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
Primary Instructor
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Spring 2018 / Spring 2020 / Fall 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. Credit not granted for this course and MATH 2002.
MATH 2130 - Introduction to Linear Algebra for Non-Mathematics Majors
Primary Instructor
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Fall 2021
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 do not plan to major in Mathematics. Degree credit not granted for this course and MATH 2135 or APPM 3310. Formerly MATH 3130.
MATH 2135 - Introduction to Linear Algebra for Mathematics Majors
Primary Instructor
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Fall 2018 / Spring 2019 / Fall 2019 / Fall 2024
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 3140 - Abstract Algebra 1
Primary Instructor
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Fall 2021 / Spring 2024
Studies basic properties of algebraic structures with a heavy emphasis on groups. Other topics, time permitting, may include rings and fields.
MATH 4000 - Foundations of Mathematics
Primary Instructor
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Fall 2024
Focuses on a complete deductive framework for mathematics and applies it to various areas. Presents Goedel's famous incompleteness theorem about the inherent limitations of mathematical systems. Uses idealized computers to investigate the capabilities and limitations of human and machine computation. Same as MATH 5000.
MATH 4140 - Abstract Algebra 2
Primary Instructor
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Spring 2024
Explores some topic that builds on material in MATH 3140. Possible topics include (but are not limited to) Galois theory, representation theory, advanced linear algebra or commutative algebra. Same as MATH 5140.
MATH 5000 - Foundations of Mathematics
Primary Instructor
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Fall 2024
Focuses on a complete deductive framework for mathematics and applies it to various areas. Presents Goedel's famous incompleteness theorem about the inherent limitations of mathematical systems. Uses idealized computers to investigate the capabilities and limitations of human and machine computation. Department enforced prerequisites: MATH 2130 and MATH 3140. Same as MATH 4000.
MATH 5140 - Abstract Algebra 2
Primary Instructor
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Spring 2024
Explores some topic that builds on material in MATH 3140. Possible topics include (but are not limited to) Galois theory, representation theory, advanced linear algebra or commutative algebra. Department enforced prerequisite: MATH 3140. Same as MATH 4140.
MATH 6010 - Computability Theory
Primary Instructor
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Spring 2019 / Spring 2021 / Fall 2023
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
Primary Instructor
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Spring 2018 / Spring 2022
Studies modules, fields and Galois theory. Department enforced prerequisite: MATH 6130. Instructor consent required for undergraduates.
MATH 6270 - Theory of Groups
Primary Instructor
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Fall 2019
Studies nilpotent and solvable groups, simple linear groups, multiply transitive groups, extensions and cohomology, representations and character theory, and the transfer and its applications. Department enforced prerequisites: MATH 6130 and MATH 6140. Instructor consent required for undergraduates.
