Discrete Mathematics curriculum & tutors

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A proof-centered discrete mathematics course covering logic, sets, relations, induction, number theory, counting, graphs, state machines, recurrences, and discrete probability.

8 public curriculum units1 tutor availableAlways Free
College bridge / mathematics for computer science

Discrete Mathematics curriculum

A proof-centered discrete mathematics course covering logic, sets, relations, induction, number theory, counting, graphs, state machines, recurrences, and discrete probability.

Pacing
8 units, 20-30 weeks self-paced
Units
8 unit sequence
Practice
640 checked answers
Support
Self-paced or tutor-guided
Outcomes
  • Write valid direct, contradiction, contrapositive, and induction proofs.
  • Model computational problems with sets, relations, graphs, state machines, and recurrences.
  • Use counting and discrete probability to analyze algorithms and uncertain systems.

Unit sequence

Built for independent progress first, then tutor support where the student gets stuck.

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  1. 01

    Logic and proof language

    • Use propositions, predicates, quantifiers, implications, equivalence, and inference rules.
    • Translate precise claims between symbols and ordinary language.

    Practice: Formalize ten claims, test validity with truth tables or inference rules, and repair every ambiguous statement.

  2. 02

    Proof methods

    • Write direct, contrapositive, contradiction, existence, uniqueness, and counterexample arguments.
    • Separate examples from proofs.

    Practice: Complete one proof by each major method and annotate the logical hinge in every argument.

  3. 03

    Sets, functions, and relations

    • Use set operations, Cartesian products, functions, injections, surjections, and bijections.
    • Analyze equivalence and partial-order relations.

    Practice: Classify functions and relations from definitions, then prove two classifications from first principles.

  4. 04

    Induction and recursion

    • Use weak and strong induction.
    • Define recursive structures and verify recursive algorithms.

    Practice: Prove a summation or divisibility claim by induction and trace a recursive definition on a small input.

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