Introduction to Real Analysis, Aug-Nov 2017
Vijay Ravikumar (vijayr at cmi dot ac dot in)
Monday 10:30 - 11:45 / Thursday 10:30 - 11:45
CMI Lecture Hall 6
('Meet Me at Dusk at the Steps of the Old Cantor Town' by Kaća Bradonjić)
('Meet Me at Dusk at the Steps of the Old Cantor Town' by Kaća Bradonjić)
1) Late homework will be accepted at half credit until exactly one week after the due date. No homework will be accepted after that point.
2) If you have difficulty with an assignment, you are encouraged to approach the instructor for help. It is also fine to discuss the problems with other students, but...
3) Your final write-up must be your own. If you have received help solving a problem, then you must cite your source(s). In particular, plagiarism, or any kind of copying, will not be tolerated. Offences will result in serious disciplinary action, up to and including a failing grade in the course.
| date | lecture # | announcements |
| Aug 7 (mon) | 1: preliminaries | |
| Aug 10 (thu) | 2: the axiom of completeness | |
| Aug 14 (mon) | 3: consequences of completeness | homework #1 due |
| Aug 17 (thu) | 4: cardinality | |
| Aug 21 (mon) | 5: the limit of a sequence | homework #2 due |
| Aug 24 (thu) | 6: algebraic and order limit theorems | |
| Aug 28 (mon) | 7: the monotone convergence theorem | homework #3 due |
| Aug 31 (thu) | 8: the bolzano-weierstrass theorem | |
| Sep 4 (mon) | 9: the cauchy criterion | homework #4 due |
| Sep 7 (thu) | 10: infinite series | |
| Sep 11 (mon) | 11: the cantor set | |
| Sep 14 (thu) | 12: open and closed sets | homework #5 due |
| Sep 18 (mon) | 13: compact sets | |
| Sep 21 (thu) | 14: perfect sets | homework #6 due |
| Oct 02 (mon) | no lecture: holiday | |
| Oct 05 (thu) | 15: connected sets | |
| Oct 09 (mon) | 16: functional limits | |
| Oct 12 (thu) | 17: continuity | |
| Oct 16 (mon) | 18: compactness | homework #7 due |
| Oct 19 (thu) | 19: intermediate value theorem | |
| Oct 23 (mon) | NO LECTURE | homework #8 due |
| Oct 26 (thu) | 20: the derivative | |
| Oct 30 (mon) | 21: mean value theorems | homework #9 due |
| Nov 02 (thu) | 22: more on the derivative | |
| Nov 06 (mon) | 23: uniform convergence of functions | homework #10 due |
| Nov 09 (thu) | 24: more on uniform convergence | |
| Nov 13 (mon) | 25: series of functions | homework #11 due |
| Notes for the differentiable | ||
| limit theorem. | ||
| Nov 16 (thu) | 26: power series | |
| Nov 20 (mon) | 27: riemann integration | homework #12 due |
| Nov 23 (thu) | 28: weierstrass approximation theorem |
('Infinite Series I' by Kaća Bradonjić)
('Infinite Series II' by Kaća Bradonjić)