This course gives a introduction to
probability theory.

Topics covered include 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 Event Time
Instructor Xingru Chen Class MWF 11:30 am - 12:35 pm
X-hour Tu 12:15 pm - 1:05 pm
Office Hour Calendar Booking
Email xingru.chen.gr@dartmouth.edu
TA Maria Roodnitsky Tutorial Th 7:00 pm - 9:00 pm
Email maria.roodnitsky.22@dartmouth.edu
Textbook

Introduction to Probability (2nd Rev Ed), Charles M. Grinstead & J. Laurie Snell, American Mathematical Society (1997). By courtesy of the authors, this book is freely available here.

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. On every Friday, problems will be posted by 11:00 pm, and due by 11:00 am next 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

  • I affirm my understanding that this course and any associated group meetings involving students and the instructor, including but not limited to scheduled and ad hoc office hours and other consultations, may be recorded within any digital platform used to offer remote instruction for this course.
  • I further affirm that the instructor owns the copyright to their instructional materials, of which these recordings constitute a part, and distribution of any of these recordings in whole or in part without prior written consent of the instructor may be subject to discipline by Dartmouth up to and including expulsion.
  • I authorize Dartmouth and anyone acting on behalf of Dartmouth to record my participation and appearance in any medium, and to use my name, likeness, and voice in connection with such recording.
  • I authorize Dartmouth and anyone acting on behalf of Dartmouth to use, reproduce, or distribute such recording without restrictions or limitation for any educational purpose deemed appropriate by Dartmouth and anyone acting on behalf of Dartmouth.

Requirement of Consent to Recordings

  • By enrolling in this course, I hereby affirm that I will not under any circumstance make a recording in any medium of any one-on-one or group meeting with the instructor and/or students without obtaining the prior written consent of all those participating, and I understand that if I violate this prohibition, I will be subject to discipline by Dartmouth up to and including expulsion, as well as any other civil or criminal penalties under applicable law.

Honor Principle

  • Academic integrity is at the core of our mission as mathematicians and educators, and we take it very seriously. We also believe in working and learning together.
    • Collaboration on homework is permitted and encouraged, but obviously it is a violation of the honor code for someone to provide the answers for you.
    • On homework, you are encouraged to work together, and you may get help from others, but you must write up the answers yourself. If you are part of a group of students that produces an answer to a problem, you cannot then copy that group answer. You must write up the answer individually, in your own words.
    • On exams, you may not give or receive help from anyone. Exams in this course are open book.
    • For more information about the Dartmouth Academic Honor Principle, see here.

Special Considerations

  • Students with disabilities who may need disability-related academic adjustments and services for this course are encouraged to see their professor privately as early in the term as possible. Students requiring disability-related academic adjustments and services must consult the Student Accessibility Services Office. Once SAS has authorized services, students must show the originally signed SAS Services and Consent Form and/or a letter on SAS letterhead to their professor. As a first step, if students have questions about whether they qualify to receive academic adjustments and services, they should contact the SAS office. All inquiries and discussions will remain confidential.
  • The academic environment at Dartmouth is challenging, our terms are intensive, and classes are not the only demanding part of your life. There are a number of resources available to you on campus to support your wellness, including your undergraduate dean, Counseling and Human Development, and the Student Wellness Center.
  • Some students may wish to take part in religious observances that occur during this academic term. If you have a religious observance that conflicts with your participation in the course, please talk to me before the end of the second week of the term to discuss appropriate accommodations.

External Links

Canvas

Github Repository

Github Page

Syllabus

The following is a tentative syllabus for the course. This page will be updated irregularly.

Date Lecture Textbook Slides
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

Download

  Homework                 1                 2                 3                 4                 5                 6                 7                 8                
  HWSolution                 1                 2                 3                 4                 5                 6                 7                 8                

Contact

Xingru Chen

  Address Kemeny 212
Department of Mathematics
27 N. Main Street
Hanover NH 03755-3551
  Phone (603) 646-9813
  Github fudab