Math 521 (Spring 2014)

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.


  • Rudin, Principles of Mathematical Analysis, 3rd Edition


Term Tests


  • 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)