Kursi · College

Discrete Mathematics

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

8 %s: Mitir 124 Waxbarasho 150 su'aalo 180 daqiiqo

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.

Ka dib: Algebra

Kursiga

  1. Logic and proof

    25 Waxbarasho
    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)
    Ku soo gal si aad u qaadato imtixaankan

  2. Induction and sequences

    11 Waxbarasho
    Sums and inductionProof by inductionProof by InductionStrong InductionStrong induction and the well-ordering principleDescribing SequencesPolynomial SequencesExponential SequencesChapter SummaryWell-orderPeano axioms
    Ku soo gal si aad u qaadato imtixaankan

  3. Sets, relations and functions

    20 Waxbarasho
    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
    Ku soo gal si aad u qaadato imtixaankan

  4. Counting

    16 Waxbarasho
    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)
    Ku soo gal si aad u qaadato imtixaankan

  5. Recursion and recurrence relations

    7 Waxbarasho
    RecursionRecurrence relationSolving linear recurrence relationsGenerating FunctionsRecurrence relationGenerating functionCatalan number
    Ku soo gal si aad u qaadato imtixaankan

  6. Graphs and trees

    18 Waxbarasho
    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
    Ku soo gal si aad u qaadato imtixaankan

  7. Boolean algebra and automata

    7 Waxbarasho
    Binary numberBoolean algebraBoolean algebra and logic circuitsFormal languageAutomata theoryFinite automata and regular languagesTuring machine
    Ku soo gal si aad u qaadato imtixaankan

  8. Algorithms and complexity

    15 Waxbarasho
    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
    Ku soo gal si aad u qaadato imtixaankan

Imtixaankii ugu dambeeyay

Su'aalaha ka mid ah mid kasta oo ka mid ah, kuwa ugu adag ee ugu dambeeyay. jawaabaha la daabacay waxaa lagu calaamadeeyay nidaamka algebra; caddayn iyo sawirka shaqada waxaa akhriya qaab; markaas qof ayaa dib u eegista warbixinta oo dhan ka hor inta aad natiijooyinka la sii daayay. Calaamada ka gudubka: 70%.

Ku soo gal

Qiimaha

Kursi

$39

Mid kasta oo iskuulka, imtixaanka ugu dambeeyay oo leh mid ka mid ah inta kale, iyo 20 tijaabooyinka shaqadaada, si ay u mid ka mid ah.

Iibso fasalka

Imtixaan dhamaadka ah

$15

A fadhi kaliya ee dhamaadka mid ka mid ah fasalka, calaamadeeyay oo dib loo eego. Si qof ka horeeya u yaqaan waxyaabaha iyo doonista in ay la tijaabiyay.

Iibso mid dhamaadka ah

Kursi kasta

$19/mi

Dhammaan su'aalaha iyo finals in fasal kasta (laba finals fasal kasta bishii) iyo 100 shahaadooyinka shaqada bishii. Cancel ka xisaabtaada.

Ku biir

Shaqada baaritaan

$9

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