Masomo · College

Discrete Mathematics

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

8 ↓ 124 masomo 150 maswali 180 mwisho wa dakika

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.

Nyotamkia baada: Algebra

Mwendo

  1. Logic and proof

    25 masomo
    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)
    Ishara ya kutumia mtihani

  2. Induction and sequences

    11 masomo
    Sums and inductionProof by inductionProof by InductionStrong InductionStrong induction and the well-ordering principleDescribing SequencesPolynomial SequencesExponential SequencesChapter SummaryWell-orderPeano axioms
    Ishara ya kutumia mtihani

  3. Sets, relations and functions

    20 masomo
    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
    Ishara ya kutumia mtihani

  4. Counting

    16 masomo
    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)
    Ishara ya kutumia mtihani

  5. Recursion and recurrence relations

    7 masomo
    RecursionRecurrence relationSolving linear recurrence relationsGenerating FunctionsRecurrence relationGenerating functionCatalan number
    Ishara ya kutumia mtihani

  6. Graphs and trees

    18 masomo
    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
    Ishara ya kutumia mtihani

  7. Boolean algebra and automata

    7 masomo
    Binary numberBoolean algebraBoolean algebra and logic circuitsFormal languageAutomata theoryFinite automata and regular languagesTuring machine
    Ishara ya kutumia mtihani

  8. Algorithms and complexity

    15 masomo
    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
    Ishara ya kutumia mtihani

Mtihani wa mwisho

Questions from every unit, the hardest ones last. Typed answers are marked by the algebra system; proofs and photographed working are read by a model; then a person reviews the whole paper before your result is released. Pass and you get a certificate with its own link. Njia za kupita: 70%.

Ishara Katika

Bei

Mwendo unapita

$39

Kila tafiti, mtihani wa mwisho wenye kufanyiwa tena jambo moja, na uchunguzi 20 wa kazi yako mwenyewe, kwa mtaala mmoja.

Nunua mtihani

Mtihani mmoja wa mwisho

$15

Kiti kimoja cha mwisho cha mtaala mmoja, kilitia alama na kupitiwa.

Nunua kisehemu cha mwisho

Kila jambo

$19/mo

Kila mmoja huulizwa maswali na kumaliza katika kila mtaala (humaliza vipindi viwili kwa mwezi) na hundi 100 za kazi kwa mwezi.

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Uchunguzi wa kazi

$9

Uchunguzi kumi: Pakua picha ya mtu yeyote anayefanya kazi, au chora aina yake, uone mahali ilipoharibika.

Nunua hundi kumi

Chunguza kipande cha kazi yako mwenyewe