Teaching Team

We are lucky to have a phenomenal Course Assistant:

I. Course Overview

While the initial foundations of computer science began in the world of discrete mathematics (after all, modern computers are digital in nature), recent years have seen a surge in the use of probability as a tool for the analysis and development of new algorithms and systems. As a result, it is becoming increasingly important for budding computer scientists to understand probability theory, both to provide new perspectives on existing ideas and to help further advance the field in new ways.

CS109: Probability for Computer Scientists starts by providing a fundamental grounding in combinatorics, and then quickly moves into the basics of probability theory. We will then cover many essential concepts in probability theory, including particular probability distributions, properties of probabilities, and mathematical tools for analyzing probabilities. Finally, the last third of the class will focus on data analysis and machine learning as a means for seeing direct applications of probability in this exciting and quickly growing subfield of computer science. This is going to be a great quarter and we are looking forward to the chance to teach you.

Learning Goals

Our goal in CS109 is to build foundational skills and give you experience in the following areas:

1. Understanding the combinatorial nature of problems: Many real problems are based on understanding the multitude of possible outcomes that may occur, and determining which of those outcomes satisfy some criteria we care about. Such understanding is important both for determining how likely an outcome is, but also for understanding what factors may affect the outcome (and which of those may be in our control).
2. Working knowledge of probability theory: Having a solid knowledge of probability theory is essential for computer scientists today. Such knowledge includes theoretical fundamentals as well as an appreciation for how that theory can be successfully applied in practice. We hope to impart both these concepts in this class.
3. Appreciation for probabilistic statements: In the world around us, probabilistic statements are often made, but are easily misunderstood. For example, when a candidate in an election is said to have a 53% likelihood of winning does this mean that the candidate is likely to get 53% of the vote, or that that if 100 elections were held today, the candidate would win 53% of them? Understanding the difference between these statements requires an understanding of the model in the underlying probabilistic analysis.
4. Applications: We are not studying probability theory simply for the joy of drawing summation symbols (okay, maybe some people are, but that's not what we're really targeting in this class), but rather because there are a wide variety of applications where probability allows us to solve problems that might otherwise be out of reach (or would be solved more poorly without the tools that probability can bring to bear). We'll look at examples of such applications throughout the class.
5. An introduction to machine learning: Machine learning is a quickly growing subfield of artificial intelligence which has grown to impact many applications in computing. It focuses on analyzing large quantities of data to build models that can then be harnessed in real problems, such as filtering email, improving web search, understanding computer system performance, predicting financial markets, or analyzing DNA.

Course Topics

Here are the broad strokes of the course (in approximate order). More information is available on our Schedule page. We cover a very broad set of topics so that you are equipped with the probability and statistics you will see in your future CS studies!

• Counting and probability fundamentals
• Single-dimensional random variables
• Probabilistic models
• Uncertainty theory
• Parameter estimation
• Introduction to machine learning

Prerequisites

The prerequisites for this course are CS103, CS106B or X, and Math 51 (or equivalent courses). Probability involves a fair bit of mathematics (set theory, calculus, and familiarity with linear algebra), and we'll be considering several applications of probability in CS that require familiarity with algorithms and data structures covered in CS106B/X. Here is a quick rundown of some of the mathematical tools from CS103 and Math 51 that we'll be using in this class: multivariate calculus (integration and differentiation), linear algebra (basic operations on vectors and matrices), an understanding of the basics of set theory (subsets, complements, unions, intersections, cardinality, etc.), and familiarity with basic proof techniques. We'll also do combinatorics in the class, but we'll be covering a fair bit of that material ourselves in the first week. Past students have managed to take CS106B concurrently with CS109 and have done just fine. CS103 is the pre-requisite that we rely on the least. Students have done well even without having taken CS103.

II. Course Structure

Lectures

Lectures are Tuesday, Thursday, and Friday from 3:00p until 4:20p. We will be holding live lectures in-person in NVIDIA Auditorium. Come to learn the material, engage in interesting problems collectively with the class. While lecture attendance isn't mandatory it is correlated with doing well in the course and mastering the material. We will be offering a small extra credit bonus for lecture attendance. Lecture attendance will be tracked via completion of the lecture attendance form linked in the day's Lecture webpage. All students will have 24 hours to complete the attendance form of the day's lecture.

Lecture Recordings

CS109 lectures are recorded. Recordings will be posted on the Canvas site.

