# Introduction to Real Analysis, Aug-Nov 2017

### CMI Lecture Hall 6

('Meet Me at Dusk at the Steps of the Old Cantor Town' by Kaća Bradonjić)

### Text:

Understanding Analysis by Stephen Abbott

Midterm exam: 30%
Final exam: 30%
Weekly Homeworks: 30%
Class participation: 10%

### Homework Policy:

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.

### Homework sets so far:

Homework #1 due on Monday August 14 in class.
Homework #2 due on Monday August 21 in class.
Homework #3 due on Monday August 28 in class.
Homework #4 due on Monday September 4 in class.
Homework #5 due on Thursday September 14 in class.
Homework #6 due on Thursday September 21 in class.
Homework #7 due on Monday October 16 in class.
Homework #8 due on Monday October 23 in class.
Homework #9 due on Monday October 30 in class.
Homework #10 due on Monday November 06 in class.
Homework #11 due on Monday November 13 in class.
Homework #12 due on Monday November 20 in class.

### Quizzes so far:

Quiz #1 happened on Thursday, August 31.

### Lecture Schedule:

 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)