Annual Foundation School - I (2019) Hyderabad


School of Mathematics & Statistics,  Hyderabad, Telangana


6th, May 2019 to 1st, Jun 2019


School Convener(s)

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



 Actual syllabus covered by each speaker with his/her affiliation


Name of the Speaker with their affiliation. No. of Lectures Detailed Syllabus
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)
Prof. R Thangadurai
HRI, Prayagraj
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
IIT Delhi
6 [SS] Fourier Transform, Class of Holomorphic functions, Paley-Wiener Theorem
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, Sub-basis 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, Stone-Cech 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 Stone-Weierstrass Theorem, Constructing Mobius Strips, Torus and higher genus surfaces, Cone construction, Glueing lemma, Quotient space, Topological Group, Orbit Space.


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


Lecture 2
Tutorial 1
Tutorial 2
  (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 May-25 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, Tamilnadu-620024 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.( 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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