CSCI 0220
✦ Discrete Structures and Probability ✦
CSCI 0220 meets Mondays, Wednesdays, and Fridays from 1:00 - 1:50 pm.
I don't know about you, but we're feeling 22!
This class, offered both semesters at Brown University, gives you the tools to explore interesting questions and convince
yourself and others of their answers. You'll be introduced to new worlds of ideas and ways of
thinking.
We'll learn about Logic, Set Theory, Number Theory, Combinatorics, and
Probability.
If these topics sound unfamiliar, not to fear—you're in exactly the right place! This course
assumes
no prior experience with these topics.
Important info before the semester starts:
- Exams are in person: Exam 1 on 10/10, Exam 2 on 11/07, Exam 3 on 11/24, and Final Exam on 12/15.
- Lectures will be streamed and recorded; attendance is strongly encouraged.
- Attendance at weekly recitation sections is required.
For the fall 2025 semester, this class will be taught by professor Ellis Hershkowitz. If needed, you can contact him at ellis_hershkowitz@brown.edu.
Assignments
Times listed are in EST. Assignments are released on Tuesdays, and are due 6:00pm on Mondays. Clicking on the Overleaf Template link will open a new Overleaf project, so you can write your homework solutions in LaTeX.
| Homework | Template | Released | Due | Solutions |
|---|---|---|---|---|
| HW0 | - | Sep 03 | Sep 08 | - |
| HW1 | Overleaf Template | Sep 09 | Sep 15 | - |
| HW2 | - | Sep 16 | Sep 22 | - |
| HW3 | - | Sep 23 | Sep 29 | - |
| HW4 | - | Sep 30 | Oct 06 | - |
| HW5 | - | Oct 14 | Oct 20 | - |
| HW6 | - | Oct 21 | Oct 27 | - |
| HW7 | - | Oct 28 | Nov 03 | - |
| HW8 | - | Nov 11 | Nov 17 | - |
| HW9 | - | Dec 02 | Dec 08 | - |
Recitation sections are held from Wednesday to Sunday. Also, if you need to miss a recitation and need to request an absence, fill out the form here.
| Recitation | Template | Released | Solution |
|---|---|---|---|
| Recitation 1 | - | Sep 10 | - |
| Recitation 2 | - | Sep 17 | - |
| Recitation 3 | - | Sep 24 | - |
| Recitation 4 | - | Oct 01 | - |
| Recitation 5 | - | Oct 15 | - |
| Recitation 6 | - | Oct 22 | - |
| Recitation 7 | - | Oct 29 | - |
| Recitation 8 | - | Nov 12 | - |
| Recitation 9 | - | Nov 19 | - |
| Recitation 10 | - | Dec 03 | - |
| Final Exam Review | - | - |
Lectures
| Lecture | Date | Topic | Recording |
|---|---|---|---|
| 1 | Sep 03 | Intro | Video |
| 2 | Sep 05 | Logic: Propositional Logic I | Video |
| 3 | Sep 08 | Logic: Propositional Logic II | Video |
| 4 | Sep 10 | Logic: Proofs in Propositional Logic | - |
| 5 | Sep 12 | Logic: First Order Logic | - |
| 6 | Sep 15 | Logic: Proofs in First Order Logic | - |
| 7 | Sep 17 | Logic: Proofs in Mathematics | - |
| 8 | Sep 19 | Logic: Induction | - |
| 9 | Sep 22 | 22 and CS: Binary and Boolean Circuits | - |
| 10 | Sep 24 | Set Theory: Intro to Set Theory | - |
| 11 | Sep 26 | Set Theory: Proofs about Sets | - |
| 12 | Sep 29 | Set Theory: Relations | - |
| 13 | Oct 01 | Set Theory: Functions as Relations | - |
| 14 | Oct 03 | Set Theory: Equivalence Relations | - |
| 15 | Oct 06 | 22 and CS: Algorithms (Djikstra's Algorithm) | - |
| 16 | Oct 08 | Number Theory: Intro to Number Theory | - |
| - | Oct 10 | EXAM 1 - Logic & Set Theory | - |
| - | Oct 13 | Ind. Peoples Day - NO CLASS | - |
| 17 | Oct 15 | Number Theory: Division and Euclidean Algorithm | Video |
| 18 | Oct 17 | Number Theory: Modular Arithmetic | Video |
| 19 | Oct 20 | Number Theory: Multiplicative Inverse, Fermat's Little Theorem | Video |
| 20 | Oct 22 | 22 and CS: Cryptography (RSA) | Video |
| 21 | Oct 24 | Combinatorics: Intro to Counting | Video |
| 22 | Oct 27 | Combinatorics: Division Rule | Video |
| 23 | Oct 29 | Combinatorics: Binomial Theorem, Subtraction Rule (Inc-Exc) | Video |
| 24 | Oct 31 | Combinatorics: Pigeonhole Principle | Video |
| 25 | Nov 03 | 22 and CS: Data Compression (Prufer Codes) | Video |
| 26 | Nov 05 | Probability: Intro to Probability | Video |
| - | Nov 07 | EXAM 2 - Number Theory & Combinatorics | - |
| 27 | Nov 10 | Probability: Conditioning and Independence | Video |
| 28 | Nov 12 | Probability: Random Variables, Expectation | Video |
| 29 | Nov 14 | Probability: Conditional Expectation | Video |
| 30 | Nov 17 | Probability: Linearity of Expectation | Video |
| 31 | Nov 19 | Probability: Bayes' Rule | Video |
| - | Nov 21 | EXAM 3 - Probability & Redo 1 | - |
| 32 | Nov 24 | Probability: Variance and Concentration | Video |
| - | Nov 26 | Thanksgiving Break - NO CLASS | - |
| - | Nov 28 | Thanksgiving Break - NO CLASS | - |
| 33 | Dec 01 | 22 and CS: Machine Learning (Naive Bayes) | Video |
| 34 | Dec 03 | CS Theory at Brown | Video |
| - | Dec 05 | Slack Day | - |
| - | Dec 15 | FINAL EXAM - IN PERSON | - |
Calendar
How do hours work?
