Corsi · 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.
Viene dopo: Algebra
Il corso
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Logic and proof
25 lezioniWhat 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 lezioni -
Sets, relations and functions
20 lezioniSetsRelations: 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 lezioniCounting: 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 lezioni -
Graphs and trees
18 lezioniGraphs: 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 lezioni -
Algorithms and complexity
15 lezioniAlgorithms 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'esame finale
Domande da ogni unità, le più difficili ultime. Le risposte digitate sono contrassegnate dal sistema di algebra; le prove e il lavoro fotografato sono letti da un modello; poi una persona esamina l'intero foglio prima che il risultato viene rilasciato. Passare e si ottiene un certificato con il proprio link. Marchio di passaggio: 70%.
AccediPrezzi
Passo del corso
$39
Ogni quiz unitario, l'esame finale con un'unica ripresa, e 20 controlli del proprio lavoro, per un solo corso.
Acquista il pass del corsoUn esame finale
$15
Una seduta singola di un corso finale, marcata e recensita. Per qualcuno che già conosce il materiale e vuole che sia testato.
Acquista una finaleOgni corso
$19/mo
Tutti i quiz e le finali in ogni corso (due finali al mese) e 100 controlli di lavoro al mese. Annulla dal tuo account.
SottoscriviControlli di lavoro
$9
Dieci controlli: caricare una foto di qualsiasi lavoro, o digitarlo, e vedere dove è andato male.
Comprate dieci assegni