Teaching

This course is the second part of a standard undergraduate introduction to modern algebra. Topics covered include rings and fields. The course has a strong focus on writing complete proofs of abstract mathematical statements about algebraic objects.

I am teaching this course at The University of the South this semester.

This is a basic course in calculus. We cover limits, continuity, differentiation, optimization, related rates, Riemann sums, and simple integrals.

I am teaching this course at The University of the South this semester. I previously taught this course at Binghamton University in Spring 2016 and Fall 2015.

This course is a standard undergraduate introduction to modern algebra. Topics covered include elementary group theory (the vast majority of the course), ring theory (including polynomial rings), and some field theory time permitting. The course has a strong focus on writing complete proofs of abstract mathematical statements about algebraic objects.

I taught this course at The University of the South in Fall 2023.

Large portions of this course are adapted to the interests of the current students—in short, I don't intend to ever teach this course the same way twice. This is a mathematics course intended for students who are interested in how mathematics might be fun. We play some mathematical games (Tic-Tac-Toe, Nim, Go, etc.), solve some puzzles (logic puzzles about truth value, sudoku, etc.), and along the way we learn some mathematics to understand them. This includes some symbolic propositional logic, Aristotelian logic, rudimentary properties of integers, set theory, enumeration, and so forth. A strong emphasis is placed on developing abstract reasoning and critical analysis skills.

I taught this course at The University of the South in Fall 2023 and Spring 2023.

This is an introduction to the history of mathematics. In this course, I try to emphasize that mathematics is a discipline with diverse origins. We discuss what we know about the role of mathematics in ancient cultures (e.g., Babylonian and Egyptian mathematics), indigenous American cultures (e.g., the Khipu in Andean cultures), developments towards rigorous mathematics (e.g., Euclid's Elements), the history of the calculus, and developments in modern logic and set theory. Students each learn about a mathematician of their choosing during the course, ultimately writing a term paper on their life and discussing some of their mathematics. Other parts of the course are tailored to the interests of the current group of students as well.

I previously taught this course at The University of the South in Spring 2023.

This is an introduction to the basic mathematics necessary for computer science students. We cover propositional logic, proofs, elementary number theory, (naive) set theory, relations, functions, elementary enumeration, and some basic graph theory at a minimum. If I have time I cover some other topics; most often I cover finite state machines and automata.

I previously taught this course at The University of the South in Fall 2022, and at Binghamton University in Spring 2022, Spring 2021 (online), Spring 2020 (online), Spring 2019, Spring 2018, and Spring 2017.

This is a course in the basics of linear algebra. We cover Gaussian elimination, reduced row echelon form, geometry in 3-space, vector spaces, linear independence, bases and dimensions, linear maps, matrices and matrix operations, determinant, eigenspaces, diagonalization, orthogonality, symmetric matrices.

I previously taught this course at Binghamton University in Spring 2021 (online).

This is a basic course on multivariate calculus. We cover real vector spaces, operations on vectors, geometry in \( \mathbb{R}^3 \), space curves, calculus on functions of several variables, multivariate optimization, multiple integrals, calculus on vector fields, and calculus on surfaces.

I previously taught this course at Binghamton University in Spring 2022, Fall 2021, Fall 2020 (online), and Fall 2019.

This is a course on techniques of integration and the basics of sequences and series. We cover the Inverse Function Theorem, L'Hospital's Rule, integration techniques (including integration by parts, trigonometric substitutions, and partial fractions), improper integrals, parametric curves, sequences and convergence, and infinite series and convergence tests.

I taught this course at The University of the South in Fall 2022, and at Binghamton University in Fall 2018, Spring 2017, and Fall 2016.

This is a course on basic ordinary differential equations with a heavy emphasis on solving various standard types of equation. We cover solving linear, exact, and separable, and a variety of other ODEs, linear systems of ODEs, and some existence and uniqueness theorems for ODE solutions.

I previously taught this course at Binghamton University in Summer 2019.

This is a basic course in calculus, with a focus on the maths necessary for economics students. We cover limits, continuity, differentiation, integration, functions of several variables, and techniques for optimization (including multivariate techniques such as Lagrange multipliers).

I previously taught this course at Binghamton University in Summer 2018.

This is a basic course in college algebra, taught for the SUNY Educational Opportunity Program; this course is given at three levels: A, B, and C in order of increasing difficulty and pacing. The course covers polynomial and rational functions, factoring, polynomial operations, and other basic mathematics to assess and prepare BEP students for their college mathematics courses.

I previously taught this course at Binghamton University in Summer 2020 (C level online, co-taught with David Cervantes Nava), Summer 2018 (B level), Summer 2017 (C level), and Summer 2016 (C level).