Kursus · 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.
Datang setelah: Algebra
Kursus
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Logic and proof
25 pelajaranWhat 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 pelajaran -
Sets, relations and functions
20 pelajaranSetsRelations: 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 pelajaranCounting: 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 pelajaran -
Graphs and trees
18 pelajaranGraphs: 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 pelajaran -
Algorithms and complexity
15 pelajaranAlgorithms 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
Ujian akhir
Pertanyaan dari setiap unit, yang paling sulit terakhir. Ketik jawaban ditandai oleh sistem aljabar; bukti dan difoto bekerja adalah dibaca oleh model; maka seseorang meninjau seluruh kertas sebelum hasil Anda dirilis. Tanda lewat: 70%.
MasukHarga
Tentu saja lulus
$39
Setiap unit kuis, ujian akhir dengan satu tes ulang, dan 20 cek Anda sendiri bekerja, untuk satu kursus.
Beli saja lulusSatu ujian akhir
$15
Satu saja yang duduk di final, ditandai dan ditinjau, untuk seseorang yang sudah tahu materi dan ingin diuji.
Beli satu finalSetiap kursus
$19/mo
Semua kuis dan final dalam setiap kursus (dua final per kursus setiap bulan) dan 100 cek kerja sebulan. Batalkan dari akun Anda.
BerlanggananPemeriksaan kerja
$9
10 cek: mengunggah foto dari semua yang bekerja, atau mengetikkannya, dan melihat di mana letak kesalahannya.
Beli sepuluh cek