Fun fact: Did you know that in quarters where CS109 was not recorded, students performed better in the course? We did an analysis of past courses and the lift was rather noticable both in terms of grades and ability! Why? Coming to class may be a better way to learn the material, and a better time management system than watching the content online. Considering that this is a foundational course, better mastery of the material seems like a great thing. We put a lot of love into the lectures. Come join in on the good times!

Units

If you are an undergraduate, you are required to take CS109 for 5 units of credit (this is by department and university policy, no exceptions). If you are a graduate student, you may enroll in CS109 for 3 or 4 units if it is necessary for you to reduce your units for administrative reasons. Taking the course for reduced units does not imply any change in the course requirements.

Sections

Active participation plays an important role in making you adept at combining probability and computer science. It has also been observed over many quarters that keeping up with the material highly correlates with improved class performance.

Each week for 1 hour you will meet in a small group with one of our teaching team members and work through problems. If you have taken any of the CS106 classes, our sections will be very similar—except with more probability. Sign-ups for sections will go out on Tuesday, June 24th and will be open until midnight Pacific Friday, June 27th. We will let you know which section you are in by Sunday, June 29th and you will have your first section that week (during Week 2).

Section attendance and participation is required of all students. Students are allowed one unexcused absence—one for which you simply don't show up and don't tell us why—in the quarter without penalty. Understand that absences can only be excused because of severe illness, family emergency, or Stanford-sponsored business or collegiate athletics travel. Regardless of why you miss section, you're responsible for all section handout content and understanding all problems and solutions.

Your section grade is automatically a 100%. If you attend all sections, then you're awesome and your section grade counts 5% toward your final grade. If you miss just one section, then you're still awesome and we'll forgive the one absence, and your seciton grade of 100% counts 5% toward your final grade. For every section you miss beyond the freebie, your section grade counts 1% less and your final exam grade counts 1% more. If you miss five or more sections, then your section grade doesn't contribute to your final grade at all.

If in any given week you can't make your assigned section, you can attend another provided you email the CA leading that section and confirm there's room.

Grading

The grade for the course will be determined according to the following breakdown:

Component	Final grade
Problem Sets	30%
Quizzes	30%
Final Exam	35-40%
Section Participation	0-5%

Problem Sets

During the course, there will be seven problem sets assigned. We put a lot of love into these problems so that they can help train you to become gifted practitioners of probability and computer science. Use them as practice. Doing well on the problem sets is the best way to prepare for life after CS109 (and the exams). Each student is to submit individual work on the problem sets. The problem sets will often include coding tasks, which will be primarily in python. We also strongly encourage you to learn LaTex, which is the interchangable markup language for typing math on a computer. We will hold review sessions for those of you who are not familiar with python.

This quarter in CS109 we are using "the psetapp", a webapp where you can solve your problem sets. Importantly, the psetapp allows you to check your work as you go! That way you can get immediate feedback as to whether you have figured out the solution. Things to know: (1) the psetapp auto saves your progress so you never need to hit a "save" button, (2) similarly, you don't need to hit submit. At the deadline you will no longer be able to edit your work and we will start grading your current saved solutions (3) You can check your answer as many times as you want. There is no penalty for retrying if you didn't get the answer correct the first time.

After you submit we will use a combination of manual and automatic grading. For every problem we expect that you show your work. For each math solution, you should provide a detailed enough explanation that someone who is fluent in CS109 would understand how to solve it. Never write down just the answer. For coding solutions, we expect you to use enough comments and good style that it is clear what process your code is using to solve the task.

After grades are released, you have one week to file a regrade request if you think that points were deducted incorrectly. We reserve the right to regrade your entire pset.

Late Policy

There may be unforeseen circumstances that make it difficult to turn in homework assignments on time. Our philosophy is to treat you as adults and thus we have a generous late policy to reflect the many different needs that may come up. However, the course will end for everyone on the same date. As such if you are late on one problem set, you will have to work extra hard to catch up. Time management can be hard and we encourage you to give it the full respect it deserves. In practice, falling behind often impacts midterm and final exam scores.

• Due Date: The on time deadline will be listed on each assignment writeup (generally at 3p). Finishing the assignment by the deadline means that you are in sync with the course. Hooray!
• Grace Period: All students will be granted a penalty-free "grace period" for submission on all problem sets except the last one. The grace period is one full day (24 hours) and allows you to submit the assignment after the original deadline, with no impact on the final grade. As an example, a problem set due on Wednesday at 3:00pm (Stanford time) may be turned in by Thursday (Stanford time) at 3:00pm for full credit. This grace period is meant to give built-in flexibility for any unexpected snags—however, we strongly recommend that students submit by the original deadline if possible, so you don't spiral into an ever-repeating need to turn work in late (especially during Summer Quarter, which goes quick).
• Long Extension: We generally allow you an additional penalty-free extension even beyond the first grace period, though you need to email us to let us know you’ll need the additional time. In general, you won’t be penalized for lateness provided you submit an assignment within two days (48 hours) of the original due date. We'd rather you do good work on the assignment and understand the material than rush to meet some deadline and put off the learning even longer than you already are.

