Syllabus to be covered in terms of modules of 6 lectures each :
Name of the Speaker with affiliation, who will cover each module of 6 lectures 
No. of Lectures 
Detailed Syllabus 
Dr. Parvati Shastri (PS) (Mumbai University) 
6 
Group Action, Cayley’s Theorem, Class Equation, Simple Group, Examples : Icosahedral group, Sylow Theorems and its applications, Free group, Generators and Relation 
Dr Santosha K Pattanayak (IIT Kanpur) (SP) 
6 
Bilinear forms, Symmetric forms : orthogonality, , orthogonal projection, Hermitian Forms, Spectral theorem for Hermitian and Normal operators, Conics and Quadric 
Dr Sachin Sharma (IIT Kanpur) (SS) 
6 
The Classical Linear Groups, Special Unitary Group SU(2) and its orthogaonal representation.SL(2,R), Oneparameter subgroups, Lie Algebra, Simple Group 
Dr Preena Samuel (IIT Kanpur) (PRS) 
6 
Group Representations, Group Invariant forms and Unitary Representations, Compact groups, Invariant Subspaces and Irreducible representations, Characters, Permutation Representations and regular representation, Schur’s Lemma and Proof of orthogonalty relations, Representations of the Group SU(2) 
Dr Sameer Chavan (IIT Kanpur) (SC) 
6 
Goursat’S Theorem, Local existence of primitives, Cauchy’s Theorem on Disc, Cauchy’s integral formulas, Liouville’s theorem, Fundamental Theorem of Algebra, Identity Theorem 
Dr Parasar Mohanty (IIT Kanpur) (PM) 
6 
Morera’s Theorem,, Sequences of holomorphic functions, Schwarz reflection principle, Runge’s approximation theorem, Zeros and Poles, Residue Formula 
Dr Saurabh Shrivastava (IISER Bhopal) (SKS) 
6 
Singularities and Meroporhic functions,The argument principle, Rouche’s theorem, Open mapping theorem, Maximum modulus principle, The complex logarithm, Fourier Series and Harmonic Functions. 
Dr Rama Rawat (IIT Kanpur) (RR)

6 
Fourier Transform, Class of Holomorphic functions on strip with moderate decay, PaleyWiener Theorem 
Dr Anant Shastri (IIT Bombay) (AS) 
6 
Metric Spaces, Open and Closed sets, Convergence, Completeness, Baire’s Theorem, Lebesgue Lemma, Continuous mappings, Space of Continuous Functions, Topological Spaces, Basis of a topology, Subbasis of a topology, Weak Topologies 
Dr Ashish Mandal (IIT Kanpur) (AM) 
6 
Compact Spaces, Product of Spaces, Tychonoff's theorem, locally compact spaces, Compactness for Metric Spaces, Ascoli's theorem, Hausdorff Spaces, Completely Regular Spaces and Normal Spaces, Urysohn's Lemma, Tietze Extension theorem 
Dr Abhijit Pal (IIT Kanpur) (AP) 
6 
Urysohn Imbedding Theorem, StoneCech Compactification, Connected Spaces, Components of a space, totally disconnected spaces, Locally connected Spaces, Weierstrass Approximation Theorem, Stone Weierstrass Theorem 
Dr Ajay Singh Thakur (IIT Kanpur) (AT) 
6 
Locally Compact Hausdorff Spaces, Extended StoneWeierstrass Theorem, Constructing Mobius Strips, Torus and higher genus surfaces, Cone construction, Glueing lemma, Quotient space, Topological Group, Orbit Space. 
References:
1. Algebra, Michael Artin
2. Complex Analysis, Stein E.M and Rami Shakarchi
3. Introduction to Topology and Modern Analysis, G.F.Simmons
4. Basic Topology, M.A. Armstrong
Names of the tutors / course associate with their affiliation and status:
1. Rajeev Gupta (Post Doc IIT Kanpur)
2. Sailesh Trivedi (Post Doc, IIT Kanpur)
3. Few more postdocs from outside Kanpur
Tentative timetable:
Day 
Date 
Lecture 1 (9.30–11.00) 
Tea (11.00 
Lecture 2 (11.30–1.00) 
Lunch (1.00–2.00) 
Tutorial 1 (2.30–3.30) 
Tea (3.304.00) 
Tutorial 2 (4.005.00) 
Tea 5.00 


speaker 

speaker 

speaker / 

speaker/ 

Mon 
7.05.18 
AS 
SC 
Topology 
Topology 

Tues 
08.05.18 
SC 
PS 
Complex 
Complex 

Wed 
09.05.18 
PS 
AS 
Algebra 
Algebra 

Thu 
10.05.18 
AS 
SC 
Topology 
Topology 

Fri 
11.05.18 
SC 
PS 
Complex 
Complex 

Sat 
12.05.18 
PS 
AS 
Algebra 
Algebra 

Sunday : Off 

Mon 
14.05.18 
PM 

SP 

Complex 

Complex 

Tue 
15.05.18 
SP 
AM 
Algebra 
Algebra 

Wed 
16.05.18 
AM 
PM 
Topology 
Topology 

Thu 
17.05.18 
PM 
SP 
Complex 
Complex 

Fri 
18.05.18 
SP 
AM 
Algebra 
Algebra 

Sat 
19.05.18 
AM 
PM 
Topology 
Topology 

Sunday : Off 

Mon 
21.05.18 
SKS 

SS 

Complex 

Complex 

Tue 
22.05.18 
SS 
AP 
Algebra 
Algebra 

Wed 
23.05.18 
AP 
SKS 
Topology 
Topology 

Thu 
24.05.18 
SKS 
SS 
Complex 
Complex 

Fri 
25.05.18 
SS 
AP 
Algebra 
Algebra 

Sat 
26.05.18 
AP 
SKS 
Topology 
Topology 

Sunday : Off 

Mon 
28.05.18 
PRS 

AT 

Algebra 

Algebra 

Tue 
29.05.18 
AT 
RR 
Topology 
Topology 

Wed 
30.05.18 
RR 
PRS 
Complex 
Complex 

Thu 
31.05.18 
PRS 
AT 
Algebra 
Algebra 

Fri 
01.06.18 
AT 
RR 
Topology 
Topology 

Sat 
02.06.18 
RR 
PRS 
Complex 
Complex 