This calendar is extremely tentative, but should give a general idea of what topics we will cover.
Course Textbooks:
| Date | Tentative class plan: |
| Tue, Feb 2 | Welcome! Notebook: The Tent Map and the Cantor Set [download] [view] |
| Thu, Feb 4 | Silva: § 2.1: Lebesgue Outer Measure Silva: § 2.2: The Cantor Set and Null Sets |
| Tue, Feb 9 | Silva: § 2.3: Lebesgue Measurable Sets Silva: § 2.4: Countable Additivity Dynamical construction of a non-measurable set |
| Thu, Feb 11 | Silva: § 2.5: Sigma-Algebras and Measure Spaces Silva: § 2.6: The Borel Sigma-Algebra |
| Tue, Feb 16 | Silva: § 3.2-3.3: Measure Preserving Transformations Finished Silva: § 2.6: The Monotone Class Theorem |
| Thu, Feb 18 | Silva: § 2.7: Approximation with Semi-rings Silva: § 3.4: Measurable transformations |
| Tue, Feb 23 | Going over homework problems. |
| Thu, Feb 25 | Silva: § 2.8: Measures from Outer Measures |
| Tue, Mar 2 | Finished Silva: § 2.8: Measures from Outer Measures Discussed example of Lebesgue measure on the Torus |
| Thu, Mar 4 | Discussed measure preserving transformations of the Torus Began discussing construction of Bernoulli measures on shift spaces |
| Tue, Mar 9 | Finish discussing Bernoulli measures on shift spaces |
| Thu, Mar 11 | Quiz 1. Silva § 3.5: Recurrence |
| Tue, Mar 16 | Flows and billiard systems |
| Thu, Mar 18 | Silva § 3.6: Almost everywhere and invariant sets Silva: § 3.7: Ergodic Transformations |
| Tue, Mar 23 | Example ergodic systems |
| Thu, Mar 25 | Midterm. |
| Tue, Mar 30 | Spring break |
| Thu, Apr 1 | Spring break |
| Tue, Apr 6 | Example ergodic systems Began Silva: § 3.10: Isomorphism |
| Thu, Apr 8 | Silva: § 3.10: Isomorphism |
| Tue, Apr 13 | Finish Silva: § 3.10: Isomorphism Silva: § 3.11: Induced Transformations |
| Thu, Apr 15 | Finish Silva: § 3.11: Induced Transformations Discuss some examples of induced transformations. Silva: § 4.2: Measurable functions |
| Tue, Apr 20 | Silva: § 4.2: Measurable functions Overview of Lebesgue Integration |
| Thu, Apr 22 | Silva: § 4.3: Integrals of Simple Functions Silva: § 4.4: Integrals of positive functions |
| Tue, Apr 27 | Silva: § 4.4: Integrals of positive functions Silva: § 4.5: Measures from integration Silva: § 4.6: Integrable Functions |
| Thu, Apr 29 | Silva: § 4.5: Measures from integration Silva: § 4.6: Integrable Functions Silva: § 5.1-5.2: The Birkhoff Ergodic Theorem (and normal numbers) |
| Tue, May 4 | Final Exam Distributed. Silva: § 5.1, 5.3: The Birkhoff Ergodic Theorem (and toral rotations) |
| Thu, May 6 | Discussion of the Final Exam (To give you a chance to ask questions about the final exam) |
| Tue, May 11 | Final Exam Collected. |
| Thu, May 13 |