Mentorship and Teaching

Relevant Document

Graduate Students

Francesca Zaffalon - November 2021 to Present

  • PhD Student

  • Co-supervising with Fatemeh Mohammadi

Directed Readings (for Undergraduate Students)

In the mathematics department at Brandeis University, graduate students, who will take on the mentor role, propose a directed reading course and are paired with undergraduate students, who take on mentee role. These are the directed reading courses I've mentored.

Functors, Representations, and Persistent Homology - Spring 2020 at Brandeis Univeristy

    • An introduction to persitent homology as both representations and functors.

    • Texts:

      1. An Introduction to Category Theory by Harold Simmons

      2. The Structure and Stability of Persistence Modules by Frédéric Chazal, Vin de Silva, Marc Glisse, and Steve Oudot

Category Theory and Topoi - Spring 2018 at Brandeis University

    • Readings to solidify an understanding of basic category theory and provide an introduction to topoi.

    • Texts:

      1. An Introduction to Category Theory by Harold Simmons

      2. Elementary Categories, Elementary Toposes by Colin McLarty

Introduction to Category Theory - Spring 2017 at Brandeis University

    • An introduction to category theory via a reading course.

    • Texts:

      1. An Introduction to Category Theory by Harold Simmons

      2. Categories for the Working Mathematician by Saunders Mac Lane

Courses

These are the courses I have been involved with, grouped by my role in the couse. Below, "recitation" means directed sessions where the students are guided through exercises and solutions relavent to the recent lectures.

As the Instructor

Applied Linear Algebra - Summer 2019 at Brandeis University (MATH 15a)

    • Matrices, determinants, linear equations, vector spaces, eigenvalues, quadratic forms, linear programming. Emphasis on techniques and applications.

    • Planned course, wrote exams, and coded online homework in the scope of the university course description.

    • Graded all assessments.

Topology (Prepcamp) - Summer 2018 at Brandeis University

    • Lecture Notes

    • Exercises

    • A refresh on point-set topology, an introduction to the notion of homotopy, and a brief introduction to the category of (based) topological spaces.

    • Taught in a 1-week prep camp for incoming graduate students.

    • Designed and conducted course (no assessment)

Techniques of Calculus (b) - Spring 2018, Fall 2017, Spring 2017, and Fall 2016 at Brandeis University (MATH 10b)

    • Introduction to integral calculus of one variable with emphasis on techniques and applications.

    • Conducted course, wrote quizzes, assisted in writing of exams.

    • Graded quizzes and exams.

Language Construction - Spring 2014 at Purdue University Northwest (HONR 390)

    • An introduction to linguistics through the construction of one's own language.

    • Special topics course for honors students

    • Designed, conducted, and graded entire course.

As a Course Assistant

Mathematical Models in Linguistics - Fall 2018 at Brandeis University (LING 160b)

    • An introduction to fundamental mathematical concepts needed for advanced work in linguistics and computational linguistics.

    • Hold office hours.

    • Grade homework and exams.

Applied Linear Algebra - Spring 2018, Fall 2017, Fall 2016, Spring 2016, and Fall 2015 at Brandeis University (MATH 15a)

    • Matrices, determinants, linear equations, vector spaces, eigenvalues, quadratic forms, linear programming. Emphasis on techniques and applications.

    • Conducted recitation and held office hours.

    • Graded exams.

Introduction to Abstract Mathematics - Spring 2010 at Purdue University Northwest (MATH 315)

    • This course is a bridge from the mainly computational mathematics courses to the upper-level abstract courses. It focuses on the development of students' abilities to construct proofs, examples and counter examples.

    • Conducted recitation.

Integrated Calculus and Analytic Geometry II - Summer 2010 and Spring 2010 at Purdue University Northwest (MATH 164)

    • Completion of introductory study of topics in plane analytic geometry and the calculus of one variable, infinite series.

    • Conducted recitation.

    • Graded homework.

Integrated Calculus and Analytic Geometry I - Fall 2010 and Fall 2009 at Purdue University Northwest (MATH 163)

    • Topics from plane analytic geometry. Introduction to differentiation and integration. Applications.

    • Conducted recitation.

    • Graded homework.

As a Course Grader

Topology II - Spring 2020 at Brandeis University (Math 151b)

    • Continuation of MATH 151a (Topology I). Manifolds and orientation, cup and cap products, Poincaré duality. Other topics as time permits.

    • Graded homework.

Introduction to Applied Mathematics - Fall 2019 at Brandeis University (MATH 40a)

    • Introduces the problems and issues of applied mathematics, with emphasis on how mathematical ideas can have a major impact on diverse fields of human inquiry.

    • Graded homework.

Mathematics for Natural Sciences - Spring 2019 at Brandeis University (MATH 121a)

    • Introduces a set of mathematical tools of great applicability to the natural sciences. It will prepare students to use these tools in concrete applications. Topics include complex numbers, power series, calculus of variations, and Laplace transform.

    • Graded homework and exams.

Introduction to Proofs - Fall 2018 at Brandeis University (MATH 23b)

    • Emphasizes the analysis and writing of proofs. Various techniques of proof are introduced and illustrated with topics chosen from set theory, calculus, algebra, and geometry.

    • Graded homework.

Introduction to Probability and Statistics - Fall 2014 at Brandeis University (MATH 8a)

    • Discrete probability spaces, random variables, expectation, variance, approximation by the normal curve, sample mean and variance, and confidence intervals.

    • Graded homework.

Teaching Workshops

These are the teaching workshops I have attended.

Brandeis Student Support Services Program

    • conducted by Jenn Morazes and Yan Zhuang

    • 11 November 2016 at Brandeis University

    • A workshop to learn about SSSP (a TRIO program) at Brandeis and what issues pertain to students in the program.

Addressing Stereotype Threat in the Classroom

    • conducted by Dr. Anique Olivier-Mason

    • 11 October 2016 at Brandeis University

    • An interactive workshop to prepare educators to identify and address diversity issues in the classroom.