| 36-710/36-752, Fall 2020 Class Schedule | Date | Lecture Topic | Readings | Scribe Notes | Notes and HW Assignments |
|---|---|---|---|---|
| Aug 31, M | Welcome! Algebra of sets. | Lecture Notes 1 | ||
| Sep 2, W | Fields and Sigma-fields. Measure. | Lecture Notes 1 | HW1 is out. | |
| Sep 7, M | No Class -- Labor Day | |||
| Sep 9, W | Continuty of measure. Unieuqness. Construction and extension. | Lecture Notes 1 | ||
| Sep 14, M | Construction and extension of measures. Measures from c.d.f.'s. Lebesgue measure. | Lecture Notes 1 and Lecture Notes 2 | ||
| Sep 16, W | Measurable functions. | Lecture Notes 2 | ||
| Sep 21, M | Measurable functions. Random variables. Integral of simple functions. | Lecture Notes 2 | HW2 is out. | |
| Sep 23, W | Integral: definition and first proerties. MCT. | Lecture Notes 2 and Lecture Notes 3 | ||
| Sep 28, M | Standard machinery, change of variable, densities, DCT. | Lecture Notes 3 | ||
| Sep 30, W | Riemann vs Lebesgue integral, Radon-Nykodim derivative. | Lecture Notes 3 | ||
| Oct 5, M | Product spaces and product measure. Tonelli/Fubini theorems. | Lecture Notes 4 | ||
| Oct 7, W | Independence. Infinite produce spaces and stochastic processes. | Lecture Notes 4 | HW3 is out. | |
| Oct 12, M | Kolmogorov's extension theorem and Brownian motion. Lp spaces. | Lecture Notes 4 and Lecture Notes 5 | ||
| Oct 14, W | Lp spaces. Convergence in probability. | Lecture Notes 5 | ||
| Oct 19, M | Convergence in probability. | Lecture Notes 5 | ||
| Oct 21, W | Comparison among convergence in LP, in probability and with probability 1. Kolomogorov's 0-1 law. Borel-Cantelli Lemmas. | Lecture Notes 5 and Lecture Notes 6 | ||
| Oct 26, M | Almost sure and L2 convergence. Law of iterated logarithms. | Lecture Notes 6 | ||
| Oct 28, W | Convergence in distribution. | Lecture Notes 7 | HW4 is out. | |
| Nov 2, M | Continuous mapping theorem. | Lecture Notes 7 | ||
| Nov 4, W | Glienko-Csntelli theorem and Op and op notaiton. | Chapter 2 of Asymptotic Statistics by A.W. van der Vaart | ||
| Nov 9, W | Delta method and characteristic function. | Lecture Notes 7 and Lecture Notes 8 | ||
| Nov 11, W | Characteristic functions and the CLT. | Lecture Notes 7 and Lecture Notes 8 | ||
| Nov 16, M | CLT and Berry-Eseeen bounds. | Lecture Notes 8 | ||
| Nov 18, W | Conditional expectation . | Lecture Notes 9 | ||
| Nov 23, M | Conditional expectation. | Lecture Notes 9 | HW5 is out. | |
| Nov 30, M | Conditional expectation and Martingales. | Lecture Notes 9 and Lecture Notes 10 | ||
| Dec 2, W | Martingales. | Lecture Notes 10 | ||
| Dec 7, M | Martingales. | Lecture Notes 10 | ||
| Dec 9, W | Measures in high dimensions. | Lecture Notes 10 | ||