My main research area is Universal Algebra with connections to Logic and Computer Science. General algebraic structures come up for example in connection with Constraint Satisfaction Problems (CSP) which generalize Boolean satisfiability, graph coloring, and scheduling problems. A typical question is then how to classify and represent these structures and how to compute with them efficiently.
MATH 2001 - Introduction to Discrete Mathematics
Spring 2018 / Spring 2020
Introduces the ideas of rigor and proof through an examination of basic set theory, existential and universal quantifiers, elementary counting, discrete probability, and additional topics. Department enforced prerequisite: MATH 1300 or MATH 1310 or APPM 1345 or APPM 1350 (minimum grade C-).
MATH 2135 - Introduction to Linear Algebra for Mathematics Majors
Fall 2018 / Spring 2019 / Fall 2019
Examines basic properties of systems of linear equations, vector spaces, inner products, linear independence, dimension, linear transformations, matrices, determinants, eigenvalues, eigenvectors and diagonalization. Intended for students who plan to major in Mathematics. Degree credit not granted for this course and MATH 2130 or APPM 3310. Formerly MATH 3135.
MATH 6010 - Computability Theory
Studies the computable and uncomputable. Shows that there are undecidable problems and from there builds up the theory of sets of natural numbers under Turing reducibility. Studies Turing reducibility, the arithmetical hierarchy, oracle constructions and end with the finite injury priority method. Department enforced prerequisite: MATH 6000.
MATH 6140 - Algebra 2
Studies modules, fields and Galois theory. Department enforced prerequisite: MATH 6130. Instructor consent required for undergraduates.