math 105: Introduction to Mathematical Ideas.

We examine the mathematics of voting systems.Math 141/142 Trigonometry (and analytic geometry)

Math 151: Calculus for Business and Social Sciences

Math 181: Calculus For the Life Sciences I (needs some updating)

Math 195: Math for Elementary Education

Math 267: Differential Equations, Laplace Transform

Math 297: Intermediate Topics in Elementary Mathematics

Math 307: Matrices and Linear Algebra

Math 317: Theory of Linear Algebra

Math 350: Elementary Number Theory

Course notes for Analytic Number Theory

**My Favorite Quote:**"Should array indices start at 0 or 1? My compromise of 0.5 was rejected without, I thought, proper consideration." -
Stan Kelly-Bootle

Pros and cons of metric vs imperial system.

This webpage is http://www.public.iastate.edu/~roettger/homepage.html

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