Boston University - Spring 2025
CAS CS 237 - Probability in Computing

Instructors and Course Staff

Name	Office Hours
Prof. Nathan Klein	Google Calendar
Prof. Tiago Januario
Teaching Fellow: Erick Jimenez Berumen
Teaching Assistants: Noah Barnes, Steve Choi, Annie Huang, Oscar Mo, Jessica Nguyen
Course Assistants: Letitia Caspersen, Michael Krah, Daniel Matuzka, Eytan Mobilio, Vi Tjiong, Sarah Yuhan

Syllabus

Introduction to basic probabilistic concepts and methods used in computer science. Develops an understanding of the crucial role played by randomness in computing, both as a powerful tool and as a challenge to confront and analyze. Emphasis on rigorous reasoning, analysis, and algorithmic thinking. This course fulfills a single unit in each of the following BU Hub areas: Quantitative Reasoning II, Critical Thinking.

Schedule

This schedule is subject, and likely, to change as we progress through the semester. Reading chapters are from the first textbook (LLM) or from the second textbook (P), referred to by the acronyms of the author names.

Lec.	Date	(Tentative) Topics	Reading	Handouts/Homework	Instructor
1	Tue, Jan 21	Course information, Tips to succeed Random experiments	P 1.1 P 1.2 OB 1B	Jupyter Lab Your first Jupyter Notebook Collaboration & Honesty Policy	TJ
2	Thu, Jan 23	Sample spaces, events Probability function	LLM 17.1 P 1.3.1-1.3.3	hw01 out	TJ
3	Tue, Jan 28	Probability axioms and rules Computing probabilities	LLM 17.3 LLM 17.5 P 2	Non-transitive Dice Video	NK
4	Thu, Jan 30	Tree diagrams The Monty Hall problem	LLM 17.2 LLM 18.1.2	hw02 out	NK
5	Tue, Feb 04	Continuous Probability Spaces Anomalies with Continuous Probability	P 1.3.5	Video Why “probability of 0” does not mean “impossible”	TJ
6	Thu, Feb 06	Random variables Sum of random variables Functions of random Variables Definition and examples	LLM 19.1 P 3.1.1 P 3.1.2	hw03 out	TJ
7	Tue, Feb 11	Distribution Functions Probality Density Function Cummulative Distribution Function	P 3.1.3 P 3.2.1 P 4.1.0 P 4.1.1	Video	TJ
8	Thu, Feb 13	Properties of PDFs and CDFs Examples and applications.	P 3.1.6 P 4.1.4	hw04 out Video	TJ
Tue, Fev 18		Substitute Monday Schedule of Classes		Check the Google Calendar for the updated office hour schedule
9	Thu, Feb 20	Conditional probability Product rule	LLM 18 P 1.4.0	hw05 out Game: higher or lower?	NK
10	Tue, Feb 25	Law of total probability Bayes' Rule	P 1.4.2 P 1.4.3	The geometry of changing beliefs Veritasium	NK
11	Thu, Feb 27	Independent events Pairwise Independence Mutual independence	LLM 18.7 LLM 18.8	hw6 out Last Day to Drop Standard Courses (without a “W” grade)	NK
12	Tue, Mar 4	People versus Collins Independence of random variables	LLM 18.9 P 1.4.1	Video	NK
13	Thu, Mar 6	Expected value of a random variable Infinite sums	LLM 19.4 P 3.2.2	Midterm practice problems out	NK
Tue, Mar 11		Spring Recess
Thu, Mar 13
14	Tue, Mar 18	Expectation of continuous random variables Linearity of Expectation	LLM 19.5 P 6.1.2	Midterm practice solutions out	NK
Thu, Mar 20		Midterm, in class, during lecture time B1 Section CGS 527 - First name starting with letter [A-K] CAS 213 - First name starting with letter [L-Z] A1 Section CGS 511 - First name starting with letter [A-R] CAS 216 - First name starting with letter [S-Z]		Covers all topics up to Lecture 13 hw07 out
15	Tue, Mar 25	Law of the unconscious statistician Conditional expectation Law of total expectation Linearity of conditional expectation	LLM 19.4.1 P 3.2.3 LLM 19.4.6		TJ
16	Thu, Mar 27	Variance Standard deviation Variance properties	LLM 20.3 P 3.2.4	hw08 out Video	TJ
17	Tue, Apr 01	Discrete distributions: - Bernoulli, - Uniform, - Binomial	LLM 19.3.1 LLM 19.3.2 P 3.1.5		TJ
18	Thu, Apr 03	Discrete distributions: - Geometric and its properties - Coupon Collector Part I	LLM 19.5.4	hw09 out	TJ
19	Tue, Apr 08	Discrete distributions: - Negative Binomial - Coupon Collector Part II	Wikipedia Stand-up Maths		TJ
20	Thu, Apr 10	Markov inequality Chebyshev inequality	LLM 20.1 LLM 20.2 P 6.2.2	hw10 out	TJ
21	Tue, Apr 15	Applications of Markov and Chebyshev's inequalities Continuous Uniform Distribution	LLM 20.1.1 LLM 20.2.1		TJ
22	Thu, Apr 17	Normal Distribution	LLM 20.2.2 P 4.2.3	hw11 out	NK
23	Tue, Apr 22	Exponential Distribution	P 4.2.2 P 11.1.2		NK
24	Thu, Apr 24	Poisson Process Poisson Distribution	P 11.1.2	HW 12 out Final Practice Problems out	NK
25	Tue, Apr 29	Probability in Algorithms: - Bucket Sort Course evaluation	CLRS 8.4	Final Practice Solutions out	NK
26	Thu, May 01	Probability in Algorithms: - Reservoir Sampling Final exam review Course evaluation	Wiki		NK
Fri, May 02		Study period begins
TBA		Final Exam Any day from May 5 to May 9 Plan to stay on campus for the whole final exam week		Cumulative and covers all topics

