18.100B | Fall 2010 | Undergraduate
Analysis I

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.

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
Course Info
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As Taught In
Fall 2010
Learning Resource Types
assignment_turned_in Problem Sets with Solutions
notes Lecture Notes
grading Exams with Solutions