Seha-pianarana · 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.
Mitranga aorian'ny: Algebra
Ny fianarana
-
Logic and proof
25 FianaranaWhat 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 Fianarana -
Sets, relations and functions
20 FianaranaSetsRelations: 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 FianaranaCounting: 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 Fianarana -
Graphs and trees
18 FianaranaGraphs: 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 Fianarana -
Algorithms and complexity
15 FianaranaAlgorithms 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
Ny fanadinana farany
Fanontaniana avy amin'ny kilasy tsirairay, ny sarotra indrindra no farany. Voamarika amin'ny rafitra algebra ny valinteny voasoratra; vakian'ny modely ny porofo sy ny asa nalaina sary; avy eo misy olona iray mijery ny lahatsoratry ny taratasy manontolo alohan'ny hamoahana ny vokatry ny asa. Lasa ianao ary mahazo fankatoavana miaraka amin'ny rohy manokana. Famantarana ny fankatoavana: 70%.
HiditraHaben'ny vidiny
Fidirana amin'ny seha-pianarana
$39
Ny fanontaniana isaky ny vondrona, ny fanadinana farany miaraka amin'ny fanadinana iray indray, ary ny 20 fitsapana ny asa ataonao, ho an'ny fianarana iray.
Mividy ny fidirana amin'ny sekolyFitsapana farany iray
$15
Fihaonana tokana amin'ny faran'ny fianarana iray, nanamarika sy nijery indray. Ho an'ny olona efa mahalala ny fitaovana ary te-hanandrana azy.
Mividy iray faranyNy kilasy rehetra
$19/mo
Ny fanontaniana rehetra sy ny fihodinana farany amin'ny kilasy tsirairay (fihodinana roa isan-kilasy isam-bolana) ary ny fitsapana 100 isan-bolana. Fafao amin'ny kaontinao.
MankasitrakaFitsapana asa
$9
Fanaraha-maso folo: mandefa sary ny zavatra miasa, na manoratra azy, ary jereo izay tsy nety.
Mividy taratasy folo