Abstract: This series of lectures will serve as an introduction to topology. Starting with the Euclidean spaces, we will introduce the notion of metric spaces and important properties such as continuity, convergence, compactness, connectedness, and so on. We then define Topological spaces by abstracting out the notion of open sets, and use those to generalize the concepts discussed in the previous talks. These ideas will enable us to discuss results for normed linear spaces.
Pre-requisites: Knowledge of elementary real analysis should be sufficient to follow every detail of this course.
Instructors:
Mayank Jangid (M. Math, 2026)
R. Vedanta (M. Math, 2026)
Schedule:
Lectures: All sessions will be held from 9:00 PM.
Sunday, 11th August 2024 (Mayank Jangid) - Notes & Video
Saturday, 17th August 2024 (R. Vedanta) - Notes & Video
Sunday, 18th August 2024 (Mayank Jangid) - Notes & Video
Spring 2024
FC2402: Measure Theory and Probability
Audience: B. Stat, 2nd year students and seniors
Abstract: We will study measures and their properties. Starting with a relatively abstract yet motivated setup, we will try to study measures, the Lebesgue Integration Theory, some major results, product measures and the Radon-Nikdoym Theorem. This would be followed by some convergence issues and probability theoretic applications.
Pre-requisites: Metric Topology, Probability and Riemann Integration.
Instructors:
Rishiraj Baul (M. Math, 2025)
Soham Mallick (M. Stat, 2025)
Schedule:
Lectures: All sessions will be held from 4:30 PM.
[TBA]
FC2401: Group Theory
Audience: B. Stat, 1st year students
Abstract: This course will be an introduction to the theory of groups, specifically its role in the study of symmetry. We will also be discussing the axiomatic foundations of group theory as well as some number theory.
Pre-requisites: None
Instructor: Snehinh Sen (M. Math, 2024)
Schedule:
Lectures: All sessions will be held from 4:30 PM, unless otherwise mentioned.
[TBA]