Teaching
📚 IISc Teaching Duties
(1) E0 298: Linear Algebra and Its Applications (August 2023 - December 2023)
I have worked as a full-time Teaching Assistant for the offline course ‘E0 298: Linear Algebra and Its Applications’ taught by Prof. Kunal Narayan Chaudhury. My responsibilities included conducting tutorial sessions, solving exam questions to assess the difficulty of the paper, and grading answer sheets and assignments.
🌟 Prime Minister Research Fellowship (PMRF) Teaching Duties
I am currently teaching two courses: Advanced Linear Algebra and Point Set Topology for Semester V and Semester VI students, respectively, at the Department of Mathematics, Maulana Azad College, Kolkata as part of the PMRF TAship scheme, conducted online. The Advanced Linear Algebra course is offered in the odd semester (August - January), while the Point Set Topology course is available in the even semester (February - July).
(1) Advanced Linear Algebra (August 2024 - Present)
The course aims to give students an intuition about several aspects of linear algebra and applications to different fields. The course covers topics such as matrix operations, linear transformations, subspaces and bases, orthogonality and least squares, determinants, eigenvalues and eigenvectors, symmetric matrices and quadratic forms. The course also introduces some concepts of inner product spaces, singular values and diagonalization. The course focuses on basic concepts which helps students to do better in competetive exams such as JAM, CSIR etc.
(2) Point-Set Topology (February 2024 - June 2024)
The course aims to introduce the students to the basic concepts and techniques of point set topology, which is the study of abstract spaces and their properties. The course will cover topics such as metric spaces, open and closed sets, bases and subbases, continuity and homeomorphisms, connectedness and path connectedness, compactness and Lindeloffness, separation axioms and Urysohn’s lemma, and metrizable spaces and completeness. The course will also provide some examples and applications of topology in analysis, geometry and algebra. The course will require some familiarity with set theory and logic, as well as some mathematical maturity and proof skills. The course will be based on lecture notes, exercises and online interactive sessions.
(3) Advanced Linear Algebra (August 2023 - January 2024)
(2) Point-Set Topology (February 2023 - June 2023)
(3) Advanced Linear Algebra (December 2022 - January 2023)
📖 Seminar on ‘Cayley Colour Graph: An Introduction to Topological Graph Theory’
MAC MATH FEST, 2021
📅 27 June, 2021
🏫 Department of Mathematics, Maulana Azad College, Kolkata
The seminar aimed to introduce some of the connections between graph theory and group theory to undergraduate mathematics students. We started by defining free groups and giving examples of how they can be constructed from words and letters. Then, we introduced the concept of Cayley colour graphs, which are labelled by group elements and have edges coloured by the group operation. We showed how Cayley colour graphs can be used to represent free groups and their subgroups. Next, we stated and proved Frucht’s theorem, which says that every finite group is the automorphism group of some graph. This means that any finite group can be realized as the set of symmetries of a certain graph. We gave some examples of graphs and their automorphism groups to illustrate the theorem. Finally, we gave a brief overview of Cayley graphs, which are special kinds of Cayley colour graphs that have only one edge colour. We explained how Cayley graphs could be used to study the topology of groups and their actions on spaces.