Lecture Notes for IEOR 3106

Classes

  1. September 4: Topics discussed. Probability Review. Chapter 1. First topic: Conditional Probability.

  2. September 6: Goats and Moreovers. Probability Review. Chapter 1. More on Conditional Probability.

  3. September 11: Topics discussed. Section 2.7. The central limit theorem.

  4. September 13: Topics discussed. Chapters 2 and 3. Random variables and transforms.

  5. September 18: Markov Mouse. Chapter 4. Introduction to Markov chains.

  6. September 20: Markov Chain Modelling. More Markov chains.

  7. September 25: Reversibility. Section 4.8

  8. September 27: more Markov chains.

  9. October 2: probabilistic analysis of the simplex method. Chapter 4. last of the discrete-time Markov chains.

  10. Thursday, October 4, and Tuesday, October 9: FIRST MIDTERM EXAM, Open Book, in class in two parts, 4:10-5:25pm, in 833 Mudd. First part on basic probability, Chapters 1-3; second part on Markov chains, Chapter 4.

  11. October 11: A Trip to the Post Office. Here are solutions for this problem with different names. Chapter 5. The exponential distribution. Concise summary of exponential and Poisson.

  12. October 16: exponential and Poisson entertainment. Chapter 5. The Poisson process. solutions

  13. October 18: Gone Fishing. Chapter 5. Even more on the Poisson process. solutions

  14. October 23: Pooh Bear. Chapter 6. Continuous-time Markov chains. Lecture Notes on CTMC's.

  15. October 25: The KL Barbershop. birth and death processes.

  16. October 30: transition probabilities. more on CTMc's

  17. November 1: reversibility. even more on CTMC's

  18. November 6: NO CLASS. Election Day.

  19. November 8: Carelton cafeteria and review.

  20. Tuesday, November 13: SECOND MIDTERM EXAM, Open Book, in class in only one part, 4:10-5:25pm, in 833 Mudd. Covers Chapters 5 and 6.

  21. November 15: renewal theory. Start Chapter 7.

  22. November 20: renewal reward process examples

  23. November 22: THANKSGIVING

  24. November 27: Went through examples handed out last class.

  25. November 29: The Age and Excess Processes.

  26. December 4: Brownian motion and martingales. Chapter 10.

  27. December 6: Last Class: More Brownian motion and martingales.