Department of Mathematical Sciences
Florida Atlantic University
Boca Raton, Florida 33431-0991, USA
Courses Taught
Markus Schmidmeier
At Charles University, Prague, 1996-1998 Representation Theory of Finite Dimensional Algebras. (Spring 1998, Prague)
Endofinite Modules (Spring 1999, Prague)
This is an introduction to the representation of finite dimensional algebras. We cover basics from homological algebra, the duality and the transpose, and introduce Auslander-Reiten sequences. As examples we consider path algebras of finite quivers. Aim is Gabriel's theorem in which the hereditary algebras of finite representation type are classified.
Literatur: M. Auslander, I. Reiten, S. O. Smaloe, Representation Theory of Artin Algebras, Cambridge Studies in Advanced Mathematics,36, Cambridge University Press 1995.
An introduction to endofinite modules (which are modules that have finite length when considered as modules over their endomorphism ring).
Literature: W. Crawley-Boevey, Modules of finite length over their endomorphism ring, in: Representations of Algebras and Related Topics, London Math. Soc. Lect. Notes Series 168, Cambridge University Press 1992.Knot Theory and Quantum Groups (Fall 1998, Prague)
In this course we give an introduction to the representation theory of the quantum groups $U_q(sl_2)$. As a byproduct, we can show the existence of a powerful invariant for knots and links, the Jones polynomial.
Literature: Chr. Kassel, Quantum Groups, Graduate texts in Mathematics 155, Springer 1995.Modular Representation Theory of Groups (Spring 1999, Prague)
In this lecture we study the operation of finite groups on k-vectorspaces. Of particular interest is the modular case, in which the characteristic of k is finite and divides the order of the group.
Literature: J. L. Alperin, Local representation theory, Cambridge studies in advanced mathematics 11, Cambridge University Press 1986/
At Florida Atlantic University, Boca Raton, since 1999 The Maple Programming Language (Fall 1999)
Calculus I (Fall 1999 , Spring 2004)
Calculus II (Spring 2000 , Fall 2001, Spring 2005)
Calculus III (Fall 2000, Spring 2001, Spring 2003, Spring 2006, and Spring 2007)
Differential Equations (Fall 2001),
Matrix Theory (Spring 2002, Fall 2002, Spring 2003, and Fall 2003),
Introductory Number Theory MAS 3203 (Fall 2007)
Modern Algebra (Summer 2003, Spring 2004, Fall 2006)
Mathematical Problem Solving (MAT 4937) (Spring 2006)
Seminar Algebraic Topology (with Dr. Klingler and Dr. Kallies, Fall 2002).
Seminar Young Tableaux (with Dr. Freeman, Fall 2004).
Seminar Cohen Macauley Modules (with Dr. Klingler and Dr. Richman, Spring 2006).
Coding Theory (MAD 6607 and MAD 4605/MAT 5932) (Fall 2004, Spring 2005)
Introductory Cryptography (MAT 4930 / MAT 5932) (Fall 2003, and Fall 2004),
Number Theory and Cryptograpy (Fall 2002),
Homological Algebra (Spring 2001)
Introductory Abstract Algebra (MAS 5311) (Fall 2006)
Introductory Abstract Algebra II (MAS 5312) (Spring 2007).
Abstract Algebra I: Module Theory (MAS 6313) (Fall 2007).
At the Norwegian University of Science and Technology, Trondheim, Fall 2005 Homological Algebra (Fall 2005)
Last modified: by Markus Schmidmeier