References
- [Armstrong] M. A. Armstrong, Basic Topology, Springer International Edition.
- [Artin] Michael Artin, Algebra, Pearson, 1991.
- [Simmons] G. F. Simmons, Introduction to Topology and Modern Analysis,McGraw-Hill, 1983.
- [Stein and Shakarchi] Elias M. Stein and Rami Shakarchi Complex Analysis, Princeton Lectures in Analysis-II, 2003.
Algebra I Linear Algebra and group theory.
[Artin] Chapters 6,7,8,9.
Analysis I Complex Analysis.
[Stein and Shakarchi] Chapters 2,3,4.
Topology I Point set topology:[Simmons] Chapters 1-7. and Quotient spaces: [Armstrong] Chapter 4 ‘Identification Spaces’.
Note: Notwithstanding what is listed above, the Faculty Members of any AFS program will have full latitude to pick and choose, or even introduce extra topics, so as to make the program more relevant to the students who have come to participate in that particular program.
Speakers and Topics
Algebra:
1. Chapter 7 of [Artin] Bilinear forms, Parvati Shastri, Mumbai Uni.
2. Chapter 6 of [Aritn] Group theory, Radhika, TIFR
3. Chapter 8 and 9 of [Artin], Linear Groups and representations, Viji Thomas, IISER Trivandrum.
Analysis
1. Chapter 2 of [Stein and Shakarchi] CR equations, analytic functions, etc. R. R. Simha TIFR
2. Chapter 3 of [Stein and Shakarchi] Line integrals, Sivaguru, TIFR
3. Chapter 4 of [Stein and Shakarchi] Homology and homotopy form of Cauchy’s theorem, A. R. Shastri IITB.
(Note: We feel that students may find the approach in [Stein and Shakarchi] difficult, and so, we shall follow the book Basic Complex Analysis of One Variable by Anant R. Shastri, MacMIllan India 2011.)
Topology
1. Chapter 1,2,3 of [Simmons] Basics of Metric topology and abstract topology, and quotient spaces from [Armstrong], A. R. Shastri IITB.
2. Chapter 4, 5 of [Simmons], Compactness and separation axioms, B. Subhash, IISER Tirupathi
3. Chapter 6 and 7 of Connectedness, Approximations [Simmons] K. Ramesh, ISI Bangalore.
Time Table for AFS-I at IISER Trivandrum
5th Dec. to 31st Dec 2016
| 09-30 to 11-00 | 11-30 to 13-00 | 14-30 to 17-00 | |||
| Lecture | Lecture | Tutorials | |||
| I-week:5th-10th Dec. 2016 | |||||
| Mon | Algebra (PS) | Tea | Analysis(RS) | L | Algebra(PS)(TBA) |
| Tue | Topology(AS) | B | Algebra(PS) | U | Analysis(RS)(TBA) |
| Wed | Analysis(RS) | R | Topology(AS) | N | Topology(AS)(TBA) |
| Thu | Algebra(PS) | E | Analysis(RS) | C | Algebra(PS)(TBA) |
| Fri | Topology(AS) | A | Algebra(PS) | H | Analysis(RS)(TBA) |
| Sat | Analysis(Rs) | K | Topology(AS) | Topology(AS)(TBA) | |
| II-week: 12th–17 Dec 2016 | |||||
| Mon | Algebra(RD) | Tea | Analysis(RS) | L | Algebra(RD)(TBA) |
| Tue | Topology(AS) | B | Algebra (RD) | U | Analysis(RS)(TBA) |
| Wed | Analysis(RS) | R | Topology (AS) | N | Topology(AS)(TBA) |
| Thu | Algebra(RD) | E | Analysis(SG) | C | Algebra(RD)(TBA) |
| Fri | Topology(BS) | A | Algebra(RD) | H | Analysis(SG)(TBA) |
| Sat | Analysis(SG) | K | Topology(BS) | Topology(BS)(TBA) | |
| III-week:19th–24th Dec. 2016 | |||||
| Mon | Algebra(VT) | Tea | Analysis(SG) | L | Algebra(VT)(TBA) |
| Tue | Topology(BS) | B | Algebra(VT) | U | Analysis(SG)(TBA) |
| Wed | Analysis(SG) | R | Topology(BS) | N | Topology(BS)(TBA) |
| Thu | Algebra(VT) | E | Analysis(SG) | C | Algebra(VT)(TBA) |
| Fri | Topology(BS) | A | Algebra(VT) | H | Analysis(SG)(TBA) |
| Sat | Analysis(AS) | K | Topology(RK) | Topology(RK)(TBA) | |
| IV-week:25th–31st Dec. 2016 | |||||
| Mon | Algebra(VT) | Tea | Analysis(AS) | L | Algebra(VT)(TBA) |
| Tue | Topology(RK) | B | Algebra(VT) | U | Analysis(AS)(TBA) |
| Wed | Analysis(AS) | R | Topology(RK) | N | Topology(AS)(TBA) |
| Thu | Algebra(VT) | E | Analysis(AS) | C | Algebra(VT)(TBA) |
| Fri | Topology(AS) | A | Algebra(VT) | H | Analysis(AS)(TBA) |
| Sat | Analysis(AS) | K | Topology(RK) | Topology(RK)(TBA) | |
- (PS) Parvati Shastri
- (RD)Radhika
- (SG)Sivaguru
- (RRS) R. R. Simha
- (AS) Anant Shastri
- (BS)B. Subhash
- (RK) Ramesh K.
- (VT)Viji Thomas
- (TBA) Course Associates (to be announced)