# Teaching

I am passionate about mathematics education. I have aimed to improve my teaching by turning my classrooms into collaborative workshops, where students learn through experimentation and creativity. Read more about my teaching philosophy.

**Courses taught:**

Current: **MAT 1341 - Introduction to Linear Algebra.** Syllabus. A first course in linear algebra for students with some background in vector geometry. This course will take a "vector spaces first" approach, introducing students to the formalism of vector spaces right at the beginning. More traditional linear algebra topics, like solving systems of equations, can then be seen as specific examples of general statements about vector spaces. Examples include spaces of matrices and of functions.

Past (at uOttawa):

**MAT 1339 - Calculus and Vectors**. Syllabus. This introductory course covered differential calculus as well as basic elements of vector geometry and arithmetic. During the vector portion of the course, I emphasized the interplay between geometric and algebraic points of view, and asked students to geometrically interpret vector operations like the dot and cross product.

Past (at UVa):

- Spring 2018:
**MATH 1110 - Probability and Finite Math.**Syllabus. A precalculus course primarily for students in non-science majors. The first part of the course was spent learning basic set theory and solving counting problems -- how many valid UVa email addresses exist? how many natural numbers between 1 and 1200 are multiples of neither 2 nor 3? We then applied these techniques to answer questions about probability. We learned about Bayes' Theorem and conditional probability, and discussed classic conundrums like the Monty Hall problem (the solution of which we verified experimentally as a class). Finally, we briefly discussed how Markov chains can be used to answer questions about the evolution of systems. Along the way, we discussed highlights from a few discrete math topics, like graph theory. Sample HW. Evaluations. - Fall 2018:
**MATH 1140 - Financial Math.**Syllabus. A precalculus course primarily for students in non-science majors. We discussed mathematical tools of finance and their applications to everyday life. There was a heavy focus on example and application, and the course was strongly student-centered. Students were routinely asked to apply tools from class to make decisions about financial problems pulled from real life. In one activity, I asked students to analyze real-life mortgage ads -- but what they didn't know was that the ads were pulled from federal prosecutions of misleading mortgage advertisements. Students correctly identified misleading claims in all of the ads. On midterm exams, students were given take-home assignments asking them to consider financial decisions -- a retirement plan in one case, and a mortgage application in the other -- and submit long-form analyses explaining mathematical concepts in plain English. Sample take-home exam. Evaluations. - Summer 2018 and 2017:
**MATH 5855 - Proofs in Algebra (abstract algebra).**A abstract algebra course for incoming math graduate students at the University of Virginia, taking place the summer before their first semester and aimed at preparing them for graduate Algebra. This is an "algebra boot camp": we covered elements of the first 10 chapters of Dummit and Foote in the course of four weeks (2.5 hours of contact time per day, 5 days a week). The course was highly student-centered, with around 1/2 of the class consisting of students presenting solutions to problems or working together to finish proofs. Evaluations (informal, solicited personally). - Spring 2017: MATH 1310 -
**Calculus I.**Syllabus. An introductory calculus course for science majors. - Fall 2016 and 2015: MATH 1210 -
**Applied Calculus I.**Syllabus. An introductory calculus course for non-science majors. - Spring 2015: MATH 1220 -
**Applied Calculus II.**Syllabus. A second calculus course for non-science majors, including some non-standard topics: multivariable calculus and calculus-based probability.