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Mathematics
4 credits

UCLA MATH 61: Introduction to Discrete Structures

MATH 61 is UCLA's discrete mathematics course: logic and proof techniques, induction, set theory, combinatorics, recurrence relations, and graph theory. It's a required foundation for the CS major and the course where students first learn to construct rigorous arguments.

Fennie is independent and not affiliated with UCLA. This is an unofficial study guide.

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What makes it hard

For many CS students it's their first proof-based course, and the shift from computing answers to constructing arguments is the real difficulty. Counting problems are deceptively easy to get subtly wrong under exam pressure, and partial-credit proof grading rewards a precision that takes most of the quarter to develop.

What you'll cover

  • • Logic and proof techniques
  • • Mathematical induction
  • • Set theory and functions
  • • Combinatorics and counting
  • • Recurrence relations
  • • Graph theory basics

The MATH 61 study guide

How to study for UCLA MATH 61, step by step.

  1. 1

    Memorize the proof templates first

    Direct, contrapositive, contradiction, and induction each have a standard skeleton. Learn the skeletons in week one so exam energy goes into the idea rather than the format, on a quarter that moves fast.

  2. 2

    Write proofs out completely, every time

    Sketching an argument mentally and writing a rigorous proof are different skills, and only the second is graded. Write full proofs for homework, then critique your own precision against the solutions.

  3. 3

    Treat counting as the danger zone

    Combinatorics problems are short to state and easy to get subtly wrong. For each, decide whether order matters and whether repetition is allowed before reaching for a formula, and verify small cases by hand.

  4. 4

    Keep a daily problem trickle, not bursts

    Proof and counting intuition build through regular contact. A daily handful of problems across the ten weeks beats pre-exam marathons, which fail badly in this course.

  5. 5

    Build the daily trickle with Fennie

    Upload the MATH 61 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 61

Daily Plans give MATH 61 the steady daily problem contact proof skill requires — cramming arguments the night before a quarter-system midterm 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 dry.

FAQ

Is MATH 61 hard at UCLA?

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 midquarter.

Do I need MATH 61 for the CS major at UCLA?

Yes — MATH 61 is a required lower-division foundation for the CS major, and its proof and counting skills underpin CS 180 and other theory courses. A solid footing here pays off directly in the upper division.

How do I study for MATH 61 exams?

Memorize the proof templates, write every practice proof out completely and grade your own precision, and treat counting as a danger zone — decide order and repetition before any formula. Daily practice beats marathon cramming on the quarter timeline.

Pass MATH 61 with a plan, not a cram

Upload your MATH 61 materials and Fennie generates a Daily Plan paced to your deadline — plus chat, flashcards, and quizzes built from the actual course content.

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