Probability Theory

• Complete the Introductory Survey, if you haven't done so already.
• Read the Syllabus and complete the Syllabus Quiz (on Moodle).
• From the textbook, read §1.1 and §1.2, and watch the accompanying video Sample Spaces, Events, and Axioms. Answer the three questions embedded in the video before class on Tuesday.
• Read §1.3 in the textbook, and watch the accompanying video Counting Methods. Answer the three questions embedded in the video before class on Tuesday.
• Take a look at Homework 1. Begin the problems from §1.1.

• Review the solutions to the problems from class.
• Re-read §1.3 in the textbook.
• Watch the video Four Types of Couting Problems and answer the questions embedded in the video before class on Thursday.
• Work on Homework 1. Try to finish the problems from §1.1 and §1.2.

• Review the solutions to the problems from class.
• Watch the video Conditional Probability and answer the questions embedded in the video before coming to class on Tuesday. Also §1.4 in the textbook, paying special attention to the examples.
• Read §1.5 in the textbook. Watch the video Independence and answer the questions embedded in the video before coming to class on Tuesday.
• Finish Homework 1. Write your solutions clearly and neatly. Upload your solutions to Homework 1 on Moodle.

Bonus video: John Urschel-NFL Math Whiz

• Review the solutions to the problems from class.
• Watch the video Simulation of Random Events and answer the questions embedded in the video before coming to class on Thursday. Also read §1.6 in the textbook.
• If possible, bring a computer with Mathematica or R to class on Thursday.
• Begin Homework 2. This homework is due next Tuesday, but it's important to start early.

• Review the solutions to the problems from class.
• Watch the video Discrete Random Variables and answer the questions embedded in the video before coming to class on Tuesday. Also read §2.1 and §2.2 in the textbook.
• Watch the video Expected Value and Standard Deviation and answer the questions embedded in the video before coming to class on Tuesday. Also read §2.3 in the textbook.
• Finish Homework 2. Write your solutions clearly and neatly. Upload your solutions to Homework 2 on Moodle.

Bonus videos: Satyan Devadoss — Blue Collar Mathematics and Mage Merlin's Unsolved Mathematical Mysteries

  MSCS Tailgate Party: Wednesday, September 28, 4:30–6:30pm in Tomson 280 (masks required) and outside

• Review the solutions to the problems from class. Also review §2.3 in the text.
• Watch the video The Binomial Distribution and answer the questions embedded in the video before coming to class on Thursday. Also read §2.4 in the textbook.
• Begin Homework 3. This homework is due next Tuesday, but it's important to start early.

• Review the solutions from the problems in class, especially those involving Chebyshev's Inequality.
• Watch the video The Poisson Distribution and answer the questions embedded in the video before coming to class on Tuesday. Also read §2.5 in the textbook.
• Finish Homework 3. Write your solutions clearly and neatly. Upload your solutions to Homework 3 on Moodle.

  Oct. 4: Math Across the Cannon featuring Satyan Devadoss colloquium 3:30pm at Carleton; public lecture 7pm in Viking Theater; extra credit opportunity

• Review the solutions to the problems from class.
• Begin Homework 4. This homework will not be collected, but you should do it before the exam. Solutions are here.
• Read the Exam 1 Information. Study for the exam.

Bonus video: Eugenia Cheng on The Late Show

• Work on Homework 4. This homework will not be collected, but you should do it before the exam. Solutions are here.
• Review the Exam 1 Information. Study for the exam.

• Complete the take-home exam problems. Bring your solutions to class on Thursday.
• Watch the videos The Hypergeometric Distribution and The Negative Binomial Distribution and answer the questions embedded in the videos. Also read §2.6 in the textbook.
• If possible, bring a computer with Mathematica to class on Thursday.

Bonus: video How Not to Be Wrong: The Power of Mathematical Thinking - with Jordan Ellenberg and article The Psychology of Statistics by Jordan Ellenberg

• Watch the videos Moment Generating Functions, Part 1 and Moment Generating Functions, Part 2 and answer the questions in the videos. Also read §2.7 in the textbook.
• If possible, bring a computer with Mathematica to class on Thursday.
• Optionally, begin Homework 5, due October 25.