CS22 hours are collaborative spaces for students to work together on problems, facilitated by TAs. Hours will be primarily in-person. More details about hours can be found in the Course Missive.
Here is a link to the course calendar (same as below).
Resources
Course Textbook
Discrete Mathematics and Its Applications — Kenneth RosenReading this textbook is not required, though many students in the past have found it helpful in reinforcing what's covered in lecture!
Course Documentation
Important Links
LaTeX Resources
LaTeX (pronounced *la-tek*) is a program that you will be using to make your homework solutions look beautiful. The sample proofs above were written in LaTeX to give you an idea of what documents written in LaTeX look like. LaTeX allows you to incorporate mathematical notation into your proofs, and because this class involves a healthy dose of mathematical notation, LaTeX is going to be very useful! Using LaTeX is required after the 2nd homework.
We don't expect you've ever done this whole LaTeX business before, and that's why we're giving you some time to learn it! To get started, we recommend creating an account on Overleaf, an online program for writing and compiling LaTeX. After you do that, here are some links to check out: Honestly, please use Overleaf. It's so much easier than installing anything on your computer. Trust me.
- CS22 LaTeX Cheat Sheet (start here!)
- A Not So Short Introduction to LaTeX
- LaTeX Symbols Guide
- Art of Problem Solving: LaTeX
- LaTeX Intro Wikibook
- LaTeX on Brown CS Systems
- LaTeX Gearup Template
- LaTeX Gearup Completed Handout
In general, a really good resource for learning LaTeX is the web. When you have a question, google it, and you'll likely find someone who had the very same question!
If you'd like to download LaTeX on your computer, here are some resources to do that:
If you're using LaTeX and you just don't know what the code for some symbol is, here is a helpful list to start:
Alternatively, this is a neat site which will return the LaTeX code based on handwritten input (although searching your question on the web is likely more efficient):
Staff
Instructors
Ellis Hershkowitz
Instructor | Arlington, VA
he/him
Hi! Call me Ellis! I'm a theoretical computer scientist that mostly works on (graph) algorithms. I also graduated from Brown in 2015 and took CS22. Excited for a fun semester!
Favorite Constellation: Little Dipper
Head TAs
Alyssa Sun
HTA | Wilsonville, OR
she/her
Hi! I am a senior studying APMA-CS. I really like bagels!
Favorite Constellation: Air Pump
Amy Qiao
HTA | Madison, WI
she/her
Hi beautiful people! I'm a senior double-concentrating in CS & Math. I love all things math and will not shut up about it. In my free time, I love figure skating and overthinking everything. Talk to me about sports analytics :)
Favorite Constellation: Leo
Ilija Ivanov
HTA | Podgorica, Montenegro
he/him
Hi! I'm a junior from Podgorica, Montenegro studying CS. Looking forward to a great semester with you all!
Favorite Constellation: Orion
UTAs
Brandon Sun
UTA | Houston, TX
he/him
I'm a junior studying CS and Health and Human Biology from Houston TX! I'm also left-handed!
Favorite Constellation: Orion!
Christopher Chen
UTA | Marlboro, NJ
he/him
Hello! I'm a senior studying APMA-CS. I really, really like playing piano.
Favorite Constellation: Ursa Minor
Grace Wang
UTA | Bellevue, WA
she/her
I'm a cancer.
Favorite Constellation: Cancer
Hailey Coval
UTA | Milton, MA
she/her
Hi! I'm a sophomore studying CS. I love board games, the Berkshires, NYT crosswords, rock climbing, and all things Taylor Swift.
Favorite Constellation: Cygnus the swan
John Rathgeber
UTA | Cottage Grove, WI
he/him
Hi! I'm a junior studying Math-CS and Music. One fun fact about me is that my favorite food is phở!
Favorite Constellation: The Big Dipper
Moses Yang
UTA | Parsippany, NJ
he/him
Hi! Thanks for scrolling all the way down! I'm a junior studying CS, and I also fence at Brown. Fun fact: I went to Chipotle 23 times the past summer...
Favorite Constellation: Orion
Nathan Phan
UTA | Manning, SC
he/him
Hey! I'm Nathan, and I am a junior concentrating in Math-CS. My favorite things are music, spicy food, and basketball nicknames.
Favorite Constellation: Gemini
Zachary Wang
UTA | College Station, TX
he/him
I can bowl 100
Favorite Constellation: Ursa Major