Teaching

Current and Upcoming Teaching

Spring 2025MATH 2185: Comprehensive Introduction to Linear AlgebraSyllabus
Spring 2025MATH 3125: Linear Algebra IISyllabus

Thesis Advising

PhD theses

Charlene Houchins, GWU PhD student (co-advised with Xingting Wang)
Charly is working to understand automorphism groups of certain Poisson algebras. She passed her specialty exam with distinction in October 2024, and is expected to graduate in spring 2026.

Undergraduate theses

Tim Neumann, GWU undergraduate
Tim defended his senior thesis “On m-general sets in AG(k, q) and PG(k, q): Sidon sets, projective arcs and error-correcting codes” in May 2024. While at GWU, he won the department’s Ruggles Prize (best undergraduate math major) and the Marvin Green Prize (best use of computation). He submitted “A new construction for large Sidon sets in AG(k, 3)” to the Pi Mu Epsilon Journal.

As of fall 2024, Tim is an MSc student in Quantum Information Science & Technology at Delft University of Technology.

YouTube Courses

Advanced Linear Algebra: Tools and ApplicationsCourse page
Linear Algebra Done RightCourse page
Introduction to Mathematical ProofCourse page

Past Teaching

George Washington University

Fall 2024MATH 2184: Linear AlgebraSyllabus
Course Notes
Fall 2024MATH 4121: Introduction to Abstract Algebra ISyllabus
Course Notes
Fall 2024MATH 6995: Reading and Research
I led a reading course on finite affine geometry for GWU undergraduate Leehe Peleg.
Spring 2024MATH 4122: Introduction to Abstract Algebra IISyllabus
Course Notes
Spring 2024MATH 6995: Reading and Research
I led a reading course on various topics in abstract algebra for GWU PhD students students Anthony Christiana, Ben Clingenpeel, Jake Rhody and Paula Souza.
Spring 2024MATH 4995: Reading and Research
Mentored undergraduate thesis research for GWU undergraduate Tim Neumann.
Fall 2023MATH 1232: Single Variable Calculus II
Section 10		Syllabus
Fall 2023MATH 4121: Introduction to Abstract Algebra ISyllabus
Course Notes
Fall 2023MATH 4995: Reading and Research
Mentored undergraduate thesis research for GWU undergraduate Tim Neumann.
Spring 2023MATH 3125: Linear Algebra IISyllabus
Course Notes
Spring 2023MATH 2185: Linear Algebra I for Math MajorsSyllabus
Course Notes
Fall 2022MATH 6101: Algebra I (Graduate course)Syllabus
Course Notes
Fall 2022MATH 1231: Single Variable Calculus I
Section 15		Syllabus
Spring 2022 MATH 2185: Linear Algebra I for Math Majors Syllabus
Fall 2021 MATH 6101: Algebra I (Graduate course)
Class photo 		Syllabus
Fall 2021 MATH 4121: Introduction to Abstract Algebra I
Class photo 		Syllabus

University of Washington

Spring 2021MATH 318: Advanced Linear Algebra: Tools and Applications
Online due to COVID-19.		Syllabus
Winter 2021MATH 300: Introduction to Mathematical Reasoning
Online due to COVID-19.
How do I type up my homework?		Syllabus
Autumn 2020MATH 300: Introduction to Mathematical Reasoning
Online due to COVID-19.
How do I type up my homework?		Syllabus (Section B)
Syllabus (Section C)
Course Notes
Summer 2020MATH 340: Abstract Linear Algebra
Online due to COVID-19.
How do I type up my homework?		Syllabus
Course Notes
Winter 2020MATH 300: Introduction to Mathematical Reasoning
Sections A and B
Class photo A and Class photo B		Syllabus (Section A)
Syllabus (Section B)
Winter 2020MATH 399: The card game SET and finite affine geometry
I continued mentoring this Washington Experimental Mathematics Lab (WXML) project which started in Autumn 2019 with four undergraduate students (Ivy Guo, Jocelin Liteanu, Avery Milandin, and Zoey Shi) and graduate TA Peter Gylys-Colwell. We worked to understand equivalence classes of 2-caps under the actions of affine transformations.		Project Description
Autumn 2019MATH 308: Matrix Algebra with Applications
Sections K and L
Class photo K and Class photo L		Syllabus (Section K)
Syllabus (Section L)
Course Notes
Autumn 2019MATH 399: The card game SET and finite affine geometry
I mentored a project through the Washington Experimental Mathematics Lab (WXML). A group of three undergraduate students (Jocelin Liteanu, Jaron Wang, and Alexander Waugh), along with graduate TA Peter Gylys-Colwell learned about finite affine geometry and wrote programs to find and visualize caps in affine spaces of order 3. They gave an eight-minute talk about their work at the end of the quarter. Jaron maintains the GitHub repository for our work.		Presentation
GitHub Repository
Summer 2019
Term B		MATH 412: Introduction to Modern Algebra for Teachers
Class photo		Syllabus
Summer 2019MATH 324: Advanced Multivariable Calculus
(Co-instructed with Jonathan Beardsley)
Class photo
Spring 2019MATH 308: Matrix Algebra with Applications
Class photo		Syllabus
Winter 2019MATH 308: Matrix Algebra with Applications
Sections E and F
Class photo E and Class photo F		Syllabus (Section E)
Syllabus (Section F)
Autumn 2018MATH 308: Matrix Algebra with Applications
Class photo		Syllabus

