Annual Foundation School  I (2019) Hyderabad
Venue: 
School of Mathematics & Statistics, Hyderabad, Telangana 
Date: 
6th, May 2019 to 1st, Jun 2019 
Name  Mohan Chintamani  Shanta Laishram 
Mailing Address  School of Mathematics & Statistics, University of Hyderabad – 500 0046 
Indian Statistical Institute 7 S J S Sansanwal Marg, New Delhi  110016 
Names of the tutors and their affiliation :

Names of the Tutors/Course associate Affiliation 1. Laba Sa University of Hyderabad 2. Mansoor Ali University of Hyderabad 3. Rubayya Y University of Hyderabad 4. Arijit Mukherjee University of Hyderabad 5. Pabitra Mandal University of Hyderabad 6. Bijay Sahoo BITS Goa 7. Bandana Pandey BITS Goa 8. Shayantan G BITS Goa 9. Pramod Ghatage SSMM, Pune 10. Biman Roy ISI, Delhi 11. Manabendra Giri ISI, Delhi 12. P Santhosh Kumar ISI Bangalore
Syllabus:
Actual syllabus covered by each speaker with his/her affiliation
Name of the Speaker with their affiliation.  No. of Lectures  Detailed Syllabus 
ALGEBRA  
Dr. Archana Morye (AM) UoH, Hyderabad  6  [Artin, Ch 6] ]Group Actions, Cayley’s Theorem, Class Equation, Simple Group & Examples, Icosahedral group, Sylow Theorems and its applications, Free group, Generators and Relations 
Prof. Sameer Chavan (SC) IIT Kanpur  6  [Artin, Ch 7] Bilinear forms, Symmetric forms : Orthogonality, Orthogonal projection, Hermitian Forms, Spectral Theorem, Conics and Quadric 
Prof. Shanta Laishram (SL) ISI Delhi  6  [Artin, Ch 8] Classical Linear Groups, Special Unitary Group SU(2) and its Orthogonal Representation SL(2,R), One parameter subgroups, Lie Algebra & Simple Groups 
Dr. Mohan Chintamani (MC) UoH, Hyderabad  6  [Artin, Ch 9] 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) 
ANALYSIS  
Prof. R Thangadurai (RT) HRI, Prayagraj (Allahabad) 
6  [SS] 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 
Prof. Purusottam Rath (PR) CMI, Chennai 
6  [SS] Morera’s Theorem,, Sequences of holomorphic functions,Schwarz reflection principle, Runge’s approximation theorem,Zeros and Poles, Residue Formula 
Prof. S. Ilangovan (SI) UoH, Hyderabad 
6  [SS] Singularities and Meroporhic functions,The argument principle, Rouche’s theorem, Open mapping theorem,Maximum modulus principle, The complex logarithm, Fourier Series and Harmonic Functions. 
