Maphunziro · 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.
Koma pambuyo: Algebra
Mfundo
-
Logic and proof
25 MaphunziroWhat 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 Maphunziro -
Sets, relations and functions
20 MaphunziroSetsRelations: 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 MaphunziroCounting: 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 Maphunziro -
Graphs and trees
18 MaphunziroGraphs: 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 Maphunziro -
Algorithms and complexity
15 MaphunziroAlgorithms 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
Mafunso a m’gulu lililonse, ovuta kwambiri ndi omwe amamaliza. Mafunso olemba amadziwika ndi dongosolo la algebra; zitsimikiziro ndi ntchito zojambula zithunzi zimawerengedwa ndi model; kenako munthu amafufuza nkhani yonseyo m’mbuyomu kuti zotsatira zanu zituluke. Kusintha: 70%.
KulowaMitengo
Course pass
$39
M’chilankhulo chilichonse pali mafunso a unit, chiyeso cha finali ndi mfundo imodzi yopitanso, ndi 20 zoyeserera za ntchito yanu, kwa m’chilankhulo chimodzi.
Gulani kuphunzira kwa kuphunziraOne final exam
$15
Kukhala ndi nthawi yokha ya kumaliza kwa phunziro limodzi, kumarked ndi kufufuzidwa. Kwa munthu amene kale amadziwa zinthuzo ndipo akufuna kuti ayesedwe.
Gulani imodzi yachiwiriMfundo zonse
$19/mphindi
Zomwe zimachitika pazokambirana zonse ndi zomaliza pazokambirana zonse (zomaliza ziwiri pazokambirana mwezi uliwonse) ndi 100 zoyeserera zogwira ntchito mwezi uliwonse.
KulembetsaKugwira ntchito zoyeserera
$9
Kuyesa kwa makumi asanu: kutsitsa chithunzi cha ntchito iliyonse, kapena kuyika, ndikuwona komwe kunali koipa.
Gulani ma cheque asanu