Natuurlik · 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.
Kome na: Algebra
Die kursus
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Logic and proof
25 lesseWhat 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 lesse -
Sets, relations and functions
20 lesseSetsRelations: 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 lesseCounting: 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 lesse -
Graphs and trees
18 lesseGraphs: 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 lesse -
Algorithms and complexity
15 lesseAlgorithms 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
Die finale eksamen
Vrae van elke eenheid, die moeilikstes laaste. Getipe antwoorde word deur die algebra-stelsel aangedui; bewyse en gefotografeerde werk word deur 'n model gelees; dan hersien 'n persoon die hele papier voordat jou resultaat vrygestel word. Gee en jy kry' n sertifikaat met sy eie skakel. Herhaling merk: 70%.
Meld aanPryse
Natuurlik verby
$39
Elke eenheid vra, die finale eksamen met een herhaal en 20 tjeks van jou eie werk, vir een kursus.
Koop die kursus verbyEen finale eksamen
$15
Vir iemand wat reeds die materiaal ken en wil hê dat dit getoets moet word, is dit'n teken en hersiening.
Koop een finaleElke kursus
$19/mo
Alle vasvrae en finale in elke kursus (twee punte per kursus per maand) en 100 werkskontroles per maand. Kanselleer van jou rekening.
Teken inWerkskontroles
$9
Tien tjeks: Laai'n foto op van enige werk, of tik dit, en kyk waar dit verkeerd geloop het.
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