Matthew McMillan

Teaching

University of Virginia

Instructor in MATH and APMA, 2023–present.
Courses: Calculus I, II, III; Probability; Applied Linear Algebra; Differential Equations.

Fall 2026
Probability (3 sections)

Spring 2026
Calculus II (2 sections), Probability
Fall 2025
Calculus II (2 sections), Probability

Spring 2025
Calculus II, Probability (2 sections)
Fall 2024
Calculus I, Calculus II (2 sections)

Spring 2024
Differential Equations (2 sections), Applied Linear Algebra
Fall 2023
Calculus III (2 sections), Probability

Course Design

University of Virginia, 2023–present.

  • Mathematics of Machine Learning (in development 2026–27)
    A new course for the proposed Minor in AI Development for engineers.
  • Probability
    Designed a hybridized mastery grading structure (Fall 2026).
  • Applied Linear Algebra
    Redesigned around matrix actions, SVD, PCA, and least squares (Spring 2024).
  • Topological Data Analysis
    Expanded, typed course notes following Slava Krushkal’s lecture sequence (Spring 2025).
  • xTensiv Library
    Complete courseware and websites for six courses published online.
  • APMA Pre-Calculus Mastery program contributor.

Undergraduate Mentoring

University of Virginia, 2023–present. I have mentored 12 UVA undergraduates on projects in software engineering, database design, web development, digital accessibility, and mathematics writing.

  • A student-built prototype mapping tool led to a software engineering internship and then a full-time position in backend development upon graduation.
  • A student-implemented static site generator now serves as the production platform hosting the xTensiv Library. This led to a research article in math education co-authored with the student.
  • Current students (CS/Math dual majors) are contributing database architecture, custom Obsidian plugin development, and accessibility features.

Earlier Teaching

2022–23
Regents School of Charlottesville (part-time), Calculus Instructor
Sole instructor for a year-long high-school Calculus I course, while writing my dissertation.
2019–22
UCLA Mathematics, Graduate Teaching Assistant
Calculus I and II, Calculus for Computational and Systems Biology
Differential Geometry
History of Mathematics
Directed Reading Program Mentor