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Welcome to Probability Theory! For course info and policies, please see the syllabus. For grades, log into Moodle. If you need help or have questions, please contact Prof. Wright.
Prof. Wright's office hours: Mon. 11–12, Tues. 1:30–2:30, Wed. 10:30–11:30, Thurs. 10–11, Fri. 12:30–1:30 (see Moodle for the Zoom link)
Help sessions: Tuesdays 6:30–8:00pm (see Moodle for the link)
Top
Today
Bottom
Friday
August 21
August 21
Introduction; what is probability?
Do the following before next class:
- Complete the Introductory Survey, if you haven't done so already.
- Read the Syllabus and complete the Syllabus Quiz.
- From the textbook, read §1.1 and §1.2, at least through page 10, and watch the accompanying video Sample Spaces, Events, and Axioms. Answer the three questions embedded in the video before class on Monday.
- Take a look at Homework 1, which is due Wednesday, August 26.
Monday
August 24
August 24
Sample spaces and events; axioms of probability
Do the following before next class:
- Review the solutions to the problems from class.
- Complete Homework 1 (due Wednesday).
- Read §1.3 in the textbook, and watch the accompanying video Counting Methods. Answer the three questions embedded in the video before class on Wednesday.
Bonus video: John Urschel-NFL Math Whiz
Do the following before next class:
- Review the solutions to the problems from class.
- Begin Homework 2 (due Monday).
- Watch the video Four Types of Couting Problems and answer the questions embedded in the video before class on Friday.
Friday
August 28
August 28
More counting methods
Do the following before next class:
- Review the solutions to the problems from class.
- Finish Homework 2 (due Monday).
- Watch the video Conditional Probability and answer the questions embedded in the video before coming to class on Monday. Also read the examples in §1.4 in the textbook.
Do the following before next class:
- Review the solutions to the problems from class.
- Begin Homework 3 (due Friday).
- Watch the video Independence and answer the questions embedded in the video before coming to class on Wednesday. Also read §1.5 in the textbook.
Wednesday
September 2
September 2
Independence
Bonus video: Hannah Fry — Beautiful equations: how insects walk on water and galaxies form
Do the following before next class:
- Review the solutions to the problems from class.
- Begin Homework 3 (due Friday).
- Watch the video Simulation of Random Events and answer the questions embedded in the video before coming to class on Friday. Also read §1.6 in the textbook.
- On Friday, we meet in RNS 410. Wear your face mask, and bring your computer with R or Mathematica.
Do the following before next class:
- Please complete the Week 3 Survey. Answers are voluntary and anonymous.
- Watch the video Discrete Random Variables and answer the questions embedded in the video before coming to class on Monday. Also read §2.1 and §2.2 in the textbook.
- Begin Homework 4 (due Wednesday).
Monday
September 7
September 7
Random variables; discrete distributions
Do the following before next class:
- Please complete the Week 3 Survey, if you haven't done so already. Answers are voluntary and anonymous.
- Watch the video Expected Value and Standard Deviation and answer the questions embedded in the video before coming to class on Wednesday. Also read §2.3 in the textbook.
- Finish Homework 4 (due Wednesday).
Bonus video: Yitang Zhang: An Unlikely Math Star Rises
Do the following before next class:
- Review the solutions from the problems in class, especially those involving Chebyshev's Inequality.
- Watch the video The Binomial Distribution and answer the questions embedded in the video before coming to class on Friday. Also read §2.4 in the textbook.
- Begin Homework 5 (due Monday).
Friday
September 11
September 11
Binomial distribution
Do the following before next class:
- Review the solutions from the problems in class.
- Watch the video The Poisson Distribution and answer the questions embedded in the video before coming to class on Monday. Also read §2.5 in the textbook.
- Finish Homework 5 (due Monday).
- Take a look at Homework 6 (due Wednesday).
Do the following before next class:
- Complete Homework 6 (due Wednesday).
- Review the Exam 1 Information. Talk with Prof. Wright if you have any questions.
Bonus video: Moon Duchin: "Political Geometry"
Work on Exam 1. Complete it before class on Monday. You may either hand in your exam at class on Monday, or submit your work electronically using this Moodle assignment link.
Friday
September 18
September 18
Exam 1: take-home, covering sections 1.1 through 2.4 in the textbook
Do the following before next class:
- Finish Exam 1. You may either hand in your exam at class on Monday, or submit your work electronically using this Moodle assignment link.
- Watch the video The Hypergeometric Distribution and answer the questions embedded in the video. Also read §2.6.1 in the textbook.
Monday
September 21
September 21
Hypergeometric distribution
Do the following before next class:
- Review the solutions to the problems from class on Monday. (See notes and solutions above.)
- Watch the video The Negative Binomial Distribution and answer the questions embedded in the video. Also read §2.6.2 in the textbook.
- Begin Homework 7 (due Friday).
Wednesday
September 23
September 23
Negative binomial and geometric distributions
Bonus: video How Not to Be Wrong: The Power of Mathematical Thinking - with Jordan Ellenberg and article The Psychology of Statistics by Jordan Ellenberg
Do the following before next class:
- Watch the video Moment Generating Functions, Part 1 and answer the questions in the video. Also read §2.7 in the textbook.
- Finish Homework 7 (due Friday).