Textbooks

You can access both books for free or support the authors by purchasing the books.

• (LLM) Mathematics for Computer Science by Eric Lehman, Tom Leighton, and Albert Meyer.
• (P) Introduction to Probability, Statistics, and Random Processes by Hossein Pishro-Nik.
• (CLRS) Cormen, Leiserson, Rivest, and Stein. Introduction to Algorithms, Fourth Edition, MIT Press.

Course atmosphere, diversity and inclusion

• We intend to provide a positive and inclusive atmosphere in classes and on the associated virtual platforms.
• If you require special accommodations for exams or coursework, please send a private message to an instructor and forward any relevant documentation from Disability and Access Services.
• If you are facing unusual circumstances during the semester, please reach out to us early on so that we can find a good arrangement.

Your suggestions are encouraged and appreciated. Please let us know ways to improve the effectiveness of the course for you personally or for other students.

Participation

• Participation will be tracked with Piazza polls.
• You will get the full participation points if you answer at least 75% of the possible Piazza polls.
• If you end up answering x% Piazza polls, where x < 75, you will get x/75 of the points.
• Most of the material covered in lectures and labs can be found in our textbooks. Read them!
• While our textbook will be very helpful, it is an imperfect substitute for in-class learning, which is the fastest (and easiest) way to learn the material.
• In all cases, you are responsible for being up to date on the material.

Homework

• Weekly homework assignments will be posted on Thursdays. Provide step-by-step explanations, not just answers. Answers without explanations will earn a small fraction of the points.
• Assignments will be due Wednesdays by 09:00 p.m. ET, electronically via Gradescope.
• Gradescope will remain open for a 3-hour grace period after the posted deadline.
• Late assignments will not be accepted after the grace period as we intend to post solutions the following day.
• Each no submission will be tread as a late submission.
• You can use up to 3 grace periods without penalty, after that, you will receive a 1% penalty on each future late submission.
• The lowest grade on your homework assignments will be dropped, after applying the penalties.
• You are responsible for submitting one single PDF file with high-quality images of your solutions. Illegible submissions will receive a 0 grade
• We highly recommend Dropbox to scan your homework before uploading it.
• Select the correct pages on Gradescope for each problem (solved or not) to avoid a 10% homework penalty. In cases where you do not have a solution to submit for a specific problem, type a brief note such as "No solution provided".
• Submissions with identically worded answers, including identical pseudocodes, are considered serious offence and will be reported to Dean's Office.
• Any use of ChatGPT or similar AI functionality to help solve homework problems violates the Collaboration & Honesty Policy.

Sometimes it's ok to submit partial results if you couldn't fully finish your assignment, don't miss the due date because of last-minute work.

Exams

• Both exams will consist of problem-solving and short questions about the material.
• Each exam duration and their locations are given in the course schedule.
• The content of the final is cumulative.
• No collaboration whatsoever is permitted on exams, any violation will be reported to the College.

Regrade Policy

• Regrade requests can be submitted up to one week (7 days) after grades for a given assignment have been posted (except the final exam).
• You must request a regrade via Gradescope, *NOT* through email .
• When we regrade a problem, your score may go up or down.

Grading

The course grade will break down as follows:

• 5% class attendance
• 5% lab attendance
• 25% weekly homework assignments
• 30% in-class midterm exam
• 35% in-class final exam. Don't make any travel plans before the final date is released
• Incompletes for this class will be granted based on CAS Policy.

Citation policy

• You can refer to anything from the textbook, lecture and discussion notes, and information given by the course staff without having to cite it.
• If you use any other information, you must include a proper citation. If you omit to do this, you are committing plagiarism.
• Searching explicitly for answers to problems on the Web or from persons not enrolled in the class this current semester is strictly forbidden.

Collaboration & Honesty Policy

• The Collaboration & Honesty Policy specifies the rules of collaboration in the course and penalties for cheating.
• We require that each student read, sign, and submit this document to Gradescope.
• Even if you get help on Piazza or during office hours from the instructors for the class for specific problems, list them as collaborators.

Miscellaneous

LaTeX resources

• TexShop is a latex editor for the Mac platform;
• TexNiCenter is a text editor for Windows;
• Overleaf is a web-based latex system (that allows you to avoid latex installation on your machine).
• Not so short intro to latex;
• A latex tutorial.

Homework template files: tex, pdf, jpg.