Prof. S Sivananthan (SS) IIT Delhi 
6  [SS] Fourier Transform, Class of Holomorphic functions, PaleyWiener Theorem 
TOPOLOGY  
Dr. TKS Moothathu (TM) UoH, Hyderabad  6  [Simmons] 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 
Prof. Sanoli Gun (SG) IMSc, Chennai  6  [Simmons] 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. Prabal Paul (PP) BITS Goa  6  [Simmons] Urysohn Imbedding Theorem, StoneCech Compactification, Connected Spaces, Components of a space, totally disconnected spaces, Locally connected Spaces, Weierstrass Approximation Theorem, Stone Weierstrass Theorem 
Prof. M S Datt (MD) UoH, Hyderabad  6  [Simmons, Armstrong] 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 [Artin]
2. Complex Analysis, Stein E.M and Rami Shakarchi [SS]
3. Introduction to Topology and Modern Analysis, G.F.Simmons [Simmons]
4. Basic Topology, M.A. Armstrong [Armstrong]
Time Table
I Week (06 May  11 May)  
Day  Lecture 1 (9.30 to 11.00) 
Tea 
Lecture 2 (11.30 to 1.00) 
Lunch (1.00 to 2.30) 
Tutorial 1 (2.30 to 3.30) 
Tea (3.30 to 4.00) 
Tutorial 2 4.00 to 5.00 
Snack 5.00 to 5.30 
(Name of the Speaker  (Name of the Speaker  (Name of the Tutor)  (Name of the Tutor)  
Mon  TM  RT  Topology (Bsa/Rb)  Topology (BSa/Rb)  
Tues  AM  TM  Analysis (MA/ShG)  Analysis (MA/ShG)  
Wed  RT  AM  Algebra (LS/Ar)  Algebra (LS/Ar)  
Thu  TM  RT  Topology (BSa/Rb)  Topology (BSa/Rb)  
Fri  AM  TM  Analysis (MA/ShG)  Analysis (MA/ShG)  
Sat  RT  Algebra (LS/Ar) May )  Algebra (LS/Ar)  
II Week (13 May – 18 May )  
Mon  PR  SG  Topology (BR/MG)  Topology (BR/MG)  
Tue  SC  PR  Analysis (LS/Ar)  Analysis (LS/Ar)  
Wed  SG  SC  Algebra (PM/PG)  Algebra (PM/PG)  
Thu  PR  SG  Topology (BR/MG)  Topology (BR/MG)  
Fri  SC  PR  Analysis (ShG/Ar)  Analysis (ShG/Ar)  
Sat  SG  SC  Algebra (PM/PG)  Algebra (PM/PG)  
III Week (20 May25 May)  
(Name of the Speaker  (Name of the Speaker  (Name of the Tutor)  (Name of the Tutor)  
Mon  SI  PP  Analysis (PM/Rb)  Analysis (PM/Rb)  
Tue  SL  SI  Topology (BP/BSa)  Topology (BP/BSa)  
Wed  SI  PP  Algebra (BR/MG)  Algebra (BR/MG)  
Thu  SL  SI  Analysis (PM/MA)  Analysis (PM/MA)  
Fri  PP  SL  Topology (BP/SK)  Topology (BP/SK)  
Sat  PP  SL  Algebra (BR/MG)  Algebra (BR/MG)  
IV Week (27 May – 01 Jun)  
Mon  MC  MD  Topology (MA/SK)  Topology (MA/SK)  
Tue  SS  MC  Analysis (BR/MG)  Algebra (LS/BP)  
Wed  SS  MD  Algebra (LS/BP)  Analysis (BR/MG)  
Thu  SS  MC  Analysis (BP/ShG)  Analysis (BP/ShG)  
Fri  SS  MD  Topology (MA/Rb)  Topology (MA/Rb)  
Sat  MC  MD  Algebra (LS/BSa)  Algebra (LS/BSa) 
List of actual Participants
Sr.n  SID  Full Name  Gender  Affiliation  Position in College/ University  University/ Institute M.Sc./ M.A.  Year of Passing M.Sc./ M.A  
1  24505  Mr Ranganath M S  Male  Vijayanagar Srikrishnadevaraya University  PhD student  Tumkur University  2016  
2  24506  Mr Mahendra D L  Male  Vijayanagara Shri Krishnadevaraya university  Research Scholar  Bangalore university  2014  
3  24514  Mr. Jeyarambharathi A.M.  Male  Hindustan Institute Of Technology And Science  PhD student  MAHER  2016  
4  24516  Ms Sarojini Sowmiya Manohar  Female  Bharathidasan University  PhD  Central University Of Tamil Nadu  2016  
5  24777  Mr Pradipkumar Laishram  Male  Manipur University  Phd  Manipur University  2017  
6  24798  Ms Shantha Kumari Y  Female  Vijayanagara Sri Krishnadevaraya University,Bellary  PhD  M.Sc  2016  
