Hopf algebras are a natural extension of groups in noncommutative algebra. Most of my research explores the parallels of the two theories and connections that can be made between them.
keywords
Noncommutative Algebra, Group Theory, Hopf Algebras
MATH 1112  Mathematical Analysis in Business
Primary Instructor

Spring 2020 / Fall 2020 / Spring 2021 / Fall 2023
Gives students experience with mathematical problem solving in real business contexts. Students will work with data and spreadsheets to build and analyze mathematical models. Themes of the course include applying logical operators to model business rules, interpreting data and using tables and graphs, finding breakeven and optimal points, and addressing uncertainty and forecasting Degree credit not granted for this course and MATH 1012.
MATH 1212  Data and Models
Primary Instructor

Spring 2018 / Fall 2018 / Spring 2020
Engages students in statistical and algebraic problem solving through modeling data and real world questions taken from the social and life sciences. The course will emphasize these skills and the mathematical background needed for a university level statistics course. Credit not granted for this course and MATH 1011.
MATH 1300  Calculus 1
Primary Instructor

Summer 2023
Topics include limits, derivatives of algebraic and transcendental functions, applications of the derivative, integration and applications of the definite integral. Students who have already earned college credit for calculus 1 are eligible to enroll in this course if they want to solidify their knowledge base in calculus 1. For more information about the math placement referred to in the "Enrollment Requirements", contact your academic advisor. Degree credit not granted for this course and APPM 1345 or APPM 1350 or ECON 1088 MATH 1081 or MATH 1310 or MATH 1330.
MATH 2001  Introduction to Discrete Mathematics
Primary Instructor

Spring 2023 / Fall 2023
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 2300  Calculus 2
Primary Instructor

Spring 2019 / Fall 2019 / Fall 2022 / Spring 2023
Continuation of MATH 1300. Topics include transcendental functions, methods of integration, polar coordinates, differential equations, improper integrals, infinite sequences and series, Taylor polynomials and Taylor series. Department enforced prerequisite: MATH 1300 or MATH 1310 or APPM 1345 or APPM 1350 (minimum grade C). Degree credit not granted for this course and APPM 1360.
MATH 2400  Calculus 3
Primary Instructor

Summer 2018 / Spring 2022 / Summer 2022 / Fall 2022 / Spring 2023 / Summer 2023
Continuation of MATH 2300. Topics include vectors, threedimensional analytic geometry, partial differentiation and multiple integrals, and vector analysis. Department enforced prerequisite: MATH 2300 or APPM 1360 (minimum grade C). Degree credit not granted for this course and APPM 2350.
MATH 2510  Introduction to Statistics
Primary Instructor

Spring 2018 / Fall 2022 / Fall 2023 / Spring 2024
Elementary statistical measures. Introduces statistical distributions, statistical inference, hypothesis testing and linear regression. Department enforced prerequisite: two years of high school algebra.
MATH 3210  Euclidean and NonEuclidean Geometry
Primary Instructor

Spring 2023
Axiomatic systems; Euclid's presentation of the elements of geometry; Hilbert's axioms; neutral, Euclidean and nonEuclidean geometries and their models.
MATH 3430  Ordinary Differential Equations
Primary Instructor

Fall 2020 / Spring 2021 / Spring 2022 / Spring 2023
Involves an elementary systematic introduction to firstorder scalar differential equations, nth order linear differential equations, and ndimensional linear systems of firstorder differential equations. Additional topics are chosen from equations with regular singular points, Laplace transforms, phase plane techniques, basic existence and uniqueness and numerical solutions. Formerly MATH 4430.
MATH 3850  Seminar in Guided Mathematics Instruction
Primary Instructor

Spring 2018 / Fall 2018 / Spring 2019 / Fall 2019 / Fall 2020 / Spring 2021 / Spring 2022 / Fall 2022 / Spring 2023
Provides learning assistants with an opportunity to analyze assessment data for formative purposes and develop instructional plans as a result of these analyses. These formative assessment analyses will build on the literature in the learning sciences. Students gain direct experiences interacting with the tools of the trade, especially with actual assessment data and models of instruction. May be repeated up to 3 total credit hours. Restricted to learning assistants in Math.
MATH 4510  Introduction to Probability Theory
Primary Instructor

Spring 2018 / Summer 2018 / Spring 2019 / Summer 2019 / Fall 2019 / Spring 2020 / Summer 2020 / Summer 2021 / Summer 2023
Studies axioms, combinatorial analysis, independence and conditional probability, discrete and absolutely continuous distributions, expectation and distribution of functions of random variables, laws of large numbers, central limit theorems, and simple Markov chains if time permits. Degree credit not granted for this course and APPM 3570 or ECEN 3810 or MATH 3510. Same as MATH 5510.
MATH 5510  Introduction to Probability Theory
Primary Instructor

Summer 2018 / Spring 2019 / Summer 2019 / Fall 2019 / Summer 2021 / Summer 2023
Studies axioms, combinatorial analysis, independence and conditional probability, discrete and absolutely continuous distributions, expectation and distribution of functions of random variables, laws of large numbers, central limit theorems, and simple Markov chains if time permits. Same as MATH 4510.
MATH 6350  Functions of a Complex Variable 1
Primary Instructor

Spring 2019
Focuses on complex numbers and the complex plane. Includes CauchyRiemann equations, complex integration, Cauchy integral theory, infinite series and products, and residue theory. Department enforced prerequisite: MATH 4001. Instructor consent required for undergraduates.