COMPSCI 240: Reasoning Under Uncertainty

UMassAmherst

Spring 2019

Course Details

The goal of this course is to help students develop mathematical reasoning skills for problems that involve uncertainty. Each concept will be illustrated by real-world examples and demonstrated through in-class and homework exercises. Topics covered include counting and probability – basic counting problems, probability definitions, mean, variance, binomial distribution, discrete random variables, continuous random variables, Markov and Chebyshev bounds, laws of large numbers, and central limit theorem, as well as probabilistic reasoning – conditional probability and odds, Bayes' law, Markov chains, Bayesian network, and Markov decision processes.

Prerequisites: COMPSCI 187 (or E&C-ENG 242) and MATH 132 or consent of instructor.

Number of credits: 4

Meeting times for lectures: MWF 9:05-9:55 AM

Location for lectures: Integrative Learning Center S131 for Section 1 (Nic Herndon), and Hasbrouck Laboratory 124 for Section 2 (Andrew Lan)

Location for discussions: LGRC A104A

Further details are available in the syllabus.

Office Hours

Nic Herndon: Fridays, 10:30 - 11:30 AM or by appointment, in LGRT 223

Andrew Lan: Wednesdays, 5:00 - 6:00 PM or by appointment, in CS 230

Assan Toleuov: Thursdays, 5:30 - 6:30 PM, in LGRT 220

Elita Lobo: Tuesdays, 9:00 - 10:00 AM, in LGRT 223

Paul Crouther: Mondays, 12:00 - 1:00 PM, in LGRT 220

Qingyang Xue: Mondays, 2:00 - 3:00 PM, in LGRT 220

Important Links at UMassAmherst

Course Materials

Textbook (required): Introduction to Probability, 2nd Edition by Dimitri P. Bertsekas and John N. Tsitsiklis.
Optional: Seeing Theory, a visual introduction to probability and statistics.

Tentative Schedule

Date Day Details
Jan 23 Wed
Lecture 1: Introductions, Syllabus, and Set Theory
Reading: 1.1
Jan 25 Fri
Lecture 2: Probabilistic models
Reading: 1.2
Jan 28 Mon
Lecture 3: Conditional probability
Reading: 1.3
Jan 30 Wed
Lecture 4: Total probability theorem and Bayes' rule
Reading: 1.4
Quiz 1 available, due Fri, Feb 1
Jan 31 Thu
Discussion 1
Feb 1 Fri
Lecture 5: Independence
Reading: 1.5
Homework 1 available, due Fri, Feb 8
Feb 4 Mon
Lecture 6: Counting
Reading: 1.6
Feb 6 Wed
Lecture 7: Counting (continued)
Reading: 1.6
Quiz 2 available, due Mon, Feb 11
Feb 7 Thu
Discussion 2
Feb 8 Fri
Lecture 8: Discrete random variables + Probability mass functions
Reading: 2.1-2.2
Feb 11 Mon
Lecture 9: Common Discrete Random Variables
Reading: 2.2
Feb 13 Wed
Class canceled due to inclement weather
Homework 2 available, due Thu, Feb 21 at 4:00 PM EST
Feb 14 Thu
Discussion 3
Feb 15 Fri
Lecture 10: Expectation, mean, and variance
Reading: 2.4
Quiz 3 available, due Tue, Feb 19
Feb 19 Tue
Lecture 11: Functions of random variables
Reading: 2.3
Feb 20 Wed
Lecture 12: Joint PMFs, Conditioning, and Independence
Reading: 2.5-2.7
Feb 21 Thu Discussion 4: Review for Midterm I
Feb 22 Fri Midterm I
Sample/practice exam: Midterm I, Fall 2018
Feb 25 Mon
Lecture 13: Continuous random variables
Reading: 3.1
Feb 27 Wed
Lecture 14: Cumulative distribution functions
Reading: 3.2
Quiz 4 available, due Mon, Mar 4
Feb 28 Thu Discussion 5
Mar 1 Fri
Lecture 15: Normal random variables
Reading: 3.3
Mar 4 Mon
Class canceled due to inclement weather
Quiz 5 available, due Fri, Mar 8
Mar 6 Wed
Lecture 16: Joint PDF of multiple random variables
Reading: 3.4
Mar 7 Thu Discussion 6
Mar 8 Fri
Lecture 17: Covariance and correlation
Reading: 4.2
Spring break
Mar 18 Mon
Lecture 18: Markov and Chebyshev inequalities
Reading: 5.1
Homework 3 available, due Mon, Mar 25
Mar 20 Wed
Lecture 19: The weak law of large numbers, and convergence in probability
Reading: 5.2-5.3
Mar 21 Thu Discussion 7
Mar 22 Fri
Lecture 20: Central limit theorem, and the strong law of large numbers
Reading: 5.4-5.5
Quiz 6 available, due Wed, Mar 27
Mar 25 Mon
Lecture 21: Game theory - part 1
Mar 27 Wed
Lecture 22: Game theory - part 2
Mar 28 Thu Discussion 8: Review for Midterm II
Mar 29 Fri Midterm II
Sample/practice exam: Midterm II, Fall 2018
Apr 1 Mon Lecture 23: Game theory - part 3
Apr 3 Wed
Lecture 24: Discrete time Markov chains
Reading: 7.1
Homework 4 available, due Wed, Apr 10
Apr 4 Thu Discussion 9
Apr 5 Fri
Lecture 25: Classification of states
Reading: 7.2
Apr 8 Mon
Lecture 26: Steady-state behavior
Reading: 7.3
Apr 10 Wed
Lecture 27: Bayesian networks - part 1
Apr 11 Thu Discussion 10
Apr 12 Fri
Lecture 28: Bayesian networks - part 2
Apr 17 Wed
Lecture 29: Bayesian networks - part 3
Apr 18 Thu Discussion 11
Apr 19 Fri
Lecture 30: Bayesian networks - part 4
Apr 22 Mon
Lecture 31: Classical Parameter Estimation
Reading: 9.1
Apr 24 Wed
Lecture 32: Linear Regression
Reading: 9.2
Apr 25 Thu Discussion 12
Apr 26 Fri
Lecture 33: Binary Hypothesis Testing
Reading: 9.3
Apr 29 Mon
Lecture 34: Significance Testing
Reading: 9.4
May 1 Wed Review for Final
May 3 Fri 8-10AM
Final exam
Sample/practice exam: Final exam, Fall 2018
Room: Integrative Learning Center S131 for Section 1