# Readings & Notes

Readings are assigned in Rudin, W. Principles of Mathematical Analysis. 3rd ed. McGraw-Hill Science/Engineering/Math, New York, NY: McGraw-Hill, 1976. ISBN: 9780070542358.

The supplementary notes are courtesy of Prof. Todd Kemp and are used with permission.

Course readings.
SES # | TOPICS | READINGS
--- | --- | ---
1 | Ordered sets and fields | Section 1.1-31
2 | Countability, Euclidean spaces | Section 1.32-38, and 2.1-17
3 | Metric spaces | Section 2.15-28
4 | Relative topology, compact sets | Section 2.29-40
5 | Compact sets | Section 2.36-44
6 | Connected sets, convergence | Section 2.45-47, and 3.1-7
7 | Sequential compactness | Notes (PDF)
8 | Completeness | Section 3.8-20
9 | Construction of the real numbers | Notes (PDF)
10 | Series | Section 3.20-37
11 | Series (cont.) | Section 3.38-55
12 | Continuity | Section 4.1-12
13 | l^p spaces | Notes (PDF)
14 | Continuity and compactness, connectedness | Section 4.13-24
15 | Discontinuities, monotone functions | Section 4.25-34
16 | Differentiability, mean value theorem | Section 5.1-11
17 | l'Hospital's rule, Taylor's theorem | Section 5.12-19
18 | Riemann integral | Section 6.1-12 with alpha(x)=x
19 | Riemann integrability and continuity almost everywhere | Notes (PDF)
20 | Stieltjes integral, fundamental theorem of calculus | Section 6.1-22
21 | Sequences and series of functions | Section 7.1-17
22 | Equicontinuity | Section 7.18-25
23 | Optional material: Weierstrass function, Devil's staircase | Weierstrass function (PDF), Devil's staircase (PDF)
24 | Review for final exam | No readings
25 | Review for final exam (cont.) | No readings