Wake Forest University

Summer 2018WFU Research Fellowship: Generalizations of capsets in affine spaces of order 3
I mentored Wake Forest undergraduate Yixuan (Alice) Huang who won a Wake Forest Research Fellowship to work with me on a project in affine geometry. Together with Michael Tait, we wrote the paper Sidon sets and 2-caps in F3n.		Alice’s Poster
Spring 2018MST 117: Discrete Mathematics
Class photo		Syllabus
Spring 2018MST 722: Abstract Algebra (Graduate course)
Class photo		Syllabus
Fall 2017MST 121: Linear Algebra
Class photo		Syllabus
Course Notes
Fall 2017MST 721: Abstract Algebra (Graduate course)
Class photo
(An important rule of group theory, needlepointed by Beth Matys.)		Syllabus
Spring 2017MTH 109: Elementary Probability and Statistics
Sections H and I		Syllabus
Fall 2016MTH 111: Calculus with Analytic Geometry I
Sections I and J		Syllabus
Fall 2016Informal Reading Course
I led a reading group of four Masters students (Mike Annunziata, Katie Greene, Rebecca Kotsonis, and Rob McConkey) in which we read Ellenberg and Gijswijt’s paper (then preprint) On large subsets of Fqn with no three-term arithmetic progression.

University of California San Diego

As Associate Instructor

Summer 2015Math 3C: PrecalculusSyllabus

As Teaching Assistant

Winter 2015Graduate-Undergraduate Learning Program: Finite affine geometry
Together with Michael Tait, I advised UCSD undergraduates Yuhui Jin, Kyle Lee, and Esther Wang on a reading project on finite affine geometries and their connections to the card game SET. This was organized through UCSD AWM’s Graduate-Undergraduate Learning Program (GULP). The students gave a presentation at the end of the quarter.
Fall 2015Math 140A: Real Analysis
Spring 2015Math 200C: Graduate Algebra
Winter 2014Math 200B: Graduate Algebra
Fall 2014Math 200A: Graduate Algebra
Summer 2014Math 20C: Calculus for Science and Engineering III
Spring 2014Math 142B: Introduction to Analysis II
Sections A01 and A02
Winter 2013Math 142A: Introduction to Analysis I
Sections A01 and A02
Fall 2013Math 109: Mathematical Reasoning
Sections B01 and B02
Summer 2013Math 20F: Linear Algebra
Spring 2013Math 20D: Differential Equations
Sections B03, B04, B05, and B06
Winter 2013Math 20F: Linear Algebra
Sections A05, A06, A07, and A08
Fall 2012Math 31AH: Honors Linear Algebra
Sections A01 and A02
Summer 2012Math 20B: Calculus for Science and Engineering II
Winter 2012Math 20B: Calculus for Science and Engineering II
Sections A03 and A04
Fall 2011Math 10A: Calculus I
Sections C01 and C02

SIR THOMAS MORE: Why not be a teacher? You’d be a fine teacher, perhaps a great one.
RICHARD RICH: If I was, who would know it?
SIR THOMAS MORE: You; your pupils; your friends; God. Not a bad public, that.

― A Man for All Seasons, Robert Bolt
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