Teaching Statement

Author

Apurva Nakade

Published

January 2, 2026

I have been teaching for more than a decade now. After all these years, I have come to understand that my role in the classroom and beyond is to support, motivate, and inspire students. I believe that the best way to learn mathematics is through making mistakes, getting confused, and struggling toward a solution. I consider myself a coach and a facilitator and teach with the core philosophy that my primary goal is to provide students with a welcoming and inclusive environment where experimentation is encouraged and honest mistakes aren’t penalized. It is important to me that students who complete my courses leave with a sense of pride and accomplishment, and with increased interest in mathematics, curiosity, and self-confidence.

My teaching experience ranges from creating advanced electives and short bootcamp courses for small groups of students to managing and teaching in-person courses with several hundred students, coordinating multi-section classes, and adapting large service courses for asynchronous education. I have contributed to open source texts using technologies such as Webwork, Quarto, Pretext, and RMarkdown, and I’m involved in the long-term project of math formalization using the Lean theorem prover. I have taught topics spanning calculus, linear algebra, differential equations, discrete math, linear programming, math formalization, manifolds, algebraic topology, Monte Carlo methods, and computational math.

Discrete Math

I have been teaching Discrete Math at JHU since Fall 2023. I have taught similar courses in the past at Northwestern University and the University of Western Ontario (UWO). At these institutions, I learned to use technological tools to my advantage. Because of Covid, I experimented extensively with the use of technology—I made online video lectures, created Webwork problems from scratch, and even administered an exam using Webwork. These experiences guided me toward revamping the Discrete Math course at Hopkins.

I incorporated three big changes into the course:

  • I wanted to rid students of the habit of rushing to a final answer and help them understand that mathematics is a creative, iterative process. As such, I allow students to resubmit their homework to recover lost points. This is a recurring theme in my teaching.
  • Three in-class midterms instead of two longer midterms. This allowed students to focus on a few topics at a time. At the same time, having more exams allowed students to avoid getting bogged down by a single bad score, providing ample opportunities to recover.
  • I switched to an online textbook with built-in exercises. I found in my first semester that students would often delay studying until homework deadlines and close to exams. This led to weaker students having extremely bad grades. With the online textbook, students are more accountable to working regularly, and I have seen drastic improvements in the grades of weaker students.

This required me to overhaul the entire course and recreate it from scratch. I’m grateful to have always had the best teaching assistants. I’m quite proud of my TAs who’ve gone on to TA for other courses after “graduating” from my course.

Monte Carlo Methods

I have been teaching Monte Carlo Methods for three semesters now. The course as designed by the previous instructor was excellent, but I found that it needed to be updated to align with the ways students learn today.

  • I rewrote my own notes with an online-first approach. There is a course website instead of a textbook: https://apurvanakade.github.io/Monte-Carlo-Methods/. Having an online textbook also allows me to incorporate code directly in the book. I intend to apply for a CTEI grant to update this textbook and further incorporate interactive components.
  • I changed each week’s homework to be part programming and part theory. The two components complement each other—the theory explaining the rationale behind the algorithms and the programming assignment immediately showing students how to apply the theory in real applications.
  • This course has a variety of fragmented topics with no central theory. As such, I felt that a big exam is not appropriate for this course, as there is nothing that we expect students to memorize. Instead, I switched to having weekly quizzes, which allow students to keep up with the fast-paced material and also reduce exam anxiety.
  • The biggest change I made to this course was adding a final project. Most of the students in this course are seniors and master’s students. These students really appreciate having some agency in how they learn and being able to showcase their skills. I have had non-math major students create polished papers and software worthy of being presented at conferences.

A big challenge in this course is adapting it to a post-AI world. I now deemphasize things that can be done better by AI and instead encourage students to use AI tools to strengthen their learning. I encourage students to use AI assistants for their programming assignments and final projects, but I only evaluate their theoretical understanding. In the final project, students are required to submit a detailed report containing the mathematical analysis.

Mathematical Foundations of AI

In the summer, I love to teach high school summer camps. I have taught Exploring Engineering Innovation and Mathematical Foundations of AI at JHU.

Teaching Mathematical Foundations of AI was a significant learning experience for me. The course was aimed at high school students who were smart, motivated, and highly interested but lacked much mathematical and programming background. I again decided to revamp the entire course to fit the audience. I made the sessions interactive, flipped most classes, and had students work with each other and discuss topics like AI ethics that got students hooked on the subject.

For the programming component, I had to teach students Python from scratch but figured out a way to teach it succinctly and get to applications quickly.

Professional Development

I have completed a Faculty Forward Fellowship and a certification course at the Teaching Academy at JHU, where I learned about several important pedagogical concepts such as inquiry-based learning, backward course design, and learning objectives, which I regularly incorporate into my own teaching. I regularly attend the workshops and seminars organized at the Center for Teaching Excellence and Innovation at JHU. I am a member of the Project NExT’20 cohort, a professional development program sponsored by the MAA for math educators at the university level. I try to keep myself updated on advances in pedagogical techniques and find it valuable to hear about other educators’ teaching experiences. In addition to providing me with new information and skills, these workshops also allow me to take on the role of a student and stay grounded.

Future Goals

A central theme in my teaching career has been adapting courses to student needs without watering down the content. I want to keep updating existing courses and create new courses that are first and foremost useful to my students. This requires considerable effort in creating new materials that are interactive and engaging. I’m planning on applying for a CTEI grant for help with this.

I also want to broaden my work from teaching to mentoring and outreach. Finally, I want to engage more with the broader teaching community. I’m looking forward to the reduced course load, which will allow me to do this.