पाठ्यक्रम · 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.
पछि आउँछ: Algebra
पाठ्यक्रम
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Logic and proof
25 पाठWhat 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 पाठ -
Sets, relations and functions
20 पाठSetsRelations: 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 पाठCounting: 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 पाठ -
Graphs and trees
18 पाठGraphs: 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 पाठ -
Algorithms and complexity
15 पाठAlgorithms 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
अन्तिम परीक्षा
हरेक इकाई देखि प्रश्न, कठिन अन्तिम. टाइप जवाफ बीजगणित प्रणाली द्वारा चिन्ह लगाइएको छन्; प्रमाण र फोटोग्राफी काम एक मोडेल द्वारा पढ्न; त्यसपछि एक व्यक्ति आफ्नो परिणाम जारी अघि सम्पूर्ण कागज समीक्षा. पास र तपाईं आफ्नो लिङ्क संग प्रमाणपत्र प्राप्त. पास मार्कर: 70%.
लगइन गर्नुहोस्मूल्य
पाठ्यक्रम पास गर्नुहोस्
$39
हरेक इकाई क्विज, एक retake संग अन्तिम परीक्षा, र 20 आफ्नो काम को जाँच, एक पाठ्यक्रम लागि.
पाठ्यक्रम पास खरीद गर्नुहोस्एक अन्तिम परीक्षा
$15
एक पाठ्यक्रम अन्तिम को एकल बस्नु, चिन्ह र समीक्षा. पहिले नै सामाग्री थाहा र यो परीक्षण चाहन्छ जो को लागि.
एक अन्तिम खरीद गर्नुहोस्प्रत्येक पाठ्यक्रम
$19/मिनेट
हरेक पाठ्यक्रम मा सबै क्विज र फाइनल (महिना प्रति पाठ्यक्रम दुई फाइनल) र 100 काम एक महिना जाँच. आफ्नो खाताबाट रद्द.
सदस्यता लिनुहोस्कार्य जाँच
$9
दस जाँच: कुनै पनि काम फोटो अपलोड, वा यो टाइप, र यो गलत कहाँ गए देखेर।
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