TEW - Linear algebra and discrete mathematics (2023)
Speakers and Syllabus
|
Name of the Speaker with affiliation |
No. of Lectures |
Detailed Syllabus |
|
Pralay Chatterjee (PC) Professor, IMSc, Chennai |
9 hours |
Vector spaces, Linear maps, Matrix representation of linear maps, Row reduction, Row reduced echelon matrix, Row rank, Column rank, Solving system of linear homogeneous and non-homogeneous equations, Cramer's rule, Eigen values, Eigen vectors, Diagonalizability, Bilnear forms, Orthogonal and symmetric matrices.
If time permits: Canonical forms, Spectral Theorem for normal operators. |
|
N. Narayanan (NN) Asst. Professor, IIT Madras |
9 hours |
Linear algebra methods in combinatorics: Dimension, rank and orthogonality. Eigen values, graph decomposition, graph properties, Google pagerank, matrix tree theorem. |
|
Amritanshu Prasad (AP) Professor, IMSc, Chennai |
6 hours |
Geometric interpretation of the determinant. Computation of determinants by computers. Combinatorial determinants, the Lindstrom-Gessel-Viennot lemma and its applications. |
References:
1. Michael Artin: Algebra
2. Serge Lang: Linear algebra
3. I N Herstein: Topics in Algebra
4. Hoffman and Kunze: Linear algebra
5. Babai and Frankl : Linear Algebra Methods
6. Stasis Jukna: Extremal Combinatorics
7. Norman Biggs: Algebraic graph theory
8. Godsil and Royle: Algebraic graph theory
9. Christian Krattenthaler: Determinants
10. Xavier Viennot: The Art of Bijective Combinatorics video book (www.viennot.org)
Time Table
|
Day |
Date |
Lecture 1 (10:00–11:00) |
Tea (11.00-11:30) |
Lecturer 2 (11.30–1.00) |
Lunch |
Lecture 4 (2.00-3.30) |
Tea (3.35 -3.55) |
Discussion (4.00-500) |
Snacks (5.05 – 5.30) |
|
|
|
(Speaker’s name) |
|
(Speaker’s name) |
|
(Speaker’s name) |
|
(Tutor’s name) |
|
|
Mon |
7 |
AP |
|
NN |
|
PC |
|
SS, AM, NN |
|
|
Tue |
8 |
AP |
|
NN |
|
PC |
|
AM, SV, PC |
|
|
Wed |
9 |
AP |
|
NN |
|
PC |
|
SV, SS, AP |
|
|
Thu |
10 |
AP |
|
NN |
|
PC |
|
SS, AM, NN |
|
|
Fri |
11 |
AP |
|
NN |
|
PC |
|
AM, SV, PC |
|
|
Sat |
12 |
AP |
|
NN |
|
PC |
|
SV, SS, AP |
|
Name of the tutors:
|
S. No. |
Name |
Affiliation |
|
1 |
Sagar Sudhirkumar Sawant (SS) |
IIT Madras |
|
2 |
S Velmurugan (SV) |
IMSc |
|
3 |
Arunabha Mukhopadhyay (AM) |
IMSc |