Teaching
I am currently teaching the following course at UCSB.
Introduction to Number Theory (Winter 2026). The broad topics covered in this course includes: Euclid's algorithms, divisibility, congruences, number-theoretic functions, primitive roots and indices, quadratic residues, and the quadratic reciprocity law etc.
I have taught for the following courses at the University of California, Santa Barbara (UCSB).
Linear Algebra-II (Fall 2025). The broad topics covered in this course includes: Eigenvalues and Eigenvectors, Diagonalizability, Inner product space, Gram–Schmidt process, Normal and Self-adjoint Operator, Spectral Theorems, Unitary Operator and Singular Value Decomposition (SVD), Nilpotent Operators and Generalized Eigenvectors, Cayley-Hamilton Theorem, Minimal Polynomial and Jordan Form etc.
Transition to Higher Mathematics (Fall 2025). The broad topics covered in the course includes: sets, logic, quantifiers, proofs, mathematical induction, arithmetic of integers, relations and functions, cardinality (countable and uncountable sets), counting, etc
Differential Equations (Spring 2025). The broad topics covered in the course included: First order ODEs ( Linear, Separable), Autonomous, Numerical approximation, Slope Fields, Second order ODE, Higher order (Constant coefficient), System of Linear ODEs, Introduction to PDEs. See [Course Outline].
Vector Calculus (Winter 2025). The broad topics covered in the course included: Vector fields, Gradient, Divergence, Curl, Green's Theorem, Stokes Theorem, Divergence Theorem, Fourier Series, Introduction to Partial Differential Equation. See [Course Outline]
Differential Equations (Winter 2025). The broad topics covered in the course included: First order ODEs ( Linear, Separable), Autonomous, Numerical approximation, Slope Fields, Second order ODE, Higher order (Constant coefficient), System of Linear ODEs, Introduction to PDEs. See [Course Outline]
Transition to Higher Mathematics (Fall 2024). The broad topics covered in the course included: sets, logic, quantifiers, proofs, mathematical induction, arithmetic of integers, relations and functions, cardinality (countable and uncountable sets), counting. See [Course Outline]
Mentoring
I served as a mentor for two students's reading project as part of the UCSB Directed Reading Program (DRP) during Winter–Spring 2025:
Pico Gilman : Algebraic K-Theory
Brandon Jensen : Category Theory and Functors
Teaching Assistant (TA)
Teaching Assistant: I served as a teaching assistant for the Topology course during the Summer Programme in Mathematics (SPIM-2023) at the Harish-Chandra Research Institute (HRI), Prayagraj, India. As part of my responsibilities, I conducted two tutorial sessions:
Session 1: It focuses on questions based on topological groups. See pdf.
Session 2: It focuses on questions based on homotopy equivalence, retract, deformation retract, contractibility etc. See pdf.