# Tentative Calendar for Math B4500, Section ST, Spring 2021

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 MeasureSilva: § 2.2: The Cantor Set and Null Sets Tue, Feb 9 Silva: § 2.3: Lebesgue Measurable SetsSilva: § 2.4: Countable AdditivityDynamical construction of a non-measurable set Thu, Feb 11 Silva: § 2.5: Sigma-Algebras and Measure SpacesSilva: § 2.6: The Borel Sigma-Algebra Tue, Feb 16 Silva: § 3.2-3.3: Measure Preserving TransformationsFinished Silva: § 2.6: The Monotone Class Theorem Thu, Feb 18 Silva: § 2.7: Approximation with Semi-ringsSilva: § 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 MeasuresDiscussed example of Lebesgue measure on the Torus Thu, Mar 4 Discussed measure preserving transformations of the TorusBegan 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 setsSilva: § 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 systemsBegan Silva: § 3.10: Isomorphism Thu, Apr 8 Silva: § 3.10: Isomorphism Tue, Apr 13 Finish Silva: § 3.10: IsomorphismSilva: § 3.11: Induced Transformations Thu, Apr 15 Finish Silva: § 3.11: Induced TransformationsDiscuss some examples of induced transformations.Silva: § 4.2: Measurable functions Tue, Apr 20 Silva: § 4.2: Measurable functionsOverview of Lebesgue Integration Thu, Apr 22 Silva: § 4.3: Integrals of Simple FunctionsSilva: § 4.4: Integrals of positive functions Tue, Apr 27 Silva: § 4.4: Integrals of positive functionsSilva: § 4.5: Measures from integrationSilva: § 4.6: Integrable Functions Thu, Apr 29 Silva: § 4.5: Measures from integrationSilva: § 4.6: Integrable FunctionsSilva: § 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

The Final Exam will be held Tuesday May 4 to Tuesday May 11 (take home).