TEW Algebra, Discrete Mathematics, Complex Analysis (2017)

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Venue: The Institute of Mathematical Sciences,  Chennai, Tamil Nadu
Date:  22nd, May 2017 to 27th, May 2017

 


 

School Convener(s)

Name K. N. Raghavan K. Srinivas
Mailing Address  Institute of Mathematical Sciences,
CIT Campus, Taramani, Chennai 600113.
Institute of Mathematical Sciences,
CIT Campus, Taramani, Chennai 600113.

 


 

Speakers and Syllabus 

Algebra:  by Sankaran Viswanath (10.5 hours)

Topics covered

  • Group actions on sets: orbits and stabilizers
  • Burnside’s Lemma
  • The class equation and applications
  • Applications of group actions to Group Theory: the Sylow Theorems
  • Applications of group actions to Combinatorics: counting necklace configurations, weighted version of Burnside’s Lemma, simple instances of Polya’s enumeration theorem.
  • Application of group actions to elementary number theory: orbits for the action of the automorphism group of a cyclic group and an identity involving d(n) (the number of divisors of n ) and φ(n) (Euler’s Totient function).

Complex Analysis: by Parameswaran Sankaran (8.5 hours)

Topics covered

  • Holomorphic functions, Cauchy-Riemann equations, power series.
  • Local properties of holomorphic functions, singularities, meromorphic functions, Laurent series.
  • Complex integration, residue calculus, Rouché’s theorem.
  • Infinite product, Weierstrass’ theorem; growth of an entire function, Hadarmard’s theorem.

The emphasis was on explaining the concepts with the help of examples rather than on proving theorems.

Complex Analysis:  by K. Srinivas (2.5 hours)
The Riemann zeta function was introduced. It was shown that

  • The Riemann zeta function ζ(s), s = σ + it , is analytic in the half-plane σ > 1
  • ζ(s) admits analytic continuation in σ > 0
  • by means of functional equation, ζ(s) extends to a meromorphic function in the entire complex
  • place with a simple pole at s = 1 with residue 1
  • ζ(s) has real zeros at s = −2, −4, · · ·
  • The following topics were briefly discussed:
  • The complex zeros of ζ(s) , Riemann Hypothesis, and Hardy’s theorem.
  • prime number theorem.

Discrete Mathematics:  by K. N. Raghavan (11.5 hours)

Topics covered

  • Colourings and exact colourings of graphs; the chromatic polynomial; acyclic orientations and statement of Stanley’s theorem that the chromatic polynomial evaluated at −1 gives, up to sign,the number of acyclic orientations.
  • Definition of heaps of pieces, enumeration of heaps.
  • Generating functions of heaps, the inversion lemma.
  • proof of Stanley’s theorem using the inversion lemma.
  • calculations with generating functions: Fibonacci sequence; Fibonacci polynomials; Dyck paths.
  • Matching polynomials of graphs; statement about all their roots being real.

The emphasis was more on examples and calculations rather than on theory.

 


 

 Time Table

Monday Tuesday Wednesday Thursday Friday Saturday
09:30 - 11:00
Discrete Mathematics
K N Raghavan
09:30 - 11:00
Complex Analysis
P Sankaran
09:30 - 11:00
Discrete Mathematics
K N Raghavan
09:30 - 11:00
Discrete Mathematics
K N Raghavan
09:30 - 11:00
Algebra
S Viswanath
09:30 - 11:00
Discrete Mathematics
K N Raghavan
Coffee/Tea Coffee/Tea Coffee/Tea Coffee/Tea Coffee/Tea Coffee/Tea
11:30 - 13:00
Algebra
S Viswanath
11:30 - 13:00
Discrete Mathematics
K N Raghavan
11:30 - 13:00
Complex Analysis
P Sankaran
11:30 - 13:00
Complex Analysis
P Sankaran
11:30 - 13:00
Algebra
S Viswanath
11:30 - 13:00
Algebra
S Viswanath
Lunch Lunch Lunch Lunch Lunch Lunch
14:00 - 15:00
Algebra
S Viswanath
14:00 - 15:00 Algebra S Viswanath 14:00 - 15:00 Algebra S Viswanath 14:00 - 15:00 Discrete Mathematics K N Raghavan 14:00 - 15:00 Complex Analysis P Sankaran 14:00 - 15:00 Complex Analysis K Srinivas
Coffee/Tea Coffee/Tea Coffee/Tea Coffee/Tea Coffee/Tea Coffee/Tea
15:15 - 16:45
Tutorial Session:
Discrete Mathematics
K N Raghavan
15:15 - 16:45
Tutorial Session: Algebra S Viswanath
15:15 - 16:45
Tutorial Session: Complex Analysis P Sankaran
15:15 - 16:45
Tutorial Session: Complex Analysis P Sankaran
15:15 - 16:45
Tutorial Session:
Discrete Mathematics
K N Raghavan
15:15 - 16:45
Tutorial Session:
Complex Analysis
K Srinivas
Snacks Snacks Snacks Snacks Snacks Snacks

