# Syllabus

## 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

Grading criteria.
ACTIVITIES | PERCENTAGES
--- | ---
Problem sets | 20%
In-class quizzes | 25%
Final exam | 45%
Discussion | 10%

## Calendar

Course 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