Computing
Discrete Mathematics
Train on Discrete Mathematics with 315 published problems. Preview a problem, explore the course outline, and work through one problem at a time.
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See a problem from Discrete Mathematics before you begin.
Course topics
Course topics
Propositional and predicate logic with proof methods
Sets, functions, relations, and equivalence classes
Induction, recursion, and invariants
Divisibility, modular arithmetic, and elementary number theory
Combinatorics and inclusion-exclusion
Recurrences, generating functions, and discrete asymptotics
Graphs, trees, connectivity, and matchings
Practice problems
Try a few Discrete Mathematics problems, each with a hint.
- Let p, q, and r be propositions Free with an accountPropositional and predicate logic with proof methods
- Let A={1,2,3,4} and B={3,4,5,6} Free with an accountPropositional and predicate logic with proof methods
- Let R be a relation on a set A Sets, functions, relations, and equivalence classes
- Use strong induction to prove that every positive integer n can be written as n=2^k m… Sets, functions, relations, and equivalence classes
- (Honors) Let uₙ be defined by u₀=0, u₁=1, and uₙ=4uₙ₋₁-4uₙ₋₂+n for n ≥ 2 Induction, recursion, and invariants
- [Honors] Using inclusion-exclusion, find the number of permutations π of {1,2,…,9} such… Induction, recursion, and invariants
- Let n be a positive integer Recurrences, generating functions, and discrete asymptotics
- RSA decryption needs Euler, and Euler needs a coprime message Divisibility, modular arithmetic, and elementary number theory
- Four labs sharing ten hours cannot exceed a per-lab cap Combinatorics and inclusion-exclusion
- BFS two-coloring is the certificate that no odd cycle exists Graphs, trees, connectivity, and matchings