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, Paley-Wiener 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, 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. |
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 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.(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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