This is the archived site for the Spring 2014 section of “Math 521: Analysis I” as taught by Matthew D. Johnston at the University of Wisconsin – Madison.
Textbook
- Rudin, Principles of Mathematical Analysis, 3rd Edition
Assignments
- Assignment 1
- Assignment 2
- Assignment 3
- Assignment 4
- Assignment 5
- Assignment 6
- Assignment 7
- Assignment 8
Term Tests
- Term Test I (Section 001) (Section 002)
- Term Test II (Section 001) (Section 002)
Lectures
- Week 1 (lecture notes) (Review and expectations, quantifiers, set notation, introduction to proofs)
- Week 2 (lecture notes) (Rational numbers, real numbers, ordered sets, density, countability)
- Week 3 (lecture notes) (Fields, supremum and infimum, upper bound property)
- Week 4 (lecture notes) (Further set notation, metric spaces, Euclidean spaces)
- Week 5 (lecture notes) (Other Metrics on Rn, Hausdorff Metric on Intervals)
- Week 6 (lecture notes) (Topology, open and closed sets, closure, connectedness)
- Week 7 (lecture notes) (Open covers, compactness)
- Week 8 (lecture notes) (Sequences, convergence)
- Week 9 (lecture notes) (Cauchy sequences, subsequences, limsup and liminf)
- Week 10 (lecture notes) (Series, Cauchy criterion, geometric and p-series, comparison test)
- Week 11 (lecture notes) (Functions on metric spaces, limits of functions, continuity)
- Week 12 (lecture notes) (Uniform continuity, continuity and topology/compactness/connectedness)
- Week 13 (lecture notes) (Derivatives, mean value theorem, continuity of derivatives, L’Hopital’s rule)
- Week 14 (lecture notes) (Riemann integration, general properties)
- Week 15 (lecture notes) (Pointwise convergence, uniform convergence, metrics on functions, review)
Matthew D. Johnston 