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

Amazon logo 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 #TOPICSKEY DATES
1Ordered sets and fields 
2Metric spaces 
3Relative topology, compact sets 
4Compact sets (cont.) 
5Connected sets, convergence 
6Sequential compactnessQuiz 1
7Completeness 
8Construction of the real numbers 
9Series 
10Series (cont.) 
11Continuity 
12l^p spacesQuiz 2
13Continuity and compactness, connectedness 
14Discontinuities, monotone functions 
15Differentiability, mean value theorem 
16l'Hospital's rule, Taylor's theorem 
17Riemann integral 
18Riemann integrability and continuity almost everywhereQuiz 3
19Stieltjes integral, fundamental theorem of calculus 
20Sequences and series of functions 
21Equicontinuity 
22Optional material: Weierstrass function, Devil's StaircaseQuiz 4
23Review for final exam 
24Review for final exam (cont.) 
25 Final exam