Program Overview

Introduction to Probability

This course provides an introduction to probability theory, covering topics such as random variables, independence and conditioning, expected value and variance, law of large numbers, central limit theorem, generating functions, random walks, and Markov chains.

General Information

Faculty and Event Schedule

• Instructor: Xingru Chen
  • Class: MWF 11:30 am - 12:35 pm
  • X-hour: Tu 12:15 pm - 1:05 pm
  • Office Hour: Calendar Booking
• TA: Maria Roodnitsky
  • Tutorial: Th 7:00 pm - 9:00 pm

Textbook

• Introduction to Probability (2nd Rev Ed), Charles M. Grinstead & J. Laurie Snell, American Mathematical Society (1997)

Grading Formula

• Homework: 25%
• Quizzes: 15%
• Midterm 1: 20%
• Midterm 2: 20%
• Final: 20%

Important Dates

• Midterm 1: July 20
• Midterm 2: August 10
• Final: August 30

Homework Policy

• Weekly homework will be assigned on a regular basis.
• Problems will be posted by 11:00 pm every Friday and due by 11:00 am the following Friday.
• Homework should be turned in and will be passed back on Canvas.
• The two lowest homework grades will be dropped.

Consent to Recording of Course and Group Office Hours

• The course and any associated group meetings may be recorded.
• The instructor owns the copyright to their instructional materials, including these recordings.
• Distribution of any of these recordings without prior written consent of the instructor may be subject to discipline.

Requirement of Consent to Recordings

• By enrolling in this course, students affirm that they will not make a recording of any one-on-one or group meeting with the instructor and/or students without obtaining prior written consent.

Honor Principle

• Academic integrity is at the core of the mission as mathematicians and educators.
• Collaboration on homework is permitted and encouraged, but it is a violation of the honor code for someone to provide the answers.
• On homework, students are encouraged to work together but must write up the answers themselves.
• On exams, students may not give or receive help from anyone.

Special Considerations

• Students with disabilities who may need disability-related academic adjustments and services should see their professor privately as early in the term as possible.
• The academic environment is challenging, and there are resources available to support wellness, including the undergraduate dean, Counseling and Human Development, and the Student Wellness Center.
• Some students may wish to take part in religious observances that occur during the academic term; please discuss appropriate accommodations with the instructor.

Syllabus

The following is a tentative syllabus for the course.

Lecture Schedule

• June 26: Course Overview (Chapter 1)
• June 29: Basic Concepts of Discrete Probability (Chapter 1)
• July 1: Continuous Probability Densities (Chapter 2)
• July 6: Permutations (Chapter 3)
• July 8: Combinations (Chapter 3)
• July 10: Combinations (Chapter 3)
• July 13: Discrete Conditional Probability (Chapter 4)
• July 15: Bayes' Theorem (Chapter 4)
• July 17: Continuous Conditional Probability (Chapter 4)
• July 20: Midterm 1 (Chapter 1 - 4)
• July 22: Midterm 1 Review
• July 24: Important Distributions (Chapter 5)
• July 27: Important Distributions (Chapter 5)
• July 29: Important Densities (Chapter 5)
• July 31: Expected Value of Discrete Random Variables (Chapter 6)
• August 3: Expected Value of Discrete Random Variables (Chapter 6)
• August 5: Variance of Discrete Random Variables (Chapter 6)
• August 7: Expected Value and Variance of Continuous Random Variables (Chapter 6)
• August 10: Midterm 2 (Chapter 5 - 6)
• August 12: Midterm 2 Review
• August 17: Sum of Random Variables (Chapter 7)
• August 19: Law of Large Numbers (Chapter 8)
• August 21: Central Limit Theorem (Chapter 9)
• August 24: Generating Functions (Chapter 10)
• August 26: Markov Chains (Chapter 11)
• August 30: Final (Everything)