Cursos · 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.
Viene después: Algebra
El curso
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Logic and proof
25 leccionesWhat 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 lecciones -
Sets, relations and functions
20 leccionesSetsRelations: 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 leccionesCounting: 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 lecciones -
Graphs and trees
18 leccionesGraphs: 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 lecciones -
Algorithms and complexity
15 leccionesAlgorithms 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
El examen final
Preguntas de cada unidad, las más difíciles último. Las respuestas escritas están marcadas por el sistema de álgebra; pruebas y fotografías de trabajo se leen por un modelo; a continuación, una persona revisa el documento completo antes de que su resultado se libera. Pase y obtendrá un certificado con su propio enlace. Marca de paso: 70%.
Iniciar sesiónPrecios
Pase de curso
$39
Cada examen de unidad, el examen final con una repetición, y 20 cheques de su propio trabajo, para un curso.
Comprar el pase de cursoUn examen final
$15
Una sola sesión de un curso final, marcado y revisado para alguien que ya conoce el material y quiere que se pruebe.
Comprar un finalCada curso
$19/mo
Todos los exámenes y finales en cada curso (dos finales por curso al mes) y 100 cheques de trabajo al mes. Cancele de su cuenta.
SuscribirseControles de trabajo
$9
Diez cheques: subir una foto de cualquier trabajo, o escribirlo, y ver dónde salió mal.
Comprar diez cheques