Teaching at postgraduate level
(Aug 2025 - Dec 2025) Will teach “Algebra I” to first year PhD students at HRI.
19th February 2025 Will teach a module on "Publishing" as a part of the Research Methodology course to PhD students at HRI (slides are here).
(Aug 2023 - Dec 2023) Taught “Algebra I” to first year PhD students at HRI. TA for this course is Rohit Pokhrel (PhD student at HRI)
2nd September 2023 I taught a module on "Publishing" as a part of the Research Methodology course to PhD students at HRI (slides are here). Also participated in taking viva on latex presentations made by students on Research Methodology and publication ethics.
(August 2022 - November 2022) I taught "Abstract algebra" course to PhD 1st year students at TCG CREST, Kolkata.
(June 2023) I gave 6 lectures (one and a half hours each) in Group theory to MSc students enrolled in the Summer Programme in Mathematics (SPIM) at HRI, Prayagraj.
Courses at The University of British Columbia.
At the University of British Columbia, I have taught large lecture classes, with between 100 and 150 students enrolled. I have used a variety of online materials. I have made screencasts to help my students study, and lecture overheads to make notes legible for students sitting in a large hall. I have experimented with relevant youtube videos in class that allow students to understand the geometric picture, and peer-graded quiz reviews that help students understand the grading process while revisiting quiz material and being exposed to the mathematical writing of their peers. I was the principal instructor for the undergraduate course "Matrix Algebra" at the University of British Columbia continuously for 4 semesters (over a period of two years).
(Jan 2020 – April 2020) "Matrix Algebra", course number 221, section 201. My class size was 102 students.
(Sept 2019- Dec 2019) "Matrix Algebra", course number 221, section 201. My class size was 98 students.
(May 2019- June 2019) "Matrix Algebra", course number 221, section 921. My class size was 125 students. This was an intensive summer course.
(Jan 2019- April 2019) "Matrix algebra", course number 221, section 205. My class size was 30 students.
Due to the outbreak of COVID-19, my Matrix Algebra class of (Jan 2020 – April 2020) went online using "Collaborative Ultra". To facilitate online learning for students I created online videos ("Math movies"). Here are some tips to create an online blackboard (using Apple ipad and Mac) which I used in my course and found very helpful.
Use the note-taking app "Goodnotes" on ipad to write on it using the Apple pencil.
Connect ipad with the Mac using (a combination of) usb cables.
Launch the Quicktime player on Mac and click on "New Movie recording". This will start recording the lecture as you write on your ipad.
Then share the Mac screen (or Quicktime application) with the students (via several online systems like Collaborative ultra, Zoom or Skype).
In Collaborative Ultra, the students can also raise their hand and ask questions. The instructors can create groups of students and ask each group to work on a specific problem and then compare their results. The instructor can also do online polls among students for multiple choice questions.
In all, the online sessions turn out to be very interactive and engaging.
At UBC, I developed effective and innovative teaching skills for undergraduate math courses. UBC is dedicated to providing world-class classroom experience to their students and runs ‘Instructional Skills Workshops’ and ‘Instructional Support Group’ to train young researchers and postdocs to achieve excellence in the classroom. These are run by exemplary instructors at UBC where they share their innovative ideas and techniques for classroom management. This year-long training includes developing skills and tools by which we can bring “mathematics to life” in the classroom. I participated in the Instructional support group and workshops from August 2018 to April 2019 which helped me develop my foundation on teaching big classes of approximately 125 students.
(Aug 2018) Program Title: Instructional Skills Workshop
Program Description: This is a 2 day intensive program run by the University of British Columbia to train young instructors/postdocs in fundamentals of “teaching techniques” in order to teach UBC undergraduate courses.
(Sept 2018 – April 2019) Program Title: Instructional Support group
Program Description: This is a year long support group of the University of British Columbia where we learn and discuss innovative classroom techniques in depth to keep our students engaged, and focussed while learning courses at UBC
I teach to bring mathematics to life. I want my students to “see” the theorems in my course rather than working through it. I think it is important because this provokes a kind of “mathematical sense” in them which promotes understanding concepts in the long run. I use geometry often in my class to draw the “big picture” in the students’ minds. This helps me to bring alive pages of textbook calculations and make it dynamic and vibrant.
Another important thing that I value is the unity of students in my class. As far as I can, I try to ensure that no student is left out in my class and encourage students’ participation. This helps in developing the class culture. A good class culture helps to deepen mathematical understanding by group works, learning from friends, also providing moral and emotional support to every student. I believe an isolated student has a higher chance of “falling back” and this is why I think that unity in class is important. Unity helps in providing the moral support the students need, promoting their eagerness to learn mathematics.
Here are the teaching strategies I employ in a typical classroom of mine.
I. Use of examples: Often in undergraduate courses, we don’t provide rigorous proofs of mathematical theorems. Instead, I want my students to “intuitively understand” the theorem by using examples. In general, I like to start my class with an example. After the students work it out, they come to a point where they have developed a rough idea of what the general theorem might be. This idea to foresee what is coming up next is what I care for. This is how I bring a math theorem to life in my students’ minds.
II. Use of pictures and physical objects and youtube videos: Pictures, graphs, diagrams, charts are indispensable objects to make mathematics alive in the classroom and keep the content interesting resulting in students’ engagement. After the students work out the example and get to a point to predict the general theorem, I take the opportunity to explain the precise theorem by drawing pictures. Sometimes, physical acts like cutting specific measurements of a piece of paper by a scissor in front of the students turn out to be very effective while explaining particular theorems (in particular limit theorems of sequences and series). I also play relevant youtube math videos (or math movies), pausing it from time and time and simultaneously working through an example to get a better "feel" of the math behind it.
