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.
_Iň soňuna: Algebra
Kurs
-
Logic and proof
25 _ÖňkiWhat 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 _Öňki -
Sets, relations and functions
20 _ÖňkiSetsRelations: 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 _ÖňkiCounting: 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 _Öňki -
Graphs and trees
18 _ÖňkiGraphs: 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 _Öňki -
Algorithms and complexity
15 _ÖňkiAlgorithms 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
The final exam
Her bir bölümden soraglar, iň kynlary soňuna çenli. Ýazan jogaplar aljebra sistemasy tarapyndan nyşanlanýar; subutnama we surata alnan iş bir model tarapyndan okalýar; soňra bir adam siziň netijeňizi çap etmekden öň ähli kagyzy synlaýar. Geçiň we öz baglanyşygy bilen bir şahadatnama alyň. Geçir: 70%.
_GünPrices
Kursy geç
$39
Her bir bölüm soragy, bir tekrar bilen sonky synag, we 20 öz işiň barlagy, bir kurs üçin.
Kursy SaýlaBir soňky synag
$15
Bir kursyň soňky bir sessiýasy, nyşanlan we gözden geçirilmiş. Maddeyi örän gowy bilýän we ony synap görmek isleýän biri üçin.
Bir soñkyny satyn alHer bir kurs
$19/10 minut
Her kursda ähli soraglar we finallar (ýolda iki final) we aýda 100 iş barlaglary. Siziň hasabyňyzdan kes.
_GünIş barlaglary
$9
On barlag: her bir işleýäniň suratyny ýükle, ýa-da ony ýaz, we nädip hata düşendigini gör.
On çek satyn al