CSCI 0220
Discrete Structures and Probability
CSCI 0220 meets Mondays, Wednesdays, and Fridays from 11:00 - 11:50 am.
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, and there will be a total of 3 in-class (non-final) exams and one final exam.
- Lectures will be streamed and recorded; attendance is strongly encouraged.
- Attendance at weekly recitation sections is required.
- Homeworks are due Mondays and released on Tuesdays.
For the Fall 2026 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 typically released on Tuesdays, and are due 5:59pm 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 9 | Sep 14 | - |
| HW1 | - | Sep 15 | Sep 21 | - |
| HW2 | - | Sep 22 | Sep 28 | - |
| HW3 | - | Sep 29 | Oct 5 | - |
| HW4 | - | Oct 6 | Oct 12 | - |
| HW5 | - | Oct 20 | Oct 26 | - |
| HW6 | - | Oct 27 | Nov 2 | - |
| HW7 | - | Nov 3 | Nov 9 | - |
| HW8 | - | Nov 17 | Nov 23 | - |
| HW9 | - | Nov 24 | Dec 2 | - |
Recitation sections are held on Mondays, Wednesdays and Thursdays. Also, if you need to miss a recitation and need to request an absence, please provide a doctor's note or dean's note, and email Prof. Ellis.
| Recitation | Template | Released | Solution |
|---|---|---|---|
| Recitation 1 | - | Sep 16 | - |
| Recitation 2 | - | Sep 23 | - |
| Recitation 3 | - | Sep 30 | - |
| Recitation 4 | - | Oct 7 | - |
| Practice Exam 1 | - | Oct 14 | - |
| Recitation 5 | - | Oct 21 | - |
| Recitation 6 | - | Oct 28 | - |
| Recitation 7 | - | Nov 4 | - |
| Practice Exam 2 | - | Nov 11 | - |
| Recitation 8 | - | Nov 18 | - |
| Recitation 9 | - | Nov 30 | - |
| Practice Exam 3 | - | Dec 4 | - |
Lectures
| Lecture | Date | Topic | Recording |
|---|---|---|---|
| 1 | Sep 9 | Intro | Video |
| 2 | Sep 11 | Propositions, Connectives, Truth Tables | Video |
| 3 | Sep 14 | Logical Equivalence | Video |
| 4 | Sep 16 | Rules of Inference and Logic Proofs | Video |
| 5 | Sep 18 | First Order Logic | Video |
| 6 | Sep 21 | Equivalence, Inference Rules, Proofs in FOL | Video |
| 7 | Sep 23 | 22 and Systems (Boolean Circuits) | Video |
| 8 | Sep 25 | Proof Techniques I (Forall, If, Contrapositive, Iff) | Video |
| 9 | Sep 28 | Proof Techniques II (Exists, Or, Contradiction) | Video |
| 10 | Sep 30 | Proof Techniques III (Induction) | Video |
| 11 | Oct 2 | Language of Set Theory | Video |
| 12 | Oct 5 | Proofs about Sets | Video |
| 13 | Oct 7 | Relations, Functions as Relations | Video |
| 14 | Oct 9 | Equivalence Relations | Video |
| - | Oct 12 | Indigenous People's Day - NO CLASS | - |
| 15 | Oct 14 | 22 and Algorithms (BFS) | Video |
| 16 | Oct 16 | Division Theorem, GCD, Euc Algorithm | Video |
| - | Oct 19 | EXAM 1 (Logic, Math Foundations) | - |
| 17 | Oct 21 | Fundamental Theorem of Arithmetic, Euclid's Lemma | Video |
| 18 | Oct 23 | Congruence, Modular Arithmetic | Video |
| 19 | Oct 26 | Multiplicative Inverse, Fermat's Little Theorem | Video |
| 20 | Oct 28 | Totient Function, Euler's Theorem | Video |
| 21 | Oct 30 | 22 and Cryptography (RSA) | Video |
| 22 | Nov 2 | Intro to Counting | Video |
| 23 | Nov 4 | Division Rule | Video |
| 24 | Nov 6 | Subtraction Rule (Inc-Exc) | Video |
| 25 | Nov 9 | Pigeonhole Principle | Video |
| 26 | Nov 11 | 22 and Data Representation | Video |
| 27 | Nov 13 | Intro to Probability | Video |
| - | Nov 16 | Exam 2 - Number Theory, Combinatorics | - |
| 28 | Nov 18 | Conditioning and Independence | Video |
| 29 | Nov 20 | Random Variables, Expectation | Video |
| 30 | Nov 23 | Grouping Outcomes by RV Value | Video |
| - | Nov 25 | Thanksgiving Break - NO CLASS | - |
| - | Nov 27 | Thanksgiving Break - NO CLASS | - |
| 31 | Nov 30 | Linearity of Expectation | Video |
| 32 | Dec 2 | Bayes' Rule | Video |
| 33 | Dec 4 | 22 and AI (LLMs) | Video |
| - | Dec 7 | Exam 3 - Probability, Redo 1 Previous (Reading Period Begins) | - |
| 34 | Dec 9 | CS Theory at Brown | - |
| - | TBD | FINAL EXAM | - |
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 Rosen
Reading 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
Staff
Instructors
D. 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 Arcade Game: Space Invaders
Head TAs
Zach Quitkin
HTA | Stratham, NH
he/him/his
Hi! My name is Zach, and I'm a senior studying computer science. I love traveling, swimming, and alternative proteins. Excited for a great semester of 22!
Favorite Arcade Game: Street Fighter
Brandon Sun
HTA | Houston, TX
he/him
Hello! I'm a senior studying Computer Science and Health and Human Biology. I'm also left handed!
Favorite Arcade Game: Mega Stacker
UTAs
Adhyayan Agrawal
UTA | Kathmandu, Nepal
he/him
Hi! I am a sophomore planning to concentrate in EE and CS. Fun fact: I make the best pani puri in the city. Super hyped up for this sem!
Favorite Arcade Game: Pong
Grace Wang
UTA | Bellevue, WA
she/her
Hi! My name is Grace, and I'm a senior concentrating in APMA-CS. I like crocheting, movies, and heytea mango coconut boom :)
Favorite Arcade Game: Dig Dug
JJ Hatcher
UTA | Ewa Beach, HI
he/him
Hey, I'm a junior and I am studying Computer Science and Psychology. Fun Fact: I went to a Bruno Mars concert this Summer
Favorite Arcade Game: Pac-Man
Moses Yang
UTA | Parsippany, New Jersey
he/him
Hi! Thanks for scrolling all the way down! I'm a senior studying CS, and I also fence at Brown. Fun fact: I went to Chipotle 23 times the past summer...
Favorite Arcade Game: Dance Dance Revolution (but I suck)
Nathan Phan
UTA | Manning, SC
he/him
Hello! I'm a senior from South Carolina studying Math and CS. My favorite things are listening to music, watching films, and eating spicy food. Looking forward to a great semester!
Favorite Arcade Game: Skeeball
Swan Tayza Aung
UTA | Yangon, Myanmar
he/him
Hi I'm a sophomore who's doing APMA-CS! One of my hobbies is to pick up languages from my friends. So far I can say 67 in 6-7 languages - 六七, ろく なな, алты жеті, altı yedi, enam tujuh, หก เจ็ด, ေခြာက်ခွန်
Favorite Arcade Game: Shoot em up / bullet hell (any title)