## Lecture Plan

The following is a tentative schedule for the course. Please check back regularly for updates as the term progresses.

Legend:
• M : David Morin, Probability: For the Enthusiastic Beginner
M Chapters in parenthesis indicate use M as a reference -the lectures will be closely tied to GS.
• GS : Charles M. Grinstead and J. Laurie Snell, Introduction to Probability, second revised edition
From week 3 the lectures will follow GS more closely
 Tues March 27 M: 1.1 -1.5, 2.6 Factorial, Sterlings Formula, Permutations, Ordered and Unordered sets Wed March 28 Introduction to Mathematical Arguments How to do proofs. Warm Up Thur March 29 M: 1.6 -1.8 Binomial Coefficients, Probability Basics Tues April 3 GS: 1.2 M: 2.1, 2.2 Discrete Probability Distributions, Formal definitions, Conditional probability, Examples Wed April 4 More Combinatorics, Independent events, dependent events, Review Thur April 5 M 2.3 GS 3.1, 3.2 Probability basics, More Permutations Combinations, Examples Tues April 10 Exam 1; in class On material covered till Apr 5 Wed April 11 Binomial Distribution and Fixed points Thur April 12 GS 4.1 (M: 2.4, 2.5) Independence, Bayes Rule Tue April 17 GS:6.1, 6.2 ( M:3.1,3.2) Joint Distributions, Expected Value, Variance (Discrete) Wed April 18 Set Theory Worksheet 2 Set theory is for practise and review Worksheet 2, Try atleast the marked problems in class Thur April 19 GS:6.1, 6.2 (M:3.1,3.2) Expected Value, Variance (Discrete) Tues April 24 GS 5.1 (M: 4.1 4.3, 4.4, 4.6) Discrete Distributions , Bernoulli, Binomial, Exponential Wed April 25 Review Thur April 26 Exam 2, in class Tues May 1 M: 4.2, 4.6, 4.7 GS 5.2 Continuous Distribution and densities, Uniform, Exponential, Poisson Wed May 2 Worksheet3 Cumulative distribution, density function, covariance Thur May 3 GS: 8.1 M: 4.7, 4.8 Normal Distribution,Markov inequality Tues May 8 GS: 8.1 Chebyshev inequality, Weak Law of Large Numbers (Discrete case), Wed May 9 Worksheet4 Chebyshev/markov inequality Thur May 10 GS: 9.1 Bernoulli Trials, Central Limit Theorem Tues May 15 GS:9.2 Central Limit Theorem, Independent Trial (Discrete case) Wed May 16 Exam 3, in class Thur May 17 11.1 Linear Algebra basics, Markov Chains Tue May 22 GS: 11.1, 11.2 Markov Chains Wed May 23 GS: 11.3 Ergodic Markov Chains Thur May 24 GS: 11.3 Ergodic Markov Chains Tuesday May 29 Course Wrap up Wednesday May 30 Review Saturday June 2 Final Exam 3 to 6 pm Kemeny 007