Kurslar · 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.
Sonra gəlir: Algebra
Kurs
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Logic and proof
25 dərsWhat 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 dərs -
Sets, relations and functions
20 dərsSetsRelations: 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 dərsCounting: 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 dərs -
Graphs and trees
18 dərsGraphs: 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 dərs -
Algorithms and complexity
15 dərsAlgorithms 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
Son imtahan
Hər bir bölmədən suallar, ən çətinləri sonuncudur. Yazılmış cavablar algebra sistemi ilə işarələnir; sübutlar və fotoşəkillər model tərəfindən oxunur; sonra nəticənizin açıqlanmasından əvvəl bir şəxs bütün əsəri nəzərdən keçirir. Keçirsənsə öz bağlantısı olan sertifikat alırsınız. Pass mark: 70%.
GirişQiymətlər
Kurs keç
$39
Hər bir bölmə test, bir təkrarla son imtahan və 20 öz işinizin yoxlaması, bir kurs üçün.
Kursu satın alSonuncu imtahan
$15
Bir kursun sonuncu tək seansı, qeyd edilmiş və araşdırılmış. Materialı artıq bilən və onu test etmək istəyənlər üçün.
Bir final satın alHər kurs
$19/%s (%s)%s
Hər kursda bütün testlər və finallar (hər kursda ayda iki final) və ayda 100 iş yoxlaması. Hesabınızdan ləğv et.
Subscribeİşlədiyim yoxlamalar
$9
On yoxlama: hər hansı bir işləyən şəkli yükləyin, ya da onu yazın və harada səhv getdiyini görün.
On çekə al