"Wide awake, counting sheep"

This page collects academic materials I have prepared over the course of my undergraduate studies. It includes structured lecture notes from courses, expository write-ups and project reports, and records of my teaching assistantship experiences. These resources reflect both my own learning process and my efforts to contribute to the academic community. For communicating any errors found or suggesting improvements to any document, the reader is requested to reach out to me at tejas.gs[at]iitb.ac.in.

Course Notes

A selection of summarised lecture notes compiled during coursework in mathematics and computer science. These notes are intended more as revision aids and references and NOT comprehensive scribes. Emphasis has been laid on clarity and succinctness. I typically write these notes when preparing for the respective course examinations and doing so offers hindsight benefit, being the second iteration of reading the topic.

As an unintended consequence, length of a notes document indicates how much time has been spent preparing for that course. If I'm studying regularly the notes will be extensive and if I'm starting a night before, the notes will (unfortunately) reflect that. It was amusing though, to note the surprising lack of correlation between time spent studying for a course and the performance thereafter.

• Semester 6 (Spring 2025)
  • MA414: Abstract Algebra
  • MA408: Measure Theory
  • MA823: Probability (PhD)
  • MA5108: Lie Algebra
• Semester 5 (Fall 2024)
  • SI419: Combinatorics
  • SI507: Numerical Analysis
  • MA417: Differential Equations
• Semester 4 (Spring 2024)
  • MA406: General Topology
  • MA412: Complex Analysis
  • MA410: Multivariable Calculus
• Semester 3 (Fall 2023)
  • MA419: Basic Algebra
  • MA403: Real Analysis
  • MA401: Linear Algebra

Expository Writing & Reports

Expository documents and project reports written to consolidate and communicate key ideas in mathematics and related areas. These include both independent explorations and formal academic submissions.

Teaching Assistantships

Details of my teaching experience as a TA for undergraduate courses. Responsibilities have included conducting tutorials, preparing supplementary material, and assisting with evaluation, with the aim of fostering an engaging and structured learning environment.