Cours · College
Discrete Mathematics
Logic, proof, induction, relations, counting, recurrences, graphs, automata and complexity: the discrete maths of a first university course.
A complete first university course in discrete mathematics, in the order it is usually taught: propositional and predicate logic and the standard proof techniques; induction in all its forms; sets, relations and functions, including countable and uncountable sets; counting with the product rule, bijections and the pigeonhole principle; recurrence relations and how to solve them; graphs, trees, Euler and Hamilton paths and colouring; Boolean algebra, circuits and finite automata; and finally algorithms, asymptotic analysis, the master theorem, satisfiability and polynomial-time reductions.
It is for anyone comfortable with school algebra who wants to reason precisely about finite and countable structures, and it is the mathematical core of a computer science degree. Each unit ends with a quiz mixing computation, concepts and short proofs; the final exam covers the whole course.
Ça vient après: Algebra
Le cours
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Logic and proof
25 leçonsWhat is Discrete Mathematics?Discrete StructuresDiscrete mathematicsTruth tablesMathematical StatementsStatements and QuantifiersCompound StatementsConstructing Truth TablesTruth Tables for the Conditional and BiconditionalImplicationsEquivalent StatementsDe Morgan’s LawsRules of LogicLogical ArgumentsPredicate logic and quantifiersProofsDirect proof, contrapositive and contradictionProofs about Discrete StructuresChapter SummaryPropositional calculusLogical connectiveTruth tableFirst-order logicQuantifier (logic)Predicate (mathematical logic) -
Induction and sequences
11 leçons -
Sets, relations and functions
20 leçonsSetsRelations: equivalence relations and partial ordersFunctionsFunctions and cardinalityIntroduction to Number TheoryCryptographyCartesian productPower setBinary relationEquivalence relationPartial orderFunction (mathematics)Injective functionSurjective functionBijectionComposite functionInverse functionCardinal numberCountable setUncountable set -
Counting
16 leçonsCounting: rules, choices and bijectionsThe pigeonhole principleVoting MethodsFairness in Voting MethodsStandard Divisors, Standard Quotas, and the Apportionment ProblemApportionment MethodsFairness in Apportionment MethodsEnumerative combinatoricsPermutationCombinationBinomial coefficientPascal's trianglePigeonhole principleInclusion–exclusion principleBijective proofDouble counting (proof technique) -
Recursion and recurrence relations
7 leçons -
Graphs and trees
18 leçonsGraphs: degrees, paths and connectivityTrees and spanning treesEuler and Hamilton pathsGraph colouringGraph theoryGraph (discrete mathematics)Degree (graph theory)Path (graph theory)Cycle (graph theory)Connectivity (graph theory)Tree (graph theory)Spanning treeEulerian pathHamiltonian pathBipartite graphPlanar graphGraph coloringAdjacency matrix -
Boolean algebra and automata
7 leçons -
Algorithms and complexity
15 leçonsAlgorithms and growth of functionsAlgorithmRate of GrowthBig O notationAsymptotic analysis, recursion trees and the master theoremSorting algorithmComputational complexity theoryDecision problems, satisfiability and reductionsMath and ArtMath and the EnvironmentMath and MedicineMath and MusicMath and SportsComputability theoryHalting problem
L'examen final
Les réponses tapées sont marquées par le système algèbre; les épreuves et le travail photographié sont lus par un modèle; puis une personne passe en revue l'ensemble du papier avant que votre résultat soit publié. Passez et vous obtenez un certificat avec son propre lien. Marque de passage: 70%.
Ouverture de la sessionPrix
Passé
$39
Chaque quiz d'unité, l'examen final avec un reprise, et 20 vérifications de votre propre travail, pour un cours.
Achetez le passe de coursUn examen final
$15
Une seule séance de la finale d'un cours, marquée et revue. Pour quelqu'un qui connaît déjà le matériel et veut qu'il soit testé.
Acheter une finaleChaque cours
$19/Les
Tous les quizz et les finales de chaque cours (deux finales par cours par mois) et 100 contrôles de travail par mois. Annuler votre compte.
S'abonnerContrôles de travail
$9
Dix vérifications : téléchargez une photo de n'importe quel travail, ou tapez-la, et voyez où elle s'est mal passée.
Acheter dix chèques