Anton Betten

Dr. Anton Betten

Department of Mathematics

Colorado State University

Fort Collins, CO 80523

USA.

phone: (970) 491 1865

fax: (970) 491 2161

betten at math dot colostate dot edu

Welcome and Brief Bio

Hi! Thanks for stopping by. I am an associate professor of mathematics at Colorado State University (CSU). My research area is Combinatorics, with particular interests in designs, codes, and finite geometries. I received my Ph.D. from Bayreuth University in Bayreuth, Germany, under the supervision of Prof A. Kerber and Prof. R. Laue. In 2001/2002, I spent one year at the University of Western Australia to work with Cheryl Praeger on a class of designs. I joined CSU in 2002. At CSU, I teach graduate and undergraduate classes like Combinatorics, Cryptography, Information and Coding Theory, Linear Algebra, Calculus, etc. I have also been involved in developing two courses: A one credit module Mathematical Algorithms in Maple and a 3 credit bridge course Introduction to Mathematical Reasoning, aimed at easing the pain of transition from Sophomore to Junior level classes. I am a fellow of the Institute of Combinatorics and its Applications.

Teaching

In Fall 2008, I am teaching MATH501 Combinatorics I, MATH501 Combinatorics I

Previously, I taught:

Spring 08	MATH369 Linear Algebra	MATH152 Mathematical Algorithms with Maple	MATH261 Calculus III
Fall 07	MATH301 Introduction to Combinatorial Theory	MATH281 Introduction to Mathematical Reasoning
Spring 07	M460 Information and Coding Theory
Fall 06	M360 Mathematics of Information Security (Section 2)	M301 Introduction to Combinatorial Theory
Spring 06	M502 Combinatorics II	M460 Information and Coding Theory
Fall 05	M501 Combinatorics I	M360 Mathematics of Information Security
Spring 2005	M602 Advanced Combinatorics II	M152 Mathematical Algorithms with Maple
Fall 2004:	M601 Advanced Combinatorics I	M360 Mathematics of Information Security
Spring 2004	M602 Advanced Combinatorics II	M161 Calculus for Physical Sciences II
Fall 2003:	M601 Advanced Combinatorics I	M360 Mathematics of Information Security
Spring 2003:	M502 Combinatorics II	M366 Introduction to Abstract Algebra
Fall 2002:	M501 Combinatorics I

Advising and Research

I have advised the following graduate students:

Tom Edgar: Finite Projective Geometries and Linear Codes (Master's paper, Spring 2004)

Cayla McBee: Clique finding in graphs and the search for ovoids in polar spaces (Master's paper, Spring 2007)

Bader Al-Shamarey (Ph.D.): Two topics in combinatorial optimization: the domino portrait problem and the maximum clique problem. April 2007

Abdullah Al-Azemi (Ph.D.) Classification Algorithms for Graphs, Digraphs and Linear Spaces. Defense July 6, 2007.

Finite Geometry

Recently, I have been working on a class of objects called BLT-sets. These are sets of q+1 points on the parabolic quadric Q(4,q) (q odd) with the property that no two are collinear and no point of the quadric is collinear to more than two points in the set. These BLT sets are related to flocks of quadratic cones and hence (among other things) to translation planes of order q². By computer, I was able to extend the known classification results somewhat. I am in the process of summarizing my results on the following page:

BLT-page

Coding Theory

I have performed some classification work for linear codes. By computer, I obtained a classification (by semilinear isometry) of the best linear codes for small parameters. The following tables contain the results from this computation. Often I computed not only the best codes. Rather I computed all codes whose minimum distance is at least a given value.

GF(2) GF(3) GF(4) GF(5) GF(8) GF(9) GF(16) GF(25) GF(27)

Also, I have a table with bounds for the optimal minimum distance of binary linear codes. bounds

Design Theory

During my days as a grad student, I wrote a program for the construction of t-designs with large automorphism groups (together with people from Bayreuth University, Germany).

The program DISCRETA is available here

Here is a manual for DISCRETA

Rocky Mountain Discrete Mathematics Days, August 2-3, 2007 hosted by Colorado State University

Rocky Mountain Discrete Mathematics Days 2007

Talks

See here for a list of talks I gave

Publications

See here for a list of publications

Refereeing

I have refereed for Journal of Combinatorial Theory A, Discrete Mathematics, Discrete and Computational Geometry, Discrete Applied Mathematics, Designs, Codes, Cryptography, Journal of Combinatorial Designs, Séminaire Lotharingien de Combinatoire, Bayreuther Mathematische Schriften, The GAP group, and some agencies.

Photos

A Domino portrait of me:

A larger version

with Rudi Mathon, Anne Delandtsheer, Cheryl Praeger in Irsee (Germany), September 2006

Rohit Gosh, Anton Betten, Ka Hin Leung, Qing Xiang, Hans Havlicek, ?, Eun Ju Cheon and Tatsuya Maruta (left-to-right) in Germany, September 2006

File translated from T_EX by T_TH, version 3.81.
On 21 Aug 2008, 16:51.