MATH 5010: Intro to Probability (Spring 2026)
Time & Place: MWF 9:40AM - 10:30AM,
CSC 10-12
Instructor:
Firas Rassoul-Agha
E-Mail:
firas@math.utah.edu,
Office:
LCB 209
Office Hour: Mondays 10:45-11:45 AM or by appointment.
CANVAS: This is where I will post quizzes, class announcements, and grades.
Prerequisites: Solid knowledge of Calculus I, II, and III.
Comfortable around double integrals.
Description: This is a course on basic undergraduate probability. It is a prerequisite for many probability and statistics courses at the department of mathematics, such as Stochastic Processes (Math 5040/5050) and Statistical Inference (Math 5080/5090).
The course aims to develop the ability to understand and describe probabilistic phenomena in a mathematical fashion, and the ability to apply mathematical tools to derive useful facts about probabilistic phenomena.
At the end of the course, the student should be able to:
- Define and work with random variables, both discrete and continuous, and use them to model probabilistic phenomena.
- Identify and characterize common probability distributions, including Bernoulli, Binomial, Geometric, Negative Binomial, Poisson, Uniform, Exponential, Gamma, and Normal distributions.
- Compute probabilities and expectations using probability mass functions, density functions, and cumulative distribution functions.
- Apply conditional probability and Bayes' rule to evaluate probabilities in multi-stage or information-dependent settings.
- Recognize and verify independence of events and random variables, and use independence to simplify probability calculations.
- Compute and interpret moments, including expectation, variance, and higher moments.
- Use moment generating functions (MGFs) to compute moments, identify distributions, and analyze sums of independent random variables.
- Apply the law of large numbers (LLN) to understand convergence of sample averages.
- Apply the central limit theorem (CLT) to approximate distributions of sums or averages and perform normal approximations.
- Work with multivariate random variables, including joint, marginal, and conditional distributions.
- Determine covariance and correlation and interpret dependence between random variables.
- Compute conditional distributions and expectations in both discrete and continuous settings.
- Model real-world problems using appropriate probability distributions and tools learned in the course.
Lecture notes: These notes summarize the material covered in the lectures.
You may find it useful to have these notes with you during the lecture and write your additional comments on top of these notes.
This will allow you to focus more on what I say during class
instead of focusing part of your attention on writing things down.
Videos: Here, you can find recorded videos from a previous semester. We may not follow these lectures word for word, but you can take advantage of these videos to clarify things you did not get during class.
Textbook: We will follow
Introduction to Probability, by Anderson, Seppäläinen, and Valkó. (
Cambridge University Press, 2018)
You do not need this book to complete this course, but you may find it a useful reference book for this course. In particular, the book has a large number of exercises, in addition to the ones in the lecture notes and, therefore, is a good source of practice problems.
Forum: We will be using
Piazza for class discussion and answering questions. The system is highly catered to getting you help fast and efficiently from classmates and myself.
Rather than emailing questions,
I highly encourage you to post your questions on
Piazza. I also highly encourage you to answer your classmate's questions, if you think you know the answer.
One advantage over CANVAS Discussion Board is that you can post anonymously, if you prefer.
You can sign up
here but you will need an access code that you can find on the version of the syllabus on
CANVAS.
Quizzes constitute 15% of your total grade. Each lecture will have a corresponding quiz that will be posted on
CANVAS.
The quiz will test your attention to the material covered in class during that lecture.
If you did not attend the lecture or you think you missed some of the concenpts covered in it you should definitely
read the lecture notes and watch the video before taking the quiz.
Each quiz will have
one or two questions.
You will be given a total of
15-20 minutes. Pay attention to the
arithmetic precision you are asked to submit your answer in.
The quiz corresponding to a given lecture opens at the end of the lecture and closes at the beginning of the following lecture.
The lowest ten quiz scores will be dropped. As such, there are
no make up quizzes.
There are homework problems at the end of each
lecture. The textbook has many more exercises, at the end of each chapter.
Needless to say, the more you practice the more you will be proficient with the material.
Homework will make 5% of your grade. It will be due at
11:59 PM each Monday. You submit it by uploading into
CANVAS.