Exams

In addition to the assignments, there will be (2) oral quizzes and a final:

• Quiz 1: Week 3
• Quiz 2: Week 6
• Final: Sat, Aug 16th, 3:30p - 6:30p PT

Quizzes: We will finalize the details for the oral quizzes during the first week of the quarter (i.e., with plenty of time for students to work out potential conflicts and/or drop the course if they need to). What we can say, for now, is that there will be some small degree of flexibility re: times and dates.

No Final Alternatives: The final exam will be a traditional in-person, pencil on paper, closed-book, closed-calculator, closed-computer exam, though you're permitted to bring six pages (i.e., 12 sides) of handwritten notes. Unless you're an SCPD student or have an accommodation on file with the OAE, you're expected to take the final during the designated time slot (yes, we know, Saturday exams are a bummer—it wasn’t up to us, either). Those requiring accommodations will of course be accommodated; just reach out to us as soon as possible so we can make alternate arrangements.

Extra Credit Challege

CS109 has traditionally held an extra credit contest, where students apply the principles in this class to explore a topic of their own choice. Participation in the contest is completely optional and prizes involve extra credit to your final course grade. More details about the contest to be posted within the first weeks of the quarter.

III. Course Resources

CS109 Course Reader

There is a CS109 course reader which contains optional reading as well as interactive demos. Course Reader Github Project.

Optional Textbook

Sheldon Ross, A First Course in Probability (10th Ed.), Pearson Prentice Hall, 2018.

This is an optional textbook, meaning that the text is not required material, but students may find Ross offers a different and useful perspective on the important concepts of the class. Suggested, optional reading assignments from the textbook (10th Ed.) are in the schedule on the course website. The 8th, 9th, and 10th editions of the textbook are all fine for this class.

Borrowing the textbook online: HathiTrust, a library archive of which Stanford is a member, has granted the university online access to the 8th edition (2010) for the duration of the Fall quarter. The "check out" system works similarly to print reserves: A user can check out the book an hour at a time as long as they are actively using it. Access guidelines are on the HathiTrust How To Use It webpage. Once you're logged in, the book is at this link.

All students should retain receipts for books and other course-related expenses, as these may be qualified educational expenses for tax purposes. If you are an undergraduate receiving financial aid, you may be eligible for additional financial aid for required books and course materials if these expenses exceed the aid amount in your award letter. For more information, review your award letter or visit the Student Budget website.

"Working" Office Hours

To help make you more successful in this class , the course staff will hold "working" office hours. The idea is to encourage you to work on your problem sets at these office hours, so you can immediately ask any questions that come up while working on your problem sets. While you are certainly not required to attend any of these working office hours, they are simply meant to encourage you to interact with the course staff more often in order to help you better understand the course material. Besides, our job is to help everyone learn the material for this class, and being more accessible to you when you are actually working on your assignments (rather than when you just have a problem) will help the course go more smoothly for you (and it'll be more fun for us).

Not all office hours are the same! The office hour calendar will indicate specific details such as the time and location of each office hours. Office hours are either in person or online. If an office hour time on the calendar says it is in person, there will be no online option — and if the calendar says an office hours session is online, please don't show up at our TAs dorms :).

Accommodations

Students who may need an academic accommodation based on the impact of a disability must initiate the request with the Office of Accessible Education (OAE). Professional staff will evaluate the request with required documentation, recommend reasonable accommodations, and prepare an Accommodation Letter for faculty. For students who have disabilities that don't typically change appreciably over time, the letter from the OAE will be for the entire academic year; other letters will be for the current quarter only. Students should contact the OAE as soon as possible since timely notice (for example, at least a week before an exam) is needed to coordinate accommodations. Students should also send your accommodation letter to instructors as soon as possible. If you require additional, or different, accommodations specific to the Summer 2025 learning environment, please contact your disability adviser directly.

IV. Honor Code

Please read our full Honor Code Policy, which specifically prohibits you from soliciting or taking solutions from other students or websites like Stack Overflow and Chegg.

Looking Forward to a Great Quarter

Genuinely, teaching CS109 is a profound joy. Thanks for coming to learn with us. We can't wait 🌱.