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, and Chapter 5 of Stein and Shakarchi’s book Fourier Analysis.

• Chapter 2 (Complex Analysis Book) – 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 (Complex Analysis Book) – Meromorphic Functions and the Logarithm: Residues,singularities and meromorphic functions, homotopies and simply connected domains, Fourier series and harmonic functions.
• Chapter 5 (Fourier Analysis Book) – The Fourier Transform: Elementary theory of the Fourier transform (Schwartz space, Fourier inversion, Plancherel formula), The Weierstrass approximation theorem, Fourier transform applications: The time-dependent heat equation on the real line, Laplace equation in the upper half-plane.
• Chapter 4 (Complex Analysis Book) – 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 2-7 of Simmons’s book and Chapter 4 of Armstrong’s book.

• 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 12 - Banach Algebras
• Chapter 13 - Structure of Commutative Banach Algebras
• 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.

Week-wise list of speakers:

Note: 1 lecture is of 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. Shankar V. (SV)	Topology I	SRMIST
4.	Dr. Murugan S. P. (MSP)	Algebra I	SRMIST
5.	Dr. Amal Shaji (AS)	Analysis I	SRMIST
6.	Dr. Tapas Mondal (TM)	Analysis I	SRMIST
7.	Dr. Shafiya M. (SM)	Topology I	SRMIST
8.	Dr. Kamalakkanan R. (KR)	Analysis I	SRMIST
9.	Dr. Karthick B. (KB)	Analysis I	SRMIST
10.	Dr. Nilay Kumar Mondal (NKM)	Algebra I	SRMIST