Daily Log
The table below contains a summary of what is covered each class day, along with any computer files (e.g. Matlab files) that were used that day.
I will post the lecture notes that I write on the screen here. They may be useful in filling in your own hand-written notes after the fact. Please do not rely on them solely.
| Date | Topics | Zoom | Notes |
|---|---|---|---|
| 12-01 |
Video |
Notes |
|
| 11-29 |
Video |
Notes |
|
| 11-23 | Dominated Convergence Theorem |
Video |
Notes |
| 11-19 | Fatou's Lemma |
Video |
Notes |
| 11-17 | Monotone Convergence Theorem |
Video |
Notes |
| 11-15 | Integrable Simple Functions |
Video |
Notes |
| 11-12 | The "Basic Construction" |
Video |
Notes |
| 11-10 | Properties of measurable functions |
Video |
Notes |
| 11-08 | A nonmeasurable set; measurable functions |
Video |
Notes |
| 11-05 | Approximation of measurable sets |
Video |
Notes |
| 11-03 | Measurable sets are a sigma algebra |
Video |
Notes |
| 11-01 | Measurable sets via Caratheodory |
Video |
Notes |
| 10-29 | Outer measure is mostly good |
Video |
Notes |
| 10-27 | Desired properties of length |
Video |
Notes |
| 10-25 | Riemann Integral |
Video |
Notes |
| 10-22 | Midterm | ||
| 10-20 | Arzela-Ascoli; Riemann Integral |
Video |
Notes |
| 10-18 | Compact subsets of C[0,1] |
Video |
Notes |
| 10-15 | Approximation in C[0,1] |
Video |
Notes |
| 10-13 | Approximation in C[0,1] |
Video |
Notes |
| 10-11 | M-Test, Power Series |
Video |
Notes |
| 10-8 | Derivatives and Uniform convergence |
Video |
Notes |
| 10-6 | Uniform convergence |
Video |
Notes |
| 10-4 | Pointwise convergence |
Video |
Notes |
| 10-1 | Equivalent Norms, Operator Norm |
Video |
Notes |
| 9-29 | Equivalent Norms |
Video |
Notes |
| 9-27 | Uniform Continuity |
Video |
Notes |
| 9-24 | Compactness |
Notes |
|
| 9-22 | Compactness |
Notes |
|
| 9-20 | Completeness |
Notes |
|
| 9-17 | Total Boundedness |
Video |
Notes |
| 9-15 | Continuity |
Video |
Notes |
| 9-13 | Continuity |
Video |
Notes |
| 9-10 | Open, Closed sets |
Video |
Notes |
| 9-8 | Triangle Inequality; Convergence |
Video |
Notes |
| 9-3 | Norms; Triangle Inequality |
Video |
Notes |
| 9-1 | Cantor Function; Metric Spaces |
Video |
Notes |
| 8-30 | Cardinality |
Video |
Notes |
| 8-27 | p-adic expansions |
Video |
Notes |
| 8-25 | Limit Supremum |
Video |
Notes |
| 8-23 | Real numbers |
Notes |