Theoretical Linear Algebra, Spring 2024
Calculus II, Spring 2024
Calculus I, Fall 2023
Calculus III, Fall 2023
Linear Algebra, Fall 2022
An introduction to linear algebra with an exploration of applications through MATLAB assignments.
Multivariable Calculus, two sections, Spring 2022, two sections, Fall 2022
A course in vector calculus and 3D geometry for math and science majors and engineers.
Proof Writing through Discrete Mathematics, Spring 2022
A course to introduce math majors to rigorous mathematical thinking and proof-writing techniques using topics in discrete math.
Calculus A, three sections, Fall 2021
An introductory course in single variable calculus.
Study guides for the midterm tests, which summarized the material and identified skills students were expected to demonstrate on the tests.
An hour of weekly group work allowed students to interact with me and with each other in an informal and less structured setting.
Daily handouts helped to keep students actively engaged on lecture days.
I was the instructor of record for the following courses:
Math 4800 Graph Theory, Spring 2017
I received a University Teaching Assistantship, a one-year award that supports graduate students to spend one semester designing a course and the following semester teaching that course.
My application for the assistantship.
The course announcement advertised the course and the course syllabus articulates my main goals: to provide students with the chance to practice presenting mathematics and doing mathematics research.
Effective course materials: I selected a textbook that is modern, readable, streamlined, and contains interesting topics for further exploration to help students generate research ideas.
Student-driven course: students presented most of the material and participated in lively discussions. I met with students before their presentations to help them improve their exposition and provided detailed feedback to each student by email after each presentation.
Free exploration: students pursued research projects based on their own interests and ambitions. Students learned what it is like to look for problems to work on, review the literature, come up with conjectures, struggle to prove those conjectures, and grapple with long-standing open problems. Each student wrote up a summary of their efforts and findings in a final report, which was presented to the class.
Interesting problems to consider in a first course on graph theory.
Math 2270 Linear Algebra, Fall 2014 and Fall 2015
A first course in linear algebra.
Weekly quizzes based on recommended homework problems allowed students to do only as many practice problems as they felt they needed.
The midterm exams included "invention" problems emphasizing fluency with the concepts and definitions and ability to generate examples, which are valuable skills to develop.
I wrote these notes and a worksheet on linear transformations to supplement the textbook.
Student projects were a fun and engaging way to end the course. It was amazing to see some students whose performance had been average submit outstanding projects. Topics included using the Singular Value Decomposition to analyze elections or compress images, transformations for 3D graphics, symmetries of polygons and solids, the Fibonacci sequence, predator-prey modeling in finance, models of bacterial contamination, special relativity, facial recognition algorithms, and more.
Math 3210 Foundations of Analysis I, Fall 2013
A rigorous and intense introduction to analysis in one variable aimed at math majors.
Course syllabus, which includes advice for understanding definitions and theorems as well as a description of mathematics as a solitaire or multi-player game.
Worksheet for understanding limits.
Midterm exams contained four types of questions: Example (give an example), Computation (perform a calculation), Precision (give a precise statement), Proof (prove a claim).
Questionnaires were used to get feedback from students to make the course more effective.
Math 2200 Discrete Mathematics, Fall 2012 and Spring 2013
I shaped the course around learning how to write proofs. The topics covered were selected with this in mind. I incorporated a unit on graph theory because learning how to translate geometric intuition into algebraic rigor is essential in many areas of mathematics.
Course textbook, which I wrote based on my lecture notes from Fall 2012 and which was used by other instructors as well.
Syllabus and course plan from Spring 2013.
All midterm exams/quizzes from Spring 2013. I discovered that asking students to "prove or disprove" claims was an effective way to teach students to explore the veracity of claims.
Homework solutions from Spring 2013 were a way to provide feedback to students in addition to the comments on their individual homework assignments.
Final exam and review for the final from Spring 2013.
Epsilon Camp is an annual mathematics summer camp for gifted 7-11 year-olds. I taught two 2-week courses, which are described below. For students with such a high energy level, active engagement was essential. Outside of class, I greatly enjoyed playing sports, chess, and other games with the students.
Neutral Geometry (selected worksheets): this course was designed together with James Farre. Birkhoff's axioms for neutral geometry (with an SAS congruence axiom rather than the SAS similarity axiom that leads to Euclidean geometry) allow for a quick development of interesting results in geometry using proofs that are closely tied to ruler and protractor constructions. One highlight for the students was using the NonEuclid applet to visualize circles and geodesics in the disk model of hyperbolic geometry.
Graph Theory (daily handouts and final thoughts): graph theory is a wonderful way to quickly expose students of any level to beautiful theories in mathematics. Students contributed to the development of the theory and were actively engaged by working on problems, playing games, and sharing solutions. The most exciting topic for students was graphs on surfaces. In hindsight, the course could have been improved by: using proof by induction as a unifying theme, as it came up repeatedly and many students were not very comfortable with it; restructuring the course to be almost entirely student-driven; and covering fewer topics more deeply.
Theory of Everything, Spring 2015 (talk notes)
Abstract: Are you frustrated because pure mathematics courses like linear algebra, analysis, and modern algebra seem completely unrelated? Do you feel like you're starting from scratch every time you take a new math course? We will explore similarities among different fields of math by looking for structures that fit an abstract template called a "category". We will discuss this abstract template and touch lightly on examples from linear algebra, analysis, algebra, and more. Then we will see how a "functor" gives us the power to travel between two categories.
Is humanity doomed?, Spring 2016
Abstract: We will investigate a non-zero-sum game in which perfect rational play leads to disappointing results. Pessimists will be tempted to conclude that the selfish, rational human species won't last much longer, but we will see that there is room for optimism. Come ready to play and find out whether second graders are the true masters of game theory!
The Gory Harp, Fall 2016 (talk notes)
Abstract: What do knight's tours, map coloring, and the internet have in common? Their internal music is graphic.
What is Algebraic Geometry? (talk notes)
Finding a way to explain and prove a simple version of Bézout's theorem at the high school level was a fun challenge.