My core interests tend to cycle around combinatorics, universal algebra, and category theory. I enjoy exploring the logic uniting these disciplines and developing their applications outside of mathematics.
Division by Zero: Development of a Relevant Algebra with Historical Context
Scholars' Day
Monroe Community College
1
2013
An Introduction to Hyperspace with a Construction of the 4-Cube
Math Awareness Month
Monroe Community College
Teaching
Advice for mathematics students
Math 8174 Algebraic Theories (2026 Spring)
Math 2001 Discrete Mathematics (2026 Spring)
Math 2130 Linear Algebra for Non-Math Majors (2025 Fall)
Math 3140 Abstract Algebra (2025 Spring)
Math 2130 Linear Algebra for Non-Math Majors (2025 Spring)
Math 2130 Linear Algebra for Non-Math Majors (2024 Fall)
Math 1952 Calculus II (2024 Spring)
Math 1150 Elementary School Mathematics from the Year 2100 (2024 Winter)
Math 2060 Elements of Linear Algebra (2023 Fall)
Math 1951 Calculus I (2023 Fall)
Math 1953 Calculus III (2023 Spring)
Math 1150 Social Choice Theory: The Mathematics of Voting and Social Welfare (2023 Winter)
Math 2060 Elements of Linear Algebra (2022 Fall)
Math 1951 Calculus I (2022 Fall)
Math 165 Linear algebra with differential equations (2021 Summer) Universal algebra and lattice theory lectures (2020 Fall)
Math 162 Calculus IIA (2020 Summer)
Other teaching experience may be found in my CV.
History
I did my graduate studies at the University of Rochester, where my PhD advisor was Jonathan Pakianathan. This chart shows my detailed mathematical lineage, as determined by The Mathematics Genealogy Project. My first postdoctoral position was at the University of Denver, where I worked with Michael Kinyon. My second postdoctoral position was at the University of Colorado Boulder, where I worked with Keith Kearnes.
A proof that everything can be described using mathematics: Recall that mathematics is the study of abstract relationships. Suppose towards a contradiction that there is some thing, say A, which is not describable in terms of math. "X is not describable in terms of Y" is a relationship between X and Y. We have then exhibited a relationship between A and math, which is a mathematical descriptor of A, contradicting our assumption that A was not amenable to such descriptions.