Sarah Mayes-Tang

Mathematician, Teacher, Scholar

Who am I?

I am an Associate Professor of Mathematics at the University of Toronto where I specialize in mathematics teching. I hold many professional roles. This job is defined by several intersecting roles.

I am a mathematician. When I'm working on pure mathematics, I mainly study groups of polynomials (equations with variables in them), and their geometric behaviour as the number of sets goes towards infinity in a predictable way (for the experts: I study the asymptotic behaviour of collections of ideals.) This falls into an area of math known as Computational Commutative Algebra, with a bit of combinatorics and algebraic geometry thrown in for good measure.

I am a teacher. I teach, coordinate, and design undergraduate math courses at the University of Toronto, and train early career educators, including Teaching Assistants and Instructors. I am passioante about providing math opportunities for all students at the University, built around their own goals and interests.

I am a community member. I work to make the math department and the broader community a better place to learn math and find friends, especially for women.

Two important perspectives guide my work.

I am a scholar. I ground all of my work - whether resesarch or teaching - on a solid intellectual foundation. My approach to working is guided by what I learned as a mathematician: keep asking questions and follow interesting pathways where they lead.

I am a feminist. I interrogate the systemic and interpersonal barriers that girls and women face when they engage with math (the subject and the culture). I contemplate questions such as: what would the field of mathematics look like if it was built by all people, not just men? What does the perception of mathematicians as `smart' have to do with our gender bias? I am working on a book with the tentative title: ``Good at math for a girl: Feminist mathematics." The working title is inspired by a refrain I used to hear often: ``You are so good at math for a girl!"

Research Interests

Computational Commutative Algebra
Feminist Mathematics
Course Design and Assessment
Early Career Teacher Training

Recent activities

Get in Touch or Request a Letter

Email: my email is sarah.mayes.tang@toronto.edu (not @utoronto.edu, as I've learned the hard way!). It is usually the best way to contact me, but please be aware that I am often slower to respond than most; thank you for your patience! If it has been more than a week or 10 days, feel free to send another prompt.

Wondering about a reference letter?

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Teaching

3 Beliefs about learning math:

  1. Mathematical understanding grows through the consistent drum beat of practice, not the silence of observation.
  2. Understanding blooms when students connect with the intellectual motivation that shapes a mathematical concept.
  3. Confidence is not a prerequisite for learning math—it is a product of being seen and supported.

University of Toronto

First-Year Calculus

Between 2017 and 2021, and again in 2024, I redesigned, coordinated, and taught the main-term offerings of MAT135 and MAT136 (Calculus 1 [A] and [B]). These are the largest courses within the mathematics department and likely across the entire university,enrolling 3000 students. A significant part of my efforts involved implementing systems for training and managing the large course instructional staff, consisting of at least 40 people each term. The syllabi for these courses are below.

As with classes all around the world, the course underwent a major transformation during the 2020-21 academic year. The efforts to put a course with an initial enrolment of 3000 students online outside of a MOOC framework was previously unprecedented, and (along with my co-coordinator Bernardo) I introduced several innovative elements to the course to stay true to my beliefs about teaching, learning, and engaging with students, even within the large-class, online framework. The syllabi for MAT135 during the online offering are below.

First-Year Seminars

Designing first-year seminars catered to students who may or may not take other University-level math classes is one of my passions as an educator. I endeavour to design courses that provide a challenging and engaging environment for all learners - whether they will become mathematicians or whether they have been fearful of mathematics for as long as they can remember. At the University of Toronto I've taught two first-year seminars: Math in Literature and Poetry and Women's Mathematics.

  • Math in Literature and Poetry
  • Women's Mathematics

    • Upper-Level Courses

    "Introduction to Abstract Mathematics", or, as I like to think of it, "Masterpieces of Mathematics", is the standard introduction to the mathematics major. We study topics like cardinality of infinities and the great results about prime numbers, in addition to thinking about questions like "what constitutes a mathematical proof?" and "what does it mean to know something in mathematics?" Working with new math majors is a lot of fun: many of them are also majoring or minoring in other subjects, and the diversity of interests and strengths makes this class a lot of fun to teach.

    Symmetry and Groups is a first course on group theory for mathematics majors. I taught it for the first time in the Winter of 2022. In this iteration I experimented with a differnet grading approach that was influenced by both standards-based grading and ungrading, but also remained flexible to the my students throughout the semester. I stepped back on the ungrading in the

    Quest University

    Quest Univeristy Canada is a private, not-for-profit liberal arts University in Squamish, British Columbia focused on undergraduate education. It was established by the Sea To Sky University Act. The insitution is unique in a number of ways; for example, it operates on the Block Plan, which means that students take one course at a time for three-and-a-half weeks each. Syllabi from the courses that I designed and taught at Quest can be found below.

     

    Mathematics Research

    Without facts, you can’t have truth. Without truth, you can't have trust. Without all three, we have no shared reality, and democracy as we know it - and all meaningful human endeavours - are dead.

    --Maria Riessa
     

    Education Research

    Selected Education and SoTL Presentations

     

    Feminist Mathematics

    Feminist Mathematics Means:

    • Listening to the voices of people who have been left out of mathematics, and welcoming them to participate in whatever way they can.
    • Recognizing mathematical thinking in unexpected places.
    • Challenging "accepeted" mathematical practices, interrogating where they come from and who they leave out.
    • Advocating for change

    Coming Up!!!:

    First Readings for Feminist Math

    Here are a few resources online to help you get started learning about Feminist Mathematics (not necessarily the best or perspectives I endorse, but places to begin!). Some of the best information is only in print, so also go to your library!