Linear algebra and discrete mathematics (2023)

Convener(s)

 
Name: Prof. Amritanshu Prasad Prof. Pralay Chatterjee
Mailing Address: The Institute of Mathematical Sciences,
Chennai 600113

The Institute of Mathematical Sciences,
Chennai 600113
Email: amri at imsc.res.in pralay at imsc.res.in

The objective of this workshop is to develop basic linear algebra in a conceptually, mathematically and pedagogically sound manner, and to illustrate applications to other areas.There will be a special focus on applications to graph theory, and physical, geometric, computational and combinatorial aspects of the determinant.

Dates: 

Monday, January 23, 2023 - 07:00 to Saturday, January 28, 2023 - 19:00

Venue: 

Venue Address: 

The Institute of Mathematical Sciences,
CIT campus, Taramani
Chennai 600113.

Venue State: 

Venue City: 

PIN: 

600113

Chrono Order: 

417

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.
Algebraic properties of determinants.

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
(1.00 – 2.00)

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

 

 

Selected Applicants: 

 

Sr.n SID Full Name Gender Affiliation Position in College / University Uni./ Institu M.Sc./ M.A. Year of Passing M.Sc./ M.A Ph.D. Deg.
1 44121 Mr. Dipon Kumar Mondal Male University of Hyderabad Msc Student University of Hyderabad 2021  
2 44127 Mr. Sridhar T Male IIITDM Kancheepuram PhD Bharathidasan University Trichy 2018  
3 44132 Dr Prakaash A S Male Panimalar engineering college chennai PhD/ Asst.Prof Thiruvallur University/ M.Sc   01/05/2021
4 44139 Mr Siva Pradeep M Male Sri Ramakrishna Mission Vidyalaya College Of Arts And Science Ph.D Student Bharathiar University 2020  
5 44142 Mr Muthukumar Manoharan Male R. M. K. Engineering College Asst.Prof Ayya Nadar Janaki Ammal College, Sivakasi 2007  
6 44151 Mr Melvin Varghese Male SRM Institute of Science and Technology PhD University of Madras 2018  
7 44207 Ms Vaanmathi M Female PSGR Krishnammal College for Women Phd student Kongunadu Arts and Science College,Msc 2019  
8 44209 Ms. Shanmuga Priya R S Female Psgr krishnammal college for women Ph.D (Research Scholar ) Bharathiyar university/m.sc 2018  
9 44212 Dr. Subhashini A Female Anna University PhD MSc 2002 18/03/
2022
10 44220 Ms. Aicevarya Devi S Female Vellore Institute of Technology  (Chennai Campus) Research Associate Madras University 2019  
11 44221 Mr. Ezhilarasan N Male Vellore Insititute of Technology, Chennai Campus, Research Associate M.Sc 2016  
12 44267 Mr. Sriram D Male mohamed sathak college of arts and science Asst.Prof University of Madras 1996  
13 44268 Ms. Divya Aggarwal Female IIIT Delhi PhD University of Delhi 2018  
14 44273 Mr Kalikambar Gnanaprakasam Male Mohammed sathak college of arts and science Asst.Prof   2015  
15 44297 Ms. Jayabharathi Jayavel Female Vellore institute of technology, Chennai Ph.d Periyar university, Salem 2021  
16 44360 Dr. D. Balraj Male K.Ramakrishnan College of Engineering, Tiruchirappalli. Asst.Prof Bharathidasan University 2011 08/01/
2021
17 44381 Mr. Deva N Male Vellore Institute Technology, Chennai Research Scholar Thiruvalluvar University, Vellore 2019  
18 45377 Ms. Shrestha Basu Female Christ (Deemed to be University), Bangalore MSc mathematics student Christ (deemed to be University), Bangalore App  
19 45388 Mr Hariharan Subramanian Male SASTRA University Undergrad Student      
20 45405 Dr Balamurugan P Male M.Kumarasamy College Of Engineering
Karur		 Asst.Prof Jamal mohamed college, Trichy 2010 10/07/
2020
21 45438 Dr. Angel Joy Rathinasamy Female Sri G. V. G Visalakshi College for Women Associate Professor in Mathematics Sri G. V. G Visalakshi College for Women, Udumalpet 1990 19/07/
2019
22 45440 Mr Sanjayprabu S Male SRMV College of Arts and Science, Bharathiar University Ph.D. Research Scholar KG College of Arts and Science, Coimbatore 2020  
23 45466 Ms Ranjitha Sengotaiyan Female K.S.Rangasamy college of arts and science, Tiruchengode Asst.Prof 90.3 2013  
24 45488 Mr. Thangeshwaran M Male Periyar University Centre For Post Graduate And Research Studies Guest Lecturer PERIYAR UNIVERSITY 2013  
25 45498 Dr. Pankajam V Female Sri G.V.G.Visalakshi College for Women Asst.Prof Bharathiar University 1999 08/07/
2013
26 45501 Ms. Prof R Malarkodi Female St Joseph's College of Engineering and Technology Asst.Prof Bharathidasan university RSGC college ll 2005  
27 45545 Mr Gokul R Male Bharathidasan University PhD Research Scholar Government Arts And Science college, Nagapattinam 2020  
28 45563 Mr P Schlenk Engineering Manivannan Male Mepco Schlenk Engineering College, Sivakasi Asst.Prof Bharathidasan University, trichy 2007  
29 45582 Ms Anjitha Ashokan Female National Institute Of Technology Phd Kannur University 2018  
30 45599 Dr Kiran Virivinti Male Osmania University Asso. Prof Osmania University 2002 31/05/
2016
31 45650 Lt. Gajendran P Male PSG Institute of Technology and Applied Research Asst.Prof Bharathidasan University 2008  
32 45679 Dr V Vijaya Lakshmi Female Sri GVG Visalakshi College for Women Asst.Prof M.Sc 2012 20/09/
2019
33 45681 Dr Dineshkumar S Male Roever Engineering College Asso. Prof Bharathidasan University 2011 21/08/
2019
34 45718 Mr. Varadha Raj Manivannan Male Sacred Heart College/ Tiruvallur University PhD student Thiruvalluvar university / Scared Heart College 2019  
35 45720 Mr. Theivaraman R Male Bharathidasan University, Tiruchirappalii-620 024. PhD M. Sc 2011  
36 45721 Ms. Herminau Jothy A Female Bharathidasan University PhD M. Sc 2020  
37 45738 Ms. Pauline Ezhilarasi A Female Periyar University PhD Chennai Mathematical Institute 2013  
38 45742 Mr Mani Shankar Pandey Male The Institute of Mathematical Sciences PDF M.Sc. 2015 28/09/
2021
39 45758 Ms. Subbulakshmi P Female Stella Maris College PhD Student Stella Maris College 2017  
40 45783 Dr. Kungumaraj E Male Akshaya College of Engineering and Technology, Asst.Prof of Mathematics Bharathiar University, Coimbatore 2010 09/04/
2021
41 45791 Mr. Azhagendran R Male National Institute of Technology PhD Bharathidasan University, Tiruchirappalli 2019  
42 45802 Mr. Vijayakumar R Male National Institute of Technology Puducherry Research Scholar Pondicherry University 2016  
43 45814 Mr. B. Baranidharan Male National Institute of Technology Puducherry Research Scholar Bharathidasan University 2020  

 

 

How to Reach: 

TBA

School Short Name: 

ladm

Last Date Application: 

Monday, October 31, 2022

School Type: 

TEW

Separate faculty form: 

0