|Christian G J Roettger
Office 463 Carver
Amongst other things, I am interested in
Galois Theory and the Ring of Sauron
Combinatorics/Algebra Seminar, ISU, April 24, 2017 Consider a polynomial f(x) over a field k with degree n and discriminant D. The Galois group G of f(x) can be viewed a a subgroup of the symmetric group Sn via its action on the roots of f(x). It is a well-known application of Galois Theory that G is contained in the alternating group An exactly if D is a square in the ground field k. Moreover, if this is not the case, then sqrt(D) generates the fixed field of the intersection of G with An. We are looking for formulas that generalize this - i.e., for any transitive subgroup H of Sn, find expressions in the coefficients of a generic polynomial of degree n which are in the ground field exactly if G is contained in H, and which generate the fixed field of the intersection of G and H otherwise. At first, it is not even clear that such expressions have to exist. But they do, and they in principle provide a way to determine G. Practical computations are lengthy and best done by computer, but the theory is very appealing and natural. In particular, we use multivariate polynomial rings and classical representation theory of finite groups (in a very basic way).
Joint work with John Gillespie.
Rashomon - Reconstructing Reality
from inexact measurements
Joint work with H Hofmann, D Cook.
MAA section meeting, Graceland University, Lamoni, IA, Oct 3, 2015
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).
Math 165: Calculus I
Math 181: Calculus For the Life Sciences I
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 166: Calculus II (recitations only)
Math 166H: Honors Calculus II
Math 195: Math for Elementary Education
Math 265: Calculus III
Math 267: Differential Equations, Laplace Transform
Math 297: Intermediate Topics in Elementary Mathematics
Math 301: Algebra I
Math 307: Matrices and Linear Algebra
Math 314: Graphs and Networks
Math 317: Theory of Linear Algebra
Math 350: Elementary Number Theory
Course notes for Analytic Number Theory
General advice, frequently asked questions
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