Kursi · College

Discrete Mathematics

Logic, proof, induction, relations, counting, recurrences, graphs, automata and complexity: the discrete maths of a first university course.

8 unit 124 mësime 150 pyetje 180 minuta

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.

Vijnë pas: Algebra

Kursi

  1. Logic and proof

    25 mësime
    What 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)
    Fillo seancën

  2. Induction and sequences

    11 mësime
    Sums and inductionProof by inductionProof by InductionStrong InductionStrong induction and the well-ordering principleDescribing SequencesPolynomial SequencesExponential SequencesChapter SummaryWell-orderPeano axioms
    Fillo seancën

  3. Sets, relations and functions

    20 mësime
    SetsRelations: equivalence relations and partial ordersFunctionsFunctions and cardinalityIntroduction to Number TheoryCryptographyCartesian productPower setBinary relationEquivalence relationPartial orderFunction (mathematics)Injective functionSurjective functionBijectionComposite functionInverse functionCardinal numberCountable setUncountable set
    Fillo seancën

  4. Counting

    16 mësime
    Counting: 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)
    Fillo seancën

  5. Recursion and recurrence relations

    7 mësime
    RecursionRecurrence relationSolving linear recurrence relationsGenerating FunctionsRecurrence relationGenerating functionCatalan number
    Fillo seancën

  6. Graphs and trees

    18 mësime
    Graphs: 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
    Fillo seancën

  7. Boolean algebra and automata

    7 mësime
    Binary numberBoolean algebraBoolean algebra and logic circuitsFormal languageAutomata theoryFinite automata and regular languagesTuring machine
    Fillo seancën

  8. Algorithms and complexity

    15 mësime
    Algorithms 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
    Fillo seancën

Prova e fundit.

Pyetja nga çdo njësi, më e vështira e fundit. Përgjigjet e shkruara shënohen nga sistemi algjebrik; provat dhe punët e fotografuara lexohen nga një model; pastaj një person e shqyrton të gjithë artikullin para se të lëshohet rezultati yt. E kalon dhe merr një çertifikatë me lidhjen e vet. Shënim i miratuar: 70%.

Futu

Çmime

Kursi

$39

Çdo pyetje, provimi përfundimtar me një riprovë dhe 20 kontrolle të punës tënde, për një kurs.

Bleni kursin

Një provim përfundimtar.

$15

Një sesion i vetëm i një kursi përfundimtar, i shënuar dhe i rishikuar për dikë që e di tashmë materialin dhe dëshiron ta provojë atë.

Ble një të fundit.

Çdo kurs

$19/Mb

Të gjitha provimet dhe finalet në çdo kurs (dy finale për kurs në muaj) dhe 100 kontrolle pune në muaj. Anullo nga llogaria jote.

Regjistrohu

Kontrolli i punës

$9

Dhjetë kontrolle: ngarko një foto të çdo gjëje që punon, ose shkruaje atë, dhe shiko se ku shkoi keq.

Ble dhjetë çek

Kontrollo një pjesë të punës tënde