| Week 1 |
Class: Williams sections 1,2 - 1.6, 1.9, 1.10, A1.2 - A1.4
Homework: From "Week 1": 1,2,3,6 (see ps and pdf files above) |
| Week 2 |
Class: Williams sections 1.7, 1.8, chapters 2, 3 (with the
execption of 3.13), A3.1, A3.2
Homework: 4 exercises from "Week 1:4" and "Week 2" |
| Week 3 |
Class: Williams chapter 5, sections 6.1, 6.2, 6.6, 6.7, 6.10, 6.13
Homework: 4 exercises from "Week 3" |
| Week 4 |
Class: Williams sections 4.1, 4.2, 8.1 - 8.5, 8.8
Homework: 4 exercises from "Week 4" |
| Week 5 |
Class: Radon-Nikodym lecture notes (in ps and in pdf) sections 2, 3 for positive measures and Williams sections
9.1, 9.2, 9.4, 9.6, 9.7 (a-g), 9.8 (a-e)
Student lecture: Vincent Leijdekker on "Completion of a measure space" Homework: 4 exercises (in total) chosen out of "Week 5" and 5.2, 5.4, 5.5, 5.9 (lecture notes) |
| Week 6 |
Class: Williams sections 9.7 and 9.8 continued, 9.9, 9.10, chapter
13
Student lecture: Anneke Hartog on "Kolmogorov's 0-1 law" Homework: 4 exercises from "Week 6" |
| Week 7 |
Class: Williams sections 10.1-10.4, 10.6-10.10, 11.1-11.5, 14.1
Student lecture: Jessica Duin on "A strong law of large numbers" Homework: 4 exercises from "Week 7" |
| Week 8 |
Class: Williams sections 14.2-14.6, 14.10-14.11
Student lectures: Enno Veerman on "Pythagoras and martingales" and Annette Schuitemaker on "Kolmogorov's three series theorem" Homework: 4 exercises from "Week 8" |
| Week 9 |
Class: Williams sections 12.1, 12.6, 12.7, 12.8, 12.13 (a), 14.12,
14.17 (partly)
Student lectures: Philip Yau on "Weierstrass's approximation theorem" and Walter Moreno on "Relations between different modes of convergence" Homework: 4 exercises from "Week 9" |
| Week 10 |
Class: Williams sections 17.1 - 17.4
Student lectures: David Visser on "Orthogonal projections" and Silvia van Brummelen on "Doob's decomposition" Homework: 4 exercises from "Week 10" |
| Week 11 |
Class: Pollard sections II.3-4 (copies
will be provided)
Student lectures: Mark Koudstaal on "Riemann integrals and Lebesgue integrals" and Tze Shao on "Doob's optional sampling theorem for UI martingales" Homework: 4 exercises from "Week 11" |
| Week 12 |
Class: Weak convergence and Brownian Motion (lecture notes in ps
and in pdf)
Student lectures: Daniel Koerhuis, Roel Seller Homework: |