Boston University - Spring 2024
CAS CS 237 - Probability in Computing

Instructors and Course Staff

Name	Office Hours
Prof. Alina Ene	Google Calendar
Prof. Tiago Januario
Teaching Fellows: Cheng-Hao Fu, Spyros Dragazis
Teaching Assistants: Eric Wang, Noah Barnes
Course Assistants: Annie Huang, Can Wang, Isaac Hu, Jessica Nguyen, Michael Krah, Munir Siddiqui, Oscar Mo, Quang Nguyen, Ruichen Liu, Sean Lin, Steve Choi

Communication

• We will use Piazza for online discussions.
• Do not send e-mails to the course staff.
• Feel free to ask or answer questions on Piazza.
• For sensitive, specific questions and solutions, use private posts.

Prerequisites

• CS 131 - Combinatoric Structures
• MA 123 - Calculus I
• CS 111 - Introduction to Computer Science I

We assume good working knowledge of elementary set theory and counting, elementary calculus (i.e., integration and differentiation), and programming in Python.

Structure

• Two 75 minutes lectures taught by one Instructor
  • Section A: LAW AUD, Tuedays and Thursdays, from 2:00pm to 3:15pm
  • Section B: CAS 522, Tuedays and Thursdays, from 3:30pm to 4:45pm
• One 50 minutes discussion lab on Fridays (check your schedule on Student Link)

The two sections of the course, A and B, will be treated as one class. The content of the two lectures is identical, assignments will be shared, students can mix-and-match A and B lecture.

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	Thu, Jan 18	Course information, Tips to succeed Random experiments	P 1.1 P 1.2 OB 1B	hw01 out Google Colab Collaboration & Honesty Policy	TJ
2	Tue, Jan 23	Sample spaces, events Probability function	LLM 17.1 P 1.3.1-1.3.3		AE
3	Thu, Jan 25	Probability axioms and rules Computing probabilities	LLM 17.3 LLM 17.5 P 2	hw02 out Non-transitive Dice Video	AE
4	Tue, Jan 30	Tree diagrams The Monty Hall problem	LLM 17.2 LLM 18.1.2		AE
5	Thu, Feb 01	Continuous Probability Spaces Anomalies with Continuous Probability	P 1.3.5	hw03 out Video	AE
6	Tue, Feb 06	Random variables Sum of random variables Functions of random Variables Definition and examples Distribution Functions Probality Density Function Cummulative Distribution Function	LLM 19.1 P 3.1.1 P 4.1.0 P 3.1.2 P 3.1.3 P 3.2.1 P 4.1.0 P 4.1.1		AE
7	Thu, Feb 08	Properties of PDFs and CDFs Examples and applications.	P 3.1.6 P 4.1.4	hw04 out Video	AE
8	Tue, Feb 13	Snow emergency Stay warm!			AE
9	Thu, Feb 15	Conditional probability Product rule	LLM 18 P 1.4.0	hw05 out Game: higher or lower?	AE
10	Tue, Feb 20	Law of total probability Bayes' Rule	P 1.4.2 P 1.4.3 3Blue1Brown Veritasium		AE
11	Thu, Feb 22	Independent events Pairwise Independence Mutual independence	LLM 18.7 LLM 18.8	hw6 out Last Day to Drop Standard Courses (without a “W” grade)	TJ
12	Tue, Feb 27	People versus Collins Independence of random variables	LLM 18.9 P 1.4.1	Video	TJ
13	Thu, Feb 29	Expected value of a random variable Infinite sums	LLM 19.4 P 3.2.2	hw07 out	TJ
14	Tue, Mar 05	Expectation of continuous random variables Linearity of Expectation	LLM 19.5 P 6.1.2		TJ
15	Thu, Mar 07	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	No homework this week Midterm practice Problems out	TJ
Tue, Mar 12		Spring Recess
Thu, Mar 14
16	Tue, Mar 19	Midterm review		Midterm Practice Problems Solution out	TJ
Thu, Mar 21		Midterm, in class, during lecture time		Covers all topics up to Lecture 13
17	Tue, Mar 26	Variance Standard deviation Variance properties	LLM 20.3 P 3.2.4	Video	TJ
18	Thu, Mar 28	Discrete distributions: - Bernoulli, - Uniform, - Binomial	LLM 19.3.1 LLM 19.3.2 P 3.1.5	hw08 out	TJ
Fri, Mar 29		"Last Day to Drop Standard Courses (with a “W” grade) Last Day for Undergraduate Students to Designate a Course as Pass/Fail"
19	Tue, Apr 02	Discrete distributions: - Geometric and its properties - Coupon Collector Part I	LLM 19.5.4		TJ
20	Thu, Apr 04	Discrete distributions: - Negative Binomial - Coupon Collector Part II	Wikipedia Stand-up Maths	hw09 out	TJ
21	Tue, Apr 09	Markov inequality Chebyshev inequality	LLM 20.1 LLM 20.2 P 6.2.2		TJ
22	Thu, Apr 11	Applications of Markov and Chebyshev's inequalities Continuous Uniform Distribution	LLM 20.1.1 LLM 20.2.1	hw10 out	TJ
23	Tue, Apr 16	Normal Distribution	LLM 20.2.2 P 4.2.3		AE
24	Thu, Apr 18	Exponential Distribution	P 4.2.2 P 11.1.2	HW 11 out	AE
25	Tue, Apr 23	Poisson Process Poisson Distribution	P 11.1.2		AE
26	Thu, Apr 25	Probability in Algorithms: - Bucket Sort - Reservoir Sampling	CLRS 8.4	Final Practice Problems out	TJ
27	Tue, Apr 30	Final exam review		Final Practice Solutions out	TJ
Thu, May 02		Study period begins
TBA		Final Exam Any day from May 6 to May 10		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.
• 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.
• You can use up to 5 grace periods without penalty, after that, you will receive a 10% penalty on each future late submission.
• Students who used no more than 2 grace periods will receive a 5% extra credit towards their overall homework score.
• The lowest grade on your homework assignments will be dropped.
• You are responsible for submitting high-quality images of your solutions. Illegible submissions will receive a 0 grade
• We highly recommend Gradescope Mobile App. You can also use your favorite app from iPhone or Android.
• Select the right pages on Gradescope for each problem (solved or not) to avoid a small homework penalty.
• 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% participation with Piazza polls
• 30% 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.

Participating in lectures, discussions, and on Piazza, bonus participation points will be awarded to students who get the most “good questions” and “good answers” on Piazza. Only good questions on the course material (not logistics) will be counted.

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

Sample nameplate
Change the name to yours in this PPTX file, print it, and bring it to the labs.

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.

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