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Discrete Mathematics

Discrete Mathematics: logic, proofs, sets, number theory, induction, combinatorics, relations, graphs, trees, Boolean algebra, and the theory of computation.

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Propositions, connectives, and truth tablesStart module 1 Starting Check for this course (6 questions)

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Up nextModule 1 · LogicPropositions, connectives, and truth tables
Not startedModule 2 · LogicLogical equivalence and normal forms
Not startedModule 3 · LogicPredicates and quantifiers
Not startedModule 4 · LogicRules of inference
Not startedModule 5 · ProofsDirect proof, contraposition, and contradiction
Not startedModule 6 · ProofsExistence and uniqueness proofs and counterexamples
Not startedModule 7 · Sets and FunctionsSet operations and identities
Not startedModule 8 · Sets and FunctionsFunctions, injections, surjections, and composition
Not startedModule 9 · Sets and FunctionsCardinality and infinite sets
Not startedModule 10 · Sequences and SumsSequences, summation notation, and special sums
Not startedModule 11 · AlgorithmsAlgorithms and pseudocode
Not startedModule 12 · AlgorithmsGrowth of functions and complexity
Not startedModule 13 · Number TheoryDivisibility and the Euclidean algorithm
Not startedModule 14 · Number TheoryPrimes and factorization
Not startedModule 15 · Number TheoryCongruences and modular arithmetic
Not startedModule 16 · Number TheoryFermat's and Euler's theorems and the CRT
Not startedModule 17 · Number TheoryModular arithmetic for cryptography
Not startedModule 18 · Induction and RecursionMathematical induction
Not startedModule 19 · Induction and RecursionStrong induction and well-ordering
Not startedModule 20 · Induction and RecursionRecursive definitions and recursive algorithms
Not startedModule 21 · CountingThe sum and product rules and the pigeonhole principle
Not startedModule 22 · CountingPermutations and combinations
Not startedModule 23 · CountingBinomial coefficients and combinatorial identities
Not startedModule 24 · Advanced CountingInclusion–exclusion
Not startedModule 25 · Advanced CountingRecurrence relations
Not startedModule 26 · Advanced CountingGenerating functions
Not startedModule 27 · Discrete ProbabilityDiscrete probability and expectation
Not startedModule 28 · RelationsRepresenting relations and their properties
Not startedModule 29 · RelationsEquivalence relations and partitions
Not startedModule 30 · RelationsPosets and Hasse diagrams
Not startedModule 31 · GraphsGraph terminology, representation, and isomorphism
Not startedModule 32 · GraphsConnectivity and paths
Not startedModule 33 · GraphsEuler and Hamilton paths
Not startedModule 34 · GraphsShortest paths and graph algorithms
Not startedModule 35 · GraphsPlanar graphs and graph coloring
Not startedModule 36 · TreesRooted trees and tree traversal
Not startedModule 37 · TreesMinimum spanning trees
Not startedModule 38 · Boolean AlgebraBoolean functions and logic circuits
Not startedModule 39 · Models of ComputationFormal languages, automata, and Turing machines