Course Guidelines
Class Teacher:
Name : Debdip Ganguly
Contact Information : ISI, Delhi
Email : debdip@isid.ac.in
debdipmath@gmail.com
Teaching Assistant:
Name : Sneha B
Contact Information : ISI, Bangalore
Email :rs_math2105@isibang.ac.in
Name : Rahul Kumar
Contact Information : ISI, Delhi
Email : rahulkumarr35@gmail.com
Sayan Acharya
Contact Information : ISI, Kolkata
Email : mr.sayanacharya1@gmail.com
Class Schedule:
First Class : 11th August, 2025
Class Timing : Monday and Wednesday : 12:00- 1:30 pm
Tutorial Timing: Thursday: 2:30- 4:00 pm
Course contents:
Brief Review : Linear Transformation, Matrix Representations, Spectrum and Diagonalisation.
Real and Complex inner product spaces, Orthogonal sets, Gram-Schmidt process, Orthogonal and Unitary Diagonalisation, Singular Value Decomposition, low rank matrix approximation using SVD
Graph Theory
1. Types of graphs, Simple Graph, Directed Graph, Undirected Graph, Complete Graph. Degree of a
vertex in an undirected graph, Indegrees and Outdegrees of a directed graph.
2. Paths and Reachability in Graphs, Graph coloring, Vertex cover, Independent set, Matching,
Representing graphs, Adjacency matrix.
3. Breadth-First Search (BFS) algorithm. Depth-First Search (DFS) algorithm. Applications.
Analysis
1. Basics of complex number system. Roots of polynomials. Power series in complex variables, complex
exponential.
2. Basic properties of metric spaces. Open and closed sets, notion of convergence and continuity,
compactness, completeness.
3. Normed vector spaces and Hilbert spaces (definition and examples). Basic properties of Hilbert
spaces: notion of complete orthogonal basis, basis expansion.
4. Multiple integrals as iterated integrals, change of variables in multiple integrals, Jacobian formula.
Reference books:
Topology and Moder Analysis by George F. Simmons
Introduction to Graph Theory by Douglas B. West
Algorithm Design by Jon Kleinberg and Eva Tardos
Linear Algebra done right by Shelden Axler
Linear Algebra and its application by Gilbert Strang
Information about the class:
Lectures: We will conduct live lectures in hybrid mode as per Schedule. We will use Zoom for the live lecture.
Tutorial sheet with practice problems will be provided.
Weekly Tutorial will be conducted.
Grading Policy:
There will be one MID-SEMESTER of 30%, one END-SEMESTER of 50%, and two quizzes which carry the remaining 20%.
Tentative examination schedule:
Quiz 1: 13th September, 2025
Mid-Semester : 6th-10th October, 2025 (Refer to Institute exam schedule)
Quiz 2 : 1st November, 2025
End-Semester : 8th- 19th December, 2025 (Refer to institute exam schedule)
Assignments
Class Notes