7  24899  Mr. Akshay Kumar  Male  university of Hyderabad  PhD  Banaras Hindu University  2017  
8  24932  Ms. Suriyapriya K  Female  National Institute of Technology  PhD Student  Bharathidasan University, Tiruchirappalli, Tamilnadu620024  2018  
9  25045  Mr. Joydev Halder  Male  University Of Hyderabad  PhD  University of Hyderabad  2017  
10  25054  Ms Bhushna Sekar  Female  Manonmaniam Sundarnar University  MPhil Student  National College  2018  
11  25079  Ms Megala M  Female  IIT tirupati  PhD  Govt arts college,tiruvannamalai.(M.sc)  2014  
12  25091  Ms J U Viharika  Female  Vijayanagara Sri Krishnadevaraya University  phD  VSK University  2018  
13  25096  Ms Archana Bhat  Female  National Institute Of Technology Warangal  PhD Student  Central University Of Karnataka, Kalaburagi  2017  
14  25097  Mr Basharat Hussain  Male  maulana azad national urdu university  PhD  jamia millia islamia  2017  
15  25113  Mr. Md Ibrahim Molla  Male  Ramakrishna Mission Vivekananda Educational and Research Institute  Ph. D  University of Calcutta, Ballygunge Science College  2018  
16  25162  Ms. Devichandrika V  Female  University Of Hyderabad  Ph.D  Central University Of Kerala  2018  
17  25355  Mr Anshid Aboobacker  Male  University of Hyderabad  MSc Student  University of Hyderabad  Appeared  
18  25376  Ms. Roshni T Roy  Female  Central University of Kerala  PhD  St Berchmans College  2017  
19  25378  Ms. Soorya P  Female  Central University of Kerala  PhD  Mahatma Gandhi College  2016  
20  25409  Mr. Sumangal Bhattacharya  Male  IIT Tirupati  PhD  Indian Institute of Engineering Science and Technology, Shibpur  2016  
21  25415  Mr Faiz Imam  Male  BITS Hyderabad  PhD  University of Hyderabad  2017  
22  25442  Ms Asha Sebastian  Female  National Institute Of Technology, Tiruchirappalli  PhD student  National Institute of Technology, Calicut  2014  
23  25445  Ms Sreenanda S B  Female  University of Hyderabad  PhD  Pondicherry University  2017  
24  25505  Mr. Sarbajit Dey  Male  Indian Statistical Institute  M. Math Student  Indian Statistical Institute  
25  25664  Ms Sangeetha K V  Female  National Institute of Technology  PhD Student  Central University of Tamil Nadu  2016  
26  25692  Mr. Aravind Vishnu S S  Male  Amrita Vishwa Vidyapeetham  PhD Student  Cochin University of Science and Technology  2017  
27  25810  Ms. Sruthi K K  Female  Cochin University of Science and Technology  MSc passed  Cochin University of Science and Technology  2018  
28  25835  Mr. Kishan Indravadan Vyas  St. Xavier's College  Asst. Professor  Gujarat University  2016  
29  25644  Mr. Navin Tomy  Male  Cochin University Of Science And Technology  PhD  Cochin University Of Science And Technology  2017  
30  25650  Ms. Rupsa Mitra  Female  IIT(ISM) Dhanbad  Ph.D.  IIT(ISM) Dhanbad  2018  
31  25663  Ms Kanaga R  Female  National Institute of Technology  PhD student  Bharathidasan University  2017  
32  24906  Mr. Bharat Kumar  Male  IIITDM, Jabalpur M.P.  Ph.D. Student  NIT Rourkela  2017  
33  25111  Mr. Suryanarayana Murty Ponnada  Male  IIT Tirupati  PhD  Andhra University  2007  
34  25424  Ms Amudhavalli B   Bharathidasan University Constituent Arts & Science College  MSC Completed  University  2018  
35  25438  Mr. Shijin T V  Central University of Kerala  PhD  Mahatma Gandhi College  2016 
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