Do the following before next class:
- Watch the video Moment Generating Functions, Part 2 and answer the questions in the video. Re-read §2.7 in the textbook.
- Begin Homework 8 (due Wednesday).
Monday
September 28
September 28
Moment-generating functions
Do the following before next class:
- Watch the video Simulation of Discrete Random Variables and answer the questions in the video. Also read §2.8 in the textbook.
- Finish Homework 8 (due Wednesday).
Bonus video: Talitha Washington — Big Ideas in STEM Innovation
Do the following before next class:
- Watch the video Continuous Random Variables and answer the questions in the video. Also read §3.1 in the textbook.
- Begin Homework 9 (due Monday).
Friday
October 2
October 2
Continuous random variables; uniform distribution
Do the following before next class:
- 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.
- Finish Homework 9 (due Monday).
Do the following before next class:
- Watch the video The Normal Distribution and answer the questions in the video. Also read §3.3 in the textbook.
- Begin Homework 10 (due Friday).
Wednesday
October 7
October 7
Normal distribution
Bonus: Why is Mathematics Useful — Robert Ghrist, and Applied Dynamical Systems Vol. 1
Do the following before next class:
- Watch the video The Exponential Distribution and answer the questions in the video. Also read §3.4.1 in the textbook.
- Finish Homework 10 (due Friday).
Do the following before next class:
- Watch the video The Gamma Distribution and answer the questions in the video. Also read §3.4.2 in the textbook.
- Begin Homework 11 (due Wednesday).
Monday
October 12
October 12
Gamma distribution
Extra credit opportunity: Attend one or more student presentations at the Northfield Undergraduate Mathematics Symposium (NUMS) on Tuesday, Oct. 13, 3:30-7:00pm. See here for details.
Do the following before next class:
- Review the Exam 2 Information. Talk with Prof. Wright if you have questions.
- Finish Homework 11 (due Wednesday).
Bonus video: Dr. Erika Camacho on Horizonte and LATMATH: Erika Camacho - "Modeling Photoreceptor Death and Rescue"
Extra credit opportunity: attend Explore MSCS on Thursday, Oct. 15, 4:00–5:00pm to earn 2 extra-credit points for your homework grade.
Work on Exam 2. Complete it before class on Monday. You may either hand in your exam at class on Monday, or submit your work electronically on Moodle.
Friday
October 16
October 16
Exam 2: take-home, covering sections 2.1 through 3.4 in the textbook
Do the following before next class:
- Finish Exam 2. You may either hand in your exam at class on Monday, or submit your work electronically via this Moodle link.
- Watch the video Transformation of a Random Varibles. Also read §3.7 in the textbook.
Monday
October 19
October 19
Transformations of continuous random variables
Do the following before next class:
- Watch the video Simulation of Continuous Random Variables and answer the questions in the video before class on Wednesday. Also read §3.8 in the textbook.
- Begin Homework 12 (due Friday).
Wednesday
October 21
October 21
Simulation of continuous random variables
Bonus video: Francis Su — Mathematics for Human Flourishing
Do the following before next class:
- Watch the video Joint Distributions and answer the questions in the video before class on Friday. Also read §4.1 in the textbook.
- Finish Homework 12 (due Friday).
Do the following before next class:
- Watch the video Covariance and Correlation and answer the questions in the video before class on Monday. Also read §4.2 in the textbook.
- Begin Homework 13 (due Wednesday).
Monday
October 26
October 26
Expected values, covariance, and correlation
MSCS Colloquium: Monday, 3:15–4:15pm
Do the following before next class:
- 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.
- Finish Homework 13 (due Wednesday).
Math Grad School Info Night: Thursday, 5–6pm
Do the following before next class:
- 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.
- Begin Homework 14 (due Monday).
Friday
October 30
October 30
Properties of linear combinations
Do the following before next class:
- Watch the video Conditional Distributions and answer the questions in the video before class on Monday. Also read §4.4 in the textbook.
- Finish Homework 14 (due Monday).
MSCS Colloquium: Monday, 3:30–4:30pm
Do the following before next class:
- 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 15 (due Friday).
Wednesday
November 4
November 4
Limit theorems
Bonus video: Digital Neuroscientist of the Future | Kathryn Hess Bellwald | TEDxLugano and Kathryn Hess Interview (AMS Notices)
Do the following before next 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.
- Finish Homework 15 (due Friday).
Do the following before next 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.
- Begin Homework 16 (due Wednesday).
Monday
November 9
November 9
The Law of Large Numbers, then Transformations (cdf method)
MSCS Colloquium: "Sharing Secrets" on Monday, November 9, 3:30–4:30pm
Do the following before next class:
- 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 16 (due Wednesday).
Bonus video: The World's Best Mathematician (*) - Numberphile and Terry Tao's Blog
Do the following before next class:
- Watch the video Order Statistics and answer the questions in the video before class on Friday. Also read §4.9 in the textbook.
- Begin Homework 17 (due Monday).
Friday
November 13
November 13
Order statistics
Do the following before next class:
- Finish Homework 17 (due Monday).
Bonus: Living Proof: Stories of Resilience Along the Mathematical Journey
We've made it to the end of the semester! A few last things to do:
- Complete the Final Exam. Scan and upload your exam to the Final Exam link on Moodle.
- Please complete the Course Evaluation.
Thursday
November 19
November 19
Final exam due at 4:00pm
