Course Meeting Times
Lectures: 2 sessions / week, 1.5 hour / session
Prerequisites
18.02 Multivariable Calculus; 18.03 Differential Equations or 18.034 Honors Differential Equations
Text
Rudin, W. Principles of Mathematical Analysis. 3rd ed. McGraw-Hill Science/Engineering/Math, New York, NY: McGraw-Hill, 1976. ISBN: 9780070542358.
Assignments
Weekly homework is due on the second day of class each week. There are 10 homework assignments; the lowest two scores will be dropped.
Exams
There are four in-class 30-minute quizzes, and one 3-hour final exam. The worst quiz score is dropped.
Grading
| ACTIVITIES | PERCENTAGES |
|---|---|
| Problem sets | 20% |
| In-class quizzes | 25% |
| Final exam | 45% |
| Discussion | 10% |
Calendar
| SES # | TOPICS | KEY DATES |
|---|---|---|
| 1 | Ordered sets and fields | |
| 2 | Metric spaces | |
| 3 | Relative topology, compact sets | |
| 4 | Compact sets (cont.) | |
| 5 | Connected sets, convergence | |
| 6 | Sequential compactness | Quiz 1 |
| 7 | Completeness | |
| 8 | Construction of the real numbers | |
| 9 | Series | |
| 10 | Series (cont.) | |
| 11 | Continuity | |
| 12 | l^p spaces | Quiz 2 |
| 13 | Continuity and compactness, connectedness | |
| 14 | Discontinuities, monotone functions | |
| 15 | Differentiability, mean value theorem | |
| 16 | l’Hospital’s rule, Taylor’s theorem | |
| 17 | Riemann integral | |
| 18 | Riemann integrability and continuity almost everywhere | Quiz 3 |
| 19 | Stieltjes integral, fundamental theorem of calculus | |
| 20 | Sequences and series of functions | |
| 21 | Equicontinuity | |
| 22 | Optional material: Weierstrass function, Devil’s Staircase | Quiz 4 |
| 23 | Review for final exam | |
| 24 | Review for final exam (cont.) | |
| 25 | Final exam | |
