Berkeley MATH 55: Discrete Mathematics

MATH 55 is Berkeley's discrete mathematics course: logic and proofs, induction, set theory, combinatorics, recurrences, number theory, graph theory, and discrete probability. It serves math majors and students outside EECS who need discrete math — CS 70 covers overlapping ground for the CS-major path, and most programs accept one or the other.

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What makes it hard

Like CS 70, it's many students' first proof-based course, and the transition from computing answers to constructing arguments is the real difficulty. Counting problems are deceptively hard to get right under exam conditions, and partial-credit proof grading rewards precision that takes a semester to develop.

What you'll cover

• Propositional logic and proof techniques
• Mathematical induction
• Set theory and functions
• Combinatorics and counting
• Recurrence relations
• Number theory and modular arithmetic
• Graph theory basics

The MATH 55 study guide

How to study for Berkeley MATH 55, step by step.

1
Learn the proof templates cold
Direct proof, contrapositive, contradiction, and induction each have a standard skeleton. Memorize the skeletons early so exam energy goes into the idea, not the format.
2
Write proofs out fully, every time
Sketching an argument in your head and writing a rigorous proof are different skills, and only the second is graded. Write complete proofs for homework and practice problems, then critique your own precision.
3
Treat counting as a danger zone
Combinatorics problems are short to state and easy to get subtly wrong. For each one, identify whether order matters and whether repetition is allowed before touching a formula — and verify small cases by brute force.
4
Do a steady trickle of problems, not bursts
Proof and counting intuition build through regular contact. A daily handful of problems through the semester outperforms pre-exam marathons by a wide margin in this course.
5
Build the daily trickle with Fennie
Upload the MATH 55 syllabus and Fennie's Daily Plans schedule daily proof and counting practice paced to your midterms, generating fresh problems and definition flashcards from your actual course materials. Free to start.
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How Fennie helps with MATH 55

Daily Plans give MATH 55 the steady daily problem contact that proof skill requires — cramming arguments the night before fails reliably. Use Fennie's chat to stress-test your proofs line by line, and generate counting problems with worked reasoning when the textbook supply runs out.

FAQ

Is MATH 55 the same as CS 70?

They overlap heavily — both cover proofs, induction, number theory, counting, and discrete probability. CS 70 is built for the CS major with more algorithmic flavor; MATH 55 is the math department's version. Most programs require one or the other, not both.

Is MATH 55 hard?

It's a real adjustment if it's your first proof-based course — the difficulty is learning to construct rigorous arguments, not any single topic. Students who write proofs out fully and practice daily find it very manageable by midsemester.

Do I need MATH 55 for the CS major at Berkeley?

CS majors take CS 70, which covers the discrete math requirement. MATH 55 serves math majors and students in other programs needing discrete mathematics — check your major's specific requirement before choosing between them.

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