III. The Strategy of “call back”: At the beginning of the course I like to set a big geometric picture behind the mathematics/calculations that I will be discussing throughout the course. At different points of the course, I call back to this big picture which aids in an intuitive understanding of the problem. This makes the content coherent and proves to the students that the mathematical theorems are not just a collection of facts. We are all working step by step to solve a single big geometric mathematical problem which is easy to visualize.
IV. The Idea of togetherness in class: I employ certain techniques to ensure that the students feel that they are with me and they are together. We are all in the same boat. I don’t like a student in my class to feel that he/she is left out or discrete. Here are a few techniques that I employ to bring this idea of togetherness:
Talk to your neighbours: I give them a problem to work on. For the first five minutes, they try on their own. Then I ask them to discuss and correct the solution of their neighbours. This helps them to learn from their friends and keep the class engaged and working.
Group work: From time to time I encourage the students to get up from their seats, get into groups of 4 and solve a particular problem. After they work on their problems, different groups share their ideas between themselves. I monitor different groups from time to time.
Ask for questions and feedback: After explaining a key mathematical concept, I stop and ask if the students are having any questions. Instead of answering the question of a particular student by myself I ask if any other students have any views/comments on the questions. This often encourages long class discussions and promotes to build unity among students enriching my class culture.
V. Ensure every student participates in class discussions (use of modern technologies in class): I employ the following technique to make sure that students in my class get the opportunity to participate in class discussions: I use technologies like Clicker. Clicker is a physical device available to every student and they can answer multiple-choice questions that I ask during my lecture. By this, I get the response of every student and get the answer voted by the majority of the class on my laptop. (For classrooms not supporting Clicker, this is also possible using web apps that connect students’ mobiles with the class computer.)
Outreach (Beyond classroom):
I believe that the students should not be confined to a “classroom experience”. I want to show them the opportunities beyond the classroom that they can do with the knowledge they are accumulating in the classroom.
Design Projects beyond textbook: I tell the students to design a project of their choice discussing an application of the content of my course in the fields that they want to major in (eg. Engineering /Chemistry / Maths / Statistics, Computer Science) which is not in the textbook. I encourage them to read reference texts/articles beyond the course curriculum but tailored to their interests and taste. This helps the student understand and appreciate the connection between differences branches of science and appreciate the depth and outreach of the subject matter that I am teaching in class.
Research opportunities and Applications of mathematics in business and companies: I like to take out 5 minutes of my class time to show the students open research opportunities that they might be interested in beyond what I am going to discuss in class. I like to show them Science cooperative programs where the companies/businesses collaborate with the university to prove a “hands-on” experience to the students where they can employ the ideas they are learning in class.
In order to increase passion among students regarding the academic content they are learning in class, it is highly important to venture out beyond the course curriculum and explore the connections there. This increases curiosity and interest among students and gives them a broader perspective opening a doorway to a wide range of applications. Therefore, I assign a certain part of course grade for students of my class to find useful applications of the theorems we are learning in class. The students are expected to do a little research on their own and write a short and coherent research project understanding the implications of math theorems (those we are learning in class) in other branches of science and engineering.
In my Matrix Algebra class, students came up with wonderful ideas of applications of matrices in
1. Image processing
2. Color coding
3. Markov Chains
4. Electrical circuits
5. Cryptography
6. Google Page Rank Algorithm
7. Mathematical modeling
8. Graph theory
9. Image representation
10. Algorithms in computer science
and much more (such as applications of matrices in non-academic world, example: video games)
Look at the cool projects here.
I have long been committed to diversity, inclusion and recognize the barriers faced by women and other minorities in engaging in science. As an undergraduate in India, I use to do free tutoring to students below poverty level. Currently, my students at UBC include historically under- represented or under-appreciated in mathematics -- visible minorities, disabled students and women. UBC has dedicated services promoting their academic development. Link given below:
https://students.ubc.ca/about-student-services/centre-for-accessibility
For these students, complying with UBC policies, I provide distraction reduced environment and extra time for exams. There are also possibilities of occasional extensions on coursework and audio-recording of lectures. I also regularly hold tutoring sessions during my office hours to help these students. I strongly believe that, with extra support and care, these students can become leading experts in mathematics.
From my personal experience, I would like to recall that most of the people who made profound impact on developing my mathematical career are females. To give examples, I would first like to recall my high school teacher Mrs Saswati Dasgupta who kindled interest in mathematics in me. One of my PhD supervisor Prof. Ariane Mézard (Université Pierre Marie Curie, Paris) is female and renowned for Breuil-Mézard conjecture. Furthermore, my current postdoc supervisor Prof. Sujatha Ramdorai is female who is a leading expert in Iwasawa Theory. Therefore, I strongly believe in the importance of female mathematicians. I also participated in “Women in Mathematics” 2018 program at UBC. There we discussed about effective techniques to increase the number of women in mathematics and science. One of the techniques we talked about is recruiting several female candidates as teachers / professors starting from the very basic primary schools, high schools and way up to university level. This will make an even distribution of female experts who can kindle interest in science among other female students. Therefore, eventually it is more likely that we could get more female candidates interested in pursuing a scientific career.
In the future, I would like to take an active leadership role in contributing to diversity. I will continue to actively help students from under-represented groups and female students. I will provide mentoring workshops for both female and minority students to encourage them in academic careers. I also have a strong interest in working with middle schools and teachers with large minority or underprivileged populations to use technology for promoting science and engineering careers, and hope to build on some of the current activities. I also propose to build relationships to facilitate research collaboration with faculty and students at historically underrepresented institutions (HBCU’s and HSI’s) and to pursue internal and external funding to support this type of collaboration.
UBC students's feedback about my teaching can be seen by clicking here.