UW–Madison CS 240: Introduction to Discrete Mathematics
CS 240 (officially COMP SCI 240) is UW–Madison's discrete math course for the CS major — logic, proofs, induction, sets, functions, counting, recurrences, and graphs — the mathematical foundation that CS 577 and the theory electives build on.
Fennie is independent and not affiliated with University of Wisconsin–Madison. This is an unofficial study guide.
Build my CS 240 study planWhat makes it hard
Proof-writing is the wall: most students arrive never having constructed a mathematical argument, and induction — the technique the course leans on hardest — feels circular until the mental model clicks. Exams present unfamiliar claims to prove, so the homework-memorization strategy that works in computational courses fails completely here.
What you'll cover
- • Propositional and predicate logic
- • Proof techniques
- • Mathematical induction
- • Sets, functions, and relations
- • Counting and combinatorics
- • Recurrences and graphs
The CS 240 study guide
How to study for UW–Madison CS 240, step by step.
- 1
Produce proofs from a blank page, always
Reading proofs builds recognition; exams demand production. After studying any example, close the notes and reconstruct the full argument — the production gap is where CS 240 grades are decided.
- 2
Drill the logic foundation until it's automatic
Quantifiers, implications, negations: every proof in the course is built from these. Practice translating English claims to formal statements and negating them until it costs no thought.
- 3
Give induction more reps than feels reasonable
It's the course's central technique and the one CS 577 assumes most heavily. Practice across integers, sums, and recursive structures until the base-case-and-step template feels mechanical.
- 4
Seek unfamiliar claims to prove weekly
Exam problems are claims you haven't seen. Pull unassigned textbook problems and practice deciding the technique — direct, contradiction, induction — as its own skill before writing anything.
- 5
Space the practice with Fennie
Upload your CS 240 materials and Fennie's Daily Plan spreads proof production across the week instead of deadline nights, synced to exams, with quizzes from your actual course content checking the definitions proofs depend on. It's free to start.
Start my CS 240 plan free
How Fennie helps with CS 240
Fennie's Daily Plans spread CS 240's proof practice across weeks — production skill only develops with spaced reps — synced to exam dates. Chat works proof strategy with you: what to assume, what to show, which technique fits, why your induction step does or doesn't hold. That feedback loop is what most students lack between discussion sections.
FAQ
Is CS 240 at UW–Madison hard?
It's a different hard than the programming sequence: no coding, all mathematical argument. Students meeting proofs for the first time — most of the room — find the middle of the course rough until induction clicks. Weekly production practice is what gets people through.
How do I get better at proofs in CS 240?
Reconstruct every studied proof from a blank page, drill logic notation until automatic, and practice on claims you haven't seen. The skill is production, not recognition — rereading solutions trains the wrong thing.
Why does CS 240 matter for the CS major?
CS 577 (Algorithms) is built directly on its induction, counting, and graph material, and theory electives assume proof fluency. Students who scrape through 240 consistently report paying for it in 577.
Pass CS 240 with a plan, not a cram
Upload your CS 240 materials and Fennie generates a Daily Plan paced to your deadline — plus chat, flashcards, and quizzes built from the actual course content.
Get started freeMore UW–Madison courses
CS 200 — Programming I
CS 200 (officially COMP SCI 200) is UW–Madison's first programming course, taught in Java — variables, control flow, methods, arrays, and an introduction to objects — serving intended CS majors, data science students, and a large population just adding programming skills. It assumes no prior experience.
CS 300 — Programming II
CS 300 (officially COMP SCI 300) is UW–Madison's object-oriented programming course in Java — classes, inheritance, interfaces, exceptions, recursion, and intro data structures like array lists and linked lists — and one of the largest courses on campus, since it gates the CS major and serves data science, engineering, and statistics students besides.
CS 400 — Programming III
CS 400 (officially COMP SCI 400) completes UW–Madison's programming sequence: data structures and their implementations — balanced search trees, hash tables, graphs — plus software development practices like version control, testing, and team projects, all in Java.
CS 252 — Introduction to Computer Engineering
CS 252 (cross-listed COMP SCI/E C E 252) introduces how computers work from the bottom up: transistors and gates, combinational and sequential logic, basic computer organization, and machine and assembly programming on the LC-3 — the first systems course in the CS and computer engineering tracks.