TEW  Group Theory, Linear Algebra and Enumerative Combinatorics
Speakers and Syllabus
Name of the Speaker with affiliation 
No. of Lectures (1.5 hours each) 
Detailed Syllabus 
Dr.Anuj Jakhar IIT Madras 
5 
Basic definitions and examples of groups and homomorphisms, including cyclic, dihedral, permutation, alternating groups, and matrix groups. Subgroups, and the induced equivalence relations, quotient groups. Introduction to Group actions. 
Dr. Chandru Hegde Mangalore University 
4 
Symmetry of plane figures, Isometries, Isometries of the plane, Finite groups of orthogonal operators on the plane. Group of symmetries of Platonic Solids. Few applications of groups in counting. 
Prof.BR Shankar NITK Surathkal 
5 
Solving system of linear homogeneous and nonhomogeneous equations, Vector spaces, Linear maps, Matrix representation of linear maps, Eigenvalues, Eigen vectors, Diagonalizability. 
Dr.A.Satyanarayana Reddy, Shiv Nadar Institution of Eminence 
4 
Basic principles of Counting: Pigeonhole principle, principle of inclusionand exclusion, permutations, binomial coefficients, bijections, Recurrence relations, Generating functions, Two way counting. 
References:

Hoffman and Kunze,Linear algebra.

M.Artin, Algebra, Second Edition.

Joseph Gallian,Contemporary Abstract Algebra.

DavidS.Dummit and Richard M.Foote,Abstract Algebra.

Miklos Bona,A Walk Through Combinatorics.

Sheldon Axler,Linear Algebra Done Right.

D.I.A.Cohen, Basic Techniques of Combinatorial Theory, John Wiley and Sons,New York, 1978.
Name of the tutors:
S.No. 
Name 
Affiliation 
1 
Dr. Prasad H. M. 
Assistant Professor,Department of Mathematics, SUIET, Mukka, Mangalore 
2 
Mr. Karthik K. 
Research Scholar,Department of Mathematics, Mangalore University 
Time Table
Day 
Date 
Lecture1 (9.30–11:00) 
Tea 
Lecturer2 (11.15–12.45) 
Lunch 
Lecture3 (2.003.30) 
Tea 
Discussion/ Tutorial (3:454:45) 
Snacks 
Mon 
05.08.2024 
AJ 
BRS 
ASR 
AJ,PHM,KK 

Tue 
06.08.2024 
ASR 
AJ 
BRS 
BRS,PHM,KK 

Wed 
07.08.2024 
CH 
BRS 
AJ 
ASR,PHM,KK 

Thu 
08.08.2024 
AJ 
ASR 
CH 
CH,PHM,KK 

Fri 
09.08.2024 
AJ 
CH 
BRS 
AJ,PHM,KK 

Sat 
10.08.2024 
CH 
BRS 
ASR 
BRS,PHM,KK 
Full forms for the abbreviations of speakers and tutors:
Speakers: AJ: Anuj Jakhar
BRS: B R Shankar
ASR: A. Satyanarayana Reddy
CH: Chandru Hegde
Tutors:
PHM: Prasad H. M.
KK: Karthik K.