Courses · 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.
नंतर येते: Algebra
कोर्स
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Logic and proof
25 उपक्रमWhat 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 उपक्रम -
Sets, relations and functions
20 उपक्रमSetsRelations: 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 उपक्रमCounting: 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 उपक्रम -
Graphs and trees
18 उपक्रमGraphs: 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 उपक्रम -
Algorithms and complexity
15 उपक्रमAlgorithms 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
अंतिम परीक्षा
प्रत्येक विभागातील प्रश्न, सर्वात कठीण प्रश्न शेवटचे. टाइप केलेले उत्तरे बीजगणित प्रणालीने चिन्हांकित केली जातात; प्रमाणपत्रे व छायाचित्रे मॉडेलने वाचली जातात; मग तुमचे निकाल प्रकाशित करण्यापूर्वी एक व्यक्ती संपूर्ण कागदपत्राची तपासणी करते. यशस्वी झाल्यानंतर तुम्हाला स्वतःच्या लिंकसह प्रमाणपत्र मिळेल. पास मार्कर: 70%.
दाखलन कराकिंमत
कोर्स पास
$39
Every unit quiz, the final exam with one retake, and 20 checks of your own working, for one course.
कोर्स पास खरेदी कराएक अंतिम परीक्षा
$15
एक विषयाच्या अंतिम एकच सत्र, चिन्हांकित व पुनरावलोकन केले. ज्याला आधीपासूनच विषय माहीत आहे व त्याचा अभ्यास करायचा आहे त्याकरीता.
एक अंतिम खरेदी कराप्रत्येक पाठ्यक्रम
$19/तास
प्रत्येक विषयातील सर्व प्रश्नोत्तरे व अंतिम (माहीतीनुसार प्रत्येक महिन्यात दोन अंतिम) आणि महिन्यातील १०० कार्यरत चाचणी. तुमच्या खात्यापासून रद्द करा.
सब्सक्रिप्शनकार्यरत तपासणी
$9
10 चेक: कोणत्याही काम करणाऱ्याचे फोटो अपलोड करा, किंवा टाइप करा, आणि ते कुठे चुकीचे झाले ते बघा.
दहा चेक विकत घ्या