 


 

Actual Participants 

 

Sr.n SID Full Name Affiliation City State
1 12068 Mr. Mani Kandan K GURU NANAK COLLEGE CHENNAI Tamil Nadu
2 12112 Mr. Hari Krishnan Thanushkodi GURU NANAK COLLEGE (AUTONOMOUS) CHENNAI Tamil Nadu
3 12201 Mrs. N.Murugammal Narayanan Prabu GURUNANAK COLLEGE CHENNAI Tamil Nadu
4 12299 Mr. Rajaji Ramasamy Patrician College of Arts and Science Chennai Tamil Nadu
5 12854 Mr. Jayasankar Sivaraman RKM Vivekananda College, Chennai 600004 Chennai Tamil Nadu
6 12874 Dr Maria Joseph St. Joseph's College(Autonomous) Trichy  
7 13004 Dr. Manikandan Mariappan Bishop Heber College Tiruchirappalli Tamil Nadu
8 13043 Dr. Devipriya Ganeshan Stella Maris College Chennai Tamil Nadu
9 13053 Ms Dhanalakshmi Arumugasamy Stella Maris College Chennai Tamil Nadu
10 13084 Mr. Mahadev Ota B S Abdur Rahman University Chennai Tamil Nadu
11 13119 Dr. S. Sarah Surya Stella Maris College Chennai Tamil Nadu
12 13125 Dr Saravanakumar Dhanabal Kalasalingam University Krishnankoil Tamil Nadu
13 13138 Mr. Christopher A Don Bosco College (Arts and Science) Karaikal Pondicherry
14 13158 Mrs Prabhavathi Viswanathan Krishnan Apollo arts &science college Chennai Tamil Nadu
15 13162 Mrs. Prabha Kumar Ethiraj college for women, chennai 600 008 chennai Tamil Nadu
16 13163 Dr V.Vijaya Bharathi National Institute of Technology Trichy Tamil Nadu
17 13169 Mrs. Archana Rajaraman kumarmangalam solutions CHENNAI Tamil Nadu
18 13177 Mr Carmel Pushpa Raj J St.Joseph's College Tiruchirappalli Tamil Nadu
19 13182 Mr Thirumal P D G Vaishnav College chenai. Tamil Nadu
20 13187 Mr Bala Samuvel J. Alpha Arts and Science College Chennai Tamil Nadu
21 13190 Mrs. Sujatha M K.S.RANGASAMY COLLEGE OF ARTS AND SCIENCE(AUTONOMOUS) THIRUCHENGODE Tamil Nadu
22 13203 Mrs Subhashini A Anna university chennai Tamil Nadu
23 13220 Mrs. Esakkiammal Esakki Sundaram S.I.V.E.T. College CHENNAI Tamil Nadu
24 13230 Mrs. Ramya Murugesan Chevalier T. Thomas Elizabeth College for Women Chennai Tamil Nadu
25 13268 Mrs Shanthi As Stella Maris College Chennai Tamil Nadu
26 13269 Dr. K. Bagee Rathi Aditanar college of Arts and Science Thoothukudi Tamil Nadu
27 13297 Dr Sadiq Basha ANNA UNIVERSITY CHENNAI Tamil Nadu
28 13299 Dr Bharathi S Bharathiar University PG Extension Centre Erode Tamil Nadu
29 13313 Prof Priya Dharshini Dr.MGR Janaki college of arts and science for women chennai Tamil Nadu
30 13321 Ms Tamilselvi Selvaraj DG VAISHNAVA COLLEGE chennai Tamil Nadu
31 13322 Mrs. Enitha Dorothy Women's Christian College, Chennai. Chennai Tamil Nadu
32 13325 Mrs Anandha Selvam THE AMERICAN COLLEGE MADURAI Tamil Nadu
33 13329 Mrs. Shanthi Muniasamy Guru Nanak College Chennai Tamil Nadu
34 13337 Mr Gnanam Mahesh Kalakaoi AGURCHAND MANMULL JAIN COLLEGE Chennai Tamil Nadu
