Course: Math 407, Probability Theory I, Spring 2023, Section 39975R
Prerequisite: MATH 226 or MATH 227 or MATH 229
Course Content: Probability spaces, discrete and continuous distributions, moments, characteristic functions, sequences of random variables, laws of large numbers, central limit theorem, special probability laws.
Last update: 26 October 2023

Instructor: Steven Heilman, stevenmheilman(@-symbol)
Office Hours: 8AM-10AM, Tuesdays, on zoom [link posted on blackboard]
Lecture Meeting Time/Location: Mondays, Wednesdays, and Fridays, 10AM-1050AM, CPA 152
TA: Quinn Le, ntle(@-symbol)
TA Office Hours: held in the Math Center.
Discussion Section Meeting Time/Location:

TA Office Hours: Occur in the Math Center.
You are not required to buy a textbook. Free lecture notes are provided below.
Recommended Textbook: D. P. Bertsekas and John N. Tsitsiklis, Introduction to Probability, 2nd edition. (The book is freely available online)
Another Recommended Textbook: Sheldon Ross, A First Course in Probability, any edition. (The book is freely available online)
Another Recommended Textbook: Elementary Probability for Applications, Durrett.

First Midterm:  Friday, February 10, 10AM-1050AM, CPA 152
Second Midterm: Friday, March 24, 10AM-1050AM, CPA 152
Final Exam: Monday, May 8, 8AM-10AM, CPA 152
Other Resources: Supplemental Problems from the textbook. An introduction to mathematical arguments, Michael Hutchings, An Introduction to Proofs, How to Write Mathematical Arguments

Email Policy:

Exam Procedures: Students must bring their USCID cards to the midterms and to the final exam. Phones must be turned off. Cheating on an exam results in a score of zero on that exam. Exams can be regraded at most 15 days after the date of the exam. This policy extends to homeworks as well. All students are expected to be familiar with the USC Student Conduct Code. (See also here.)
Accessibility Services: If you are registered with accessibility services, I would be happy to discuss this at the beginning of the course. Any student requesting accommodations based on a disability is required to register with Accessibility Services (OSAS) each semester. A letter of verification for approved accommodations can be obtained from OSAS. Please be sure the letter is delivered to me as early in the semester as possible. OSAS is located in 301 STU and is open 8:30am-5:00pm, Monday through Friday.
213-740-0776 (phone)
213-740-6948 (TDD only)
213-740-8216 (fax)

Discrimination, sexual assault, and harassment are not tolerated by the university. You are encouraged to report any incidents to the Office of Equity and Diversity or to the Department of Public Safety This is important for the safety whole USC community. Another member of the university community - such as a friend, classmate, advisor, or faculty member - can help initiate the report, or can initiate the report on behalf of another person. The Center for Women and Men provides 24/7 confidential support, and the sexual assault resource center webpage describes reporting options and other resources.

Exam Resources: Here are the exams I used when I previously taught a similar course: Exam 1 Exam 1 Solution Exam 1v2 Exam 1v2 Solution Exam 2 Exam 2 Solution Exam 2v2 Exam 2v2 Solution Final Final Solution Finalv2 Finalv2 Solution Exam 1 Exam 1 Solutions Exam 2 Exam 2 Solutions. Final Final Solutions. Exam 1 Exam 1 Solutions Exam 2 Exam 2 Solutions. Final Final Solutions. Exam 1 Exam 1 Solutions Exam 2 Exam 2 Solutions. Final Final Solutions. Here is a page containing old exams for another similar class. Here is a practice midterm (with solutions). Here are some more exams from a second quarter probability course: Exam 1 Exam 1 Solution Exam 2 Exam 2 Solution Final Final Solution. Exam 1 Exam 1 Solutions Exam 2 Exam 2 Solutions Final Final Solutions. Occasionally these exams will cover slightly different material than this class, or the material will be in a slightly different order, but generally, the concepts should be close if not identical.

Homework Policy:

Grading Policy:

Tentative Schedule: (This schedule may change slightly during the course.)

Week Monday Tuesday Wednesday Thursday Friday
1 Jan 9: 1.1, Sets Jan 11: 1.2, Probabilistic Models Jan 12: Homework 0 due (ungraded) Jan 13: 1.2, Probabilistic Models
2 Jan 16: No class: Jan 18: 1.3, Conditional Probability Jan 19: Homework 1 due Jan 20: 1.3, Conditional Probability
3 Jan 23: 1.4, Total Probability Theorem and Bayes' Rule Jan 25: 1.5, Independence Jan 26: Homework 2 due Jan 27: 1.5, Independence
4 Jan 30: 1.6, Counting Feb 1: 2.1, Discrete Random Variables Feb 2: Homework 3 due Feb 3: 2.2, Probability Mass Function
5 Feb 6: 2.3, Functions of Random Variables Feb 8: 2.4, Expectation and Variance Feb 9: No homework due Feb 10: Midterm #1
6 Feb 13: 2.5, Joint PMFs, Covariance and Variance Feb 15: 2.6, Conditioning Feb 16: Homework 4 due Feb 17: 2.6, Conditioning
7 Feb 20: No class Sep 30: 2.7, Independence Feb 23: Homework 5 due Feb 24: 2.7, Independence
8 Feb 27: 3.1, Continuous random variables and PDFs Mar 1: 3.1, Continuous random variables and PDFs Mar 2: Homework 6 due Mar 3: 3.2, Cumulative Distribution Functions
9 Mar 6: 3.3, Normal Random Variables Mar 8: Joint PDFs of Multiple Random Variables Mar 9: Homework 7 due Mar 10: 3.5, Conditioning
10 Mar 13: No class (spring break) Mar 15: No class (spring break) Mar 16: No class Mar 17: No class (spring break)
11 Mar 20: 3.5, Conditioning Mar 22: 4.2, Covariance Mar 23: No homework due. Mar 24: Midterm #2
12 Mar 27: 4.4, Moment Generating Function Mar 29: 4.4, Fourier Transform Mar 30: Homework 8 due Mar 31: 4.2 Convolution
13 Apr 3: 7.1, Markov and Chebyshev Inequalities Apr 5: 7.2, Weak Law of Large Numbers Apr 6: Homework 9 due. Apr 7: 7.3, Convergence in Probability
14 Apr 10: 7.4, Central Limit Theorem Apr 12: 7.4, Central Limit Theorem Apr 13: Homework 10 due Apr 14: 7.4, Central Limit Theorem
15 Apr 17: 7.5, Strong Law of Large Numbers Apr 19: 7.5, Strong Law of Large Numbers Apr 20: Homework 11 due Apr 21: 7.5, Strong Law of Large Numbers
16 Apr 24: Leeway Apr 26: Leeway Apr 27: Homework 12 due Apr 28: Leeway

Advice on succeeding in a math class:


Homework .tex files


Supplementary Notes