MSCS Colloquium: "Gerrymandering and the Attainment of Impossible Electoral Results" by Prof. Steve McKelvey; Friday, October 21, 3:30pm in RNS 310

MSCS Colloquium: "Painful Regressions: Probability and Statistics in Clinical Medicine and Pain Management" by Dr. Akshar Rambachan '12 MD, MPH; Monday, October 24, 3:30pm in RNS 310

• Review the solutions to the problems from class.
• Finish Homework 5. Write your solutions clearly and neatly. Upload your solutions to Homework 5 on Moodle.
• Watch the video Simulation of Discrete Random Variables and answer the questions in the video. Optionally, read §2.8 in the textbook.
• Watch the video Continuous Random Variables and answer the questions in the video. Also read §3.1 in the textbook.
• If possible, bring a computer with Mathematica or R to class on Tuesday.

Bonus video: Moon Duchin: "Political Geometry" and DistrictR

• Review the problems and solutions from class.
• Watch the video Expected Values of Continuous Random Variables and answer the questions in the video. Also read §3.2 in the textbook.
• Begin Homework 6, due next Tuesday. Work on the moment-generating function problems and ask questions later this week.

• Review the problems and solutions from class.
• Watch the video The Normal Distribution and answer the questions in the video. Also read §3.3 in the textbook.
• Watch the video The Exponential Distribution and answer the questions in the video. Also read §3.4.1 in the textbook.
• Finish Homework 6 and upload your solutions to Moodle.

Bonus: Federico Ardila on Math, Music and the Space of Possibilities

• Review the solutions to the problems from class.
• Begin Homework 7. This homework will not be collected, but you should do it before the exam. Solutions are here.
• Read the Exam 2 Information. Study for the exam.
• Watch the video The Gamma Distribution and answer the questions in the video. Also read §3.4.2 in the textbook.

• Work on Homework 7. This homework will not be collected, but you should do it before the exam. Solutions are here.
• Read the Exam 2 Information. Study for the exam.

• Complete the take-home exam problems. Bring your solutions to class on Thursday.
• Watch the video Transformation of a Random Varible. Also read §3.7 in the textbook.
• Watch the video Simulation of Continuous Random Variables.

Bonus: Susan D'Agostino book and interview

• Review the solutions to the problems from class.
• Do Homework 8, which is due Tuesday. This homework is shorter than usual, but it's still wise to start early and ask questions.
• Watch the video Joint Distributions and answer the questions in the video before class on Friday. Also read §4.1 in the textbook.
• Watch the video Covariance and Correlation and answer the questions in the video before class on Monday. Also read §4.2 in the textbook.

• Review the solutions to the problems from class.
• Begin Homework 9, which is due next Tuesday. This homework involves problems on transformations of random variables. It's important to start early and ask questions!
• Watch the video Linear Combinations, Part 1 and answer the questions in the video before class on Wednesday. Also read from the beginning of §4.3 up to the §4.3.1 heading.

Bonus video: Yitang Zhang: An Unlikely Math Star Rises

• Review the solutions to the problems from class.
• Finish Homework 9, which is due Tuesday.
• Watch the video Linear Combinations, Part 2 and answer the questions in the video before class on Friday. Also read the rest of §4.3 in the textbook.

Bonus: Why is Mathematics Useful — Robert Ghrist, and Applied Dynamical Systems Vol. 1

• Review the solutions to the problems from class. For another perspective on convolutions, watch But what is a convolution? by 3Blue1Brown.
• Watch the video Conditional Distributions and answer the questions in the video before class on Monday. Also read §4.4 in the textbook.
• Watch the video The Central Limit Theorem and answer the questions in the video before class on Wednesday. Also read §4.5 through the end of §4.5.3.
• Begin Homework 10, which is due on Tuesday, December 6.

Bonus video: Christmas Lectures 2019: How to Get Lucky — Hannah Fry

• Review the solutions to the problems from class.
• Watch the video The Law of Large Numbers and answer the questions in the video before class on Friday. Also read §4.5.4 in the textbook.
• Work on Homework 10, which is due next Tuesday.
• If possible, bring a computer with Mathematica or R to class on Thursday.

• Review the solutions to the problems from class.
• Watch the video Bivariate Transformations, Part 1 and answer the questions in the video before class on Monday. Also read §4.6 in the textbook.
• Watch the video Bivariate Transformations, Part 2 and answer the questions in the video before class on Wednesday. Re-read §4.6 in the textbook.
• Finish Homework 10, which is due on Tuesday.

Bonus video: Francis Su — Mathematics for Human Flourishing

• Review the solutions to the problems from class.
• Watch the video Order Statistics and answer the questions in the video before class on Monday. Also read §4.9 in the textbook.
• Begin Homework 11.

• Review the solutions to the problems from class.
• Finish Homework 11.
• Read the Final Exam Information.
• Please bring a computer to class on Tuesday.

Bonus: Living Proof: Stories of Resilience Along the Mathematical Journey