35 13343 Ms. Logu S M. G. R Janaki college of arts and science Chennai Tamil Nadu
36 12203 Mr. Thilakraj.E Elumalai.V GURUNANAK COLLEGE(AUTONOMOUS) CHENNAI Tamil Nadu
37 12983 Ms Krishnaveni Cheruvu MARIS STELLA COLLEGE VIJAYAWADA Andhra Pradesh
38 13266 Dr. Uma S Thiruvalluvar University Constituent Arts and Science College, Kallakurichi - 606213
Villupuram District
Kallakurichi, Villupuram Tamil Nadu
39 13301 Dr Kalamani D Bharathiar University PG extension Centre, Erode erode Tamil Nadu
40   K.Karunagaran Bharat university Chennai  
41   NANDAKUMAR VELU Bharat university Chennai  
42   P.BHATHMANABAN Bharat university Chennai  
43   Usha Sangale SRTM University Nanded, Maharashtra  
44   Sharanya C Bhaktavatsalam memorial college for women Chennai  
45   A Murugan Anna University Chennai  
46   G. Jagadeesh Anna University Chennai  
47   Divya S. Raj DGVC Chennai  
48   V. Pusparaj MOHAMED SATHAK COLLEGE OF ARTS AND SCIENCE Chennai  
49   A. Marimuthu MOHAMED SATHAK COLLEGE OF ARTS AND SCIENCE Chennai  
50   P. Gangeshwari Kumararani Meena Muthiah College of Arts and Sciences Chennai  
51   S. Elumalai RMKV College Chennai  
52   R. Siluvai Dasan Tagore Group of Institutions Chennai  
53   Hanna Bright Ethiraj College for Women Chennai  
54 13301 Dr Kalamani D Bharathiar University PG extension Centre, Erode erode Tamil Nadu
55 13143 Mr G Jagadeesh ANNA UNIVERSITY-CEG CAMPUS GUINDY Tamil Nadu
56 13179 Mr. Marimuthu A MOHAMED SATHAK COLLEGE OF ARTS AND SCIENCE CHENNAI Tamil Nadu
57 13275 Mr. Pusparaj V MOHAMED SATHAK COLLEGE OF ARTS AND SCIENCE CHENNAI Tamil Nadu
58 13333 Ms. Saranya.C Saranya.C R.Chandra Mohan Bhaktavatsalam memorial college for women chennai Tamil Nadu
59 13346 Ms Divya S Raj DG VAISHNAV COLLEGE CHENNAI Tamil Nadu

 


How to reach

 

The Chennai neé Madras, and to IMSc, the Institute of Mathematical Sciences. Here is some information on getting to the Institute. Address and phone numbers are

THE INSTITUTE OF MATHEMATICAL SCIENCES
C I T CAMPUS, TARAMANI, CHENNAI 600 113
Telephone Numbers

Here are some maps to give you a rough idea of the layout of Madras and the area around the Institute.

The Institute of Mathematical Sciences is located in a campus-like area variously known as the ``CIT Campus'' or the ``CPT Campus''. Many people in Madras may not have heard of the Institute, but almost everyone would have heard of the M.G.R. Film City and Tidel Park which are further down in the same campus area. IMSc has two complexes. One houses the main Institute building, the library building and the new building. The other has the students' hostel and Guest House. These two complexes are across the road from each other.