AFS-I - Annual Foundation School - I (2026) Kattankulathur

Speakers and Syllabus

Syllabus to be covered in terms of modules of 6 lectures each:

    • Algebra I (Linear Algebra and Group Theory): We will cover most of the material found in Chapters 6, 7, 8, and 9 in Michael Artin’s book Algebra.
Chapter 6 – Symmetry: Isometries of a plane, finite groups of orthogonal operators on the plane, counting formula, permutation representations.
Chapter 7 – More Group Theory: Cayley’s theorem, Class equation, Conjugation in symmetric group, Sylow theorems.
Chapter 8 – Bilinear forms: Bilinear, symmetric, and Hermitian forms, Orthogonal projection, spectral theorem, conics and quadrics.
Chapter 9 – Linear Groups: The classical groups, Special unitary group SU2, The rotation group SO3, one-parameter groups.

    • Analysis I (Complex Analysis): We will cover most of the material found in Chapters 2, 3, and 4 of Stein and Shakarchi’s book Complex Analysis.
Chapter 2 – Cauchy’s Theorem and Its Applications: Goursat’s theorem, Cauchy’s theorem in a disc, Cauchy’s integral formulas, applications of Cauchy’s theorem.
Chapter 3 – Meromorphic Functions and the Logarithm: Residues, singularities and meromorphic functions, homotopies and simply connected domains, Fourier series and harmonic functions.
Chapter 4 – The Fourier Transform: Action of the Fourier transform on a special class of functions, Paley-Wiener theorem.

    • Topology I (Point Set Topology): We will cover most of the material found in Chapters 1-7 of Simmons’s book and Chapter 4 of Armstrong’s book.
Chapter 1 – Sets and Functions
Chapter 2 – Metric spaces: Convergence, completeness, Baire’s theorem, space of continuous mappings.
Chapter 3 – Topological spaces: Bases, weak topologies, function algebras.
Chapter 4 – Compactness: Product spaces, Tychonoff’s theorem, and Ascoli’s theorem.
Chapter 5 – Separation: T1, T2, T3, T4-spaces, and Urysohn imbedding theorem.
Chapter 6 – Connectedness: Components, Totally disconnected and Locally connected spaces.
Chapter 7 – Approximation: The Weierstrass approximation theorem and Stone-Weierstrass theorem
Chapter 4 (Armstrong) – Identification spaces: Mobius strips, Topological groups, and orbit spaces.
References:
    1. Michael Artin, Algebra, Pearson, 1991, Prentice-Hall of India, New Delhi, 2003.
    2. Elias Stein and Rami Shakarchi: Complex Analysis, Princeton Lectures in Analysis-II, 2003
    3. G.F. Simmons: Introduction to Topology and Modern Analysis, McGraw-Hill, 1983.
    4. M. A. Armstrong: Basic Topology, Springer-Verlag New York Inc., 1983.

Name of the Speakers with affiliation.	No.of Lectures	Modules
Prof. K. N. Raghavan (KNR), Krea University	4	Algebra I
Prof. Akash Anand (AA), IITKanpur	4	Algebra I
Prof. R. Venkatesh (RV), IISc Bangalore	4	Algebra I
Dr.Sunil Kumar Prajapati (SKP), IIT Bhubaneswar	4	Algebra I
Prof. G.P. Youvaraj (GPY), Ramanujan Institute for Advanced Study in Mathematics, Madras University	4	Analysis I
Prof. Sameer Chavan (SC), IIT Kanpur	4	Analysis I
Dr.Surjit Kumar (SK), IIT Madras	4	Analysis I
Dr. Anwoy Maitra (AM), IIT Madras	4	Analysis I
Prof. K. Parthasarathy (KP), Ramanujan Institute for Advanced Study in Mathematics, Madras University	4	Topology I
Dr. Ramesh Kasilingam (RK), IIT Madras	4	Topology I
Dr. Suhas Jaykumar Pandit (SJP), IIT Madras	4	Topology I
Dr. Arpan Kabiraj (AK), IIT Palakkad	4	Topology I

    Note:1 lecture is 1.5 hours

Names of the tutors / course associate with their affiliation:

S.N.	Tutors	Subject	Affiliation
1.	Dr. Ayush Udeep (AU)	Algebra I	SRMIST
2.	Dr. Selvakumar A. (SA)	Topology I	SRMIST
3.	Dr.Sankar K. (SRK)	Analysis I	SRMIST
4.	Dr.Murugan S. P. (MSP)	Topology I	SRMIST
5.	Dr. Awanish Kumar Tiwari (AKT)	Algebra I	SRMIST
6.	Dr. Vijay Pal Bajiya (VPB)	Algebra I	SRMIST
7.	Dr. Shafiya M. (SM)	Topology I	SRMIST
8.	Dr. Kamalakkanan R. (KR)	Analysis I	SRMIST
9.	Dr. Vignesh P. (VP)	Analysis I	SRMIST
10.	Dr. Karthick B. (KB)	Analysis I	SRMIST
11.	Dr. Nilay Kumar Mondal (NKM)	Algebra I	SRMIST

Time Table

 Tentative time-table mentioning the names of speakers with their affiliation:

Note:InLj, and Tjdenotelectureand tutorialnumber.