The Teacher Enrichment Workshop (TEW) is a programme funded by the National Centre for Mathematics (A joint centre of TIFR & IIT Bombay). The TEW is meant for only local college teachers and therefore there is no provision for travel reimbursement to the outstation teachers. The lectures in this workshop covers specific topics which are relevant for the teachers' classroom instructions. The usual length of the TEW is 5/6 days. An important component of this programme is the discussion hour during which the teachers will have opportunities to get their doubts cleared and work-out routine to an advanced exercises.
Syllabus
| Name of the Speaker with affiliation | No. of Lectures | Detailed Syllabus |
| Mahender Singh IISER Mohali |
06 | Homotopy, retract, deformation retract, contractible spaces and homotopy type, fundamental group and its properties, The fundamental group of circle, van Kampen theorem (statement without proof),definition and examples of covering spaces, path lifting and homotopy lifting property. |
| Dr. Aribam Chandrakant Sharma IISER Mohali |
06 | Field extensions, algebraic extensions, perfect fields, separable and normal extensions, Finite fields, algebraically closed fields, automorphisms of extensions, Galois extensions and Galois group, fundamental theorem of Galois theory, glimpses of algebraic number theory. |
| Prof. Rama Rawat IIT Kanpur |
06 | Introduction to Fourier series, definition and examples.Convergence of a Fourier series, Convolutions and good kernels.Continuous function with diverging Fourier series. Riemann-Lebesgue lemma. Some applications including the Isoperimetric inequality. The notion of Fourier transform on R, some properties and Fourier inversion and Plancherel’s formula. |
| Dr. Rajendra Prasad Pant VNIT Nagpur | 06 |
Review of point set topology, definition and examples of topological spaces, continuous maps, separation axioms, compactness and |
References:
1. R. C. Lyndon, P. E. Schupp, Combinatorial Group Theory, Classics in Mathematics, Springer, 1977.
2. S. Lang, Algebra, Third Edition, Springer (India) (2004).
3. J. R. Munkres, Topology, Pearson Education, Second Edition (2005).
4. Fourier Analysis- E M Stein & R Shakarchi
5. Fourier Series- R Bhatia
6. Lectures on Fourier Analysis- S Thanagvelu
7. Advanced Calculus- Widder
8.William Massey, Algebraic Topology: An Introduction, Springer Graduate Texts in Mathematice Vol. 127 (1977).
9.Allen Hatcher, Algebraic Topology, Cambridge University Press (2002).
Time-table (with names of speakers and tutors ):
| Day | Date | Lecture 1 (9.30–10.30) |
Tea (10.35-10.55) |
Lecturer 2 (11.00–12.00) |
Lecture 3 (12.00–1.00) |
Lunch (1.00 – 2.20) |
Lecture 4 (2.30- 3.30) |
Tea (3.35 - 3.55) |
Discussion (4.00-500) |
Snacks (5.05 – 5.35) |
| Mon | Oct 9 | Pant | Sharma | Rawat |
|
Pant |
|
Sharma | ||
| Tue | Oct 10 | Pant | Sharma | Rawat | Pant | Rawat | ||||
| Wed | Oct 11 | Pant | Sharma | Rawat | Pant | Pant | ||||
| Thur | Oct 12 | Singh | Sharma | Rawat | Singh | Sharma | ||||
| Fri | Oct 14 | Singh | Sharma | Rawat | Singh | Rawat | ||||
| Sat | Oct 14 | Singh | Sharma | Rawat | Singh | Singh |
Name of tutors
| S. No. | Name | Affiliation |
| 1 | Dr. Mahender Singh | IISER Mohali |
| 2 | Dr. Aribam Chandrakant Sharma | IISER Mohali |
| 3 | Dr. Rajendra Prasad Pant | VNIT Nagpur |
| 4 | Prof. Rama Rawat | IIT Kanpur |