Homework will not be graded for correctness.
You will get 1 point for the whole homework set if you attempted at least one of the
assigned homework problems.
However, you should know that
Exam questions will be very similar to
the homework problems.
Therefore, the BEST way to
keep up with the pace
of this course
and to prepare for tests is to
solve, at the very least,
these homework problems in a timely fashion.
Exams and grades aside, to learn
the subject well you really need to solve as many
problems as you can (
beyond the ones in the notes).
Doing the math is the ONLY way to learn math.
Solutions to the homework problems that are not from the textbook appear at the end of the notes.
Use them wisely. If you peek at a solution, then consider that you do not yet know how to solve that type of problems and look for more similar problems to work on.
There will be
four 50-minute in-class tests that count 20% each. These tests replace the midterm and final exams. Each test takes place after we complete a group of topics and tests your knowledge of this group of topics. The tests are
mostly not comulative, though a few tests do have some overlap.
The lectures that each test covers are listed on the Syllabus page in
the
lecture notes.
Tests will be on
Monday February 2,
Monday March 2,
Friday April 3, and
Monday April 20.
If you know you will miss a lecture on which we have a test, because of a
documented reason such as an illness, a doctor's appointment, or similar, please contact me
as soon as possible to arrange for a make-up test.
IMPORTANT: You are allowed to use calculators, your notes, and your textbook during quizzes and exams. However, you are NOT allowed to seek help from others, including online resources
such as Chegg or Stack Exchange. Soliciting help from such sites will be considered as academic misconduct and will be dealt with accordingly.
Further important information:
Updated mandatory syllabus policies regarding the ADA Act, Safety at the U, Addressing Sexual Misconduct, and Academic Misconduct can be viewed here
It is the student's responsibility to regularly check their Umail or have it forwarded to an address they check regularly. The Umail is the only way for me to communicate privately with the student. There will be occasions during the semester that we may need to reach out to individual students (e.g. regarding a grade or assignment) and it is in their best interest to respond promptly.
I would like to encourage the students to email me only if it is something personal that requires individual attention. For questions about logistics of the class, course material and assignments, and anything else the classmates may wonder about as well, please post a question on Piazza. This way the information is shared quickly to the entire class, and everyone can benefit from seeing other classmates’ questions.
The T. Benny Rushing Mathematics Tutoring Center offers free tutoring. The Learning Center has additional tutoring available for our class. The math department also maintains a list of private tutors.
Please stay updated by regularly checking: the announcements on Canvas, your Umail, the posts on Piazza, and pay attention to the announcements given in class.
Students are expected to log in and check canvas regularly for posted announcements and assignments. Students are also strongly advised to set up notifications for canvas so they do not miss any important notifications.
Respectful participation in all aspects of the course will make our time together productive and engaging. Zoom lectures, discussion threads, emails and canvas are all considered equivalent to classrooms and student behavior within those environments shall conform to the student code.
COVID-19 Campus Guidlines
Drop/Withdrawal Policies: Students may drop a course within the first two weeks of a given semester without any penalties.
Students may officially withdraw (W) from a class or all classes after the drop deadline through the midpoint of a course. A “W” grade is recorded on the transcript and appropriate tuition/fees are assessed. The grade “W” is not used in calculating the student’s GPA.
For deadlines to withdraw from full-term, first, and second session classes, see the U's Academic Calendar.
Wellness at the U: Your personal health and wellness are essential to your success as a student. Personal concerns like stress, anxiety, relationship difficulties, depression, or cross-cultural differences can interfere with a student’s ability to succeed and thrive in this course and at the University of Utah.
Please feel welcome to reach out to your instructor or TA to handle issues regarding your coursework.
For helpful resources to manage your personal wellness and counseling options, contact the Center for Campus Wellness at 801-581-7776.
Office of the Dean of Students The Office of the Dean of Students is dedicated to being a resource to students through support, advocacy, involvement, and accountability. It serves as a support for students facing challenges to their success as students, and assists with the interpretation of University policy and regulations. Please consider reaching out to the Office of Dean of Students for any questions, issues and concerns. 200 South Central Campus Dr., Suite 270. Monday-Friday 8 am-5 pm.
