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Discrete Math for Computer Science - Logic & Set Theory · LearnSpace
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Discrete Math for Computer Science - Logic & Set Theory

Курс от The Hong Kong University of Science and Technology
Начальный≈ 9.4 чАнглийский
О курсеНавыкиПрограммаПреподаватели

О курсе

This course introduces the foundational concepts of discrete mathematics that are essential for computer science, with a focus on logic, formal reasoning, and set theory. Discrete mathematics studies structures that are non-continuous and symbolic, making it the natural mathematical language of computation. You will begin by learning propositional and predicate logic, developing the ability to translate natural-language statements into precise formal expressions. The course covers logical operators, equivalence, quantifiers, and rules of inference, providing the tools needed to construct and evaluate rigorous arguments and proofs. The course then introduces set theory and functions, which form the backbone of data modeling and abstraction in computer science. Topics include set operations, relations, functions, and cardinality, along with their close connections to logical reasoning. Emphasizing understanding and problem-solving over memorization, this course builds the mathematical maturity required for algorithm design, program correctness, and advanced topics in the specialization.

Навыки, которые вы освоите

Computational LogicDeductive ReasoningLogical ReasoningMathematics and Mathematical ModelingAlgorithmsComputer ScienceTheoretical Computer Science

Программа курса

5 модулей · 110 учебных материалов

01Introduction to Discrete Mathematics3 материалов
Introduction to Discrete MathematicsВидеоIntroduction to Discrete MathematicsЧтениеIntroduction to Discrete Math for Computer Science (Logic & Set Theory)Чтение
02Propositional Logic22 материалов

Учитесь у экспертов

Kenneth Wai-Ting Leung

Associate Professor of Engineering Education

Discrete Math for Computer Science - Logic & Set Theory
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Обучение на Coursera

≈ 9.4 ч

5 модулей

Язык: Английский

Часть программы вашего университета
Propositional LogicЧтение
Propositional logic OverviewВидео
L01-01 What is Logic?Видео
Propositions_ IntroВидео
(Optional) Propositions_ ExampleВидео
Compound Propositions_ IntroВидео
Compound Propositions_ Logical Operator and Truth TableВидео
Compound Propositions_ Conditional Statement and Biconditional Statement, Necessary and sufficient conditionsВидео
Compound Propositions_ Conditional Statement in Eng and ExampleВидео
Compound Propositions_ Converse, Inverse, ContrapositiveВидео
Compound Propositions_ Precedence of Logical OperatorsВидео
Propositional Equivalences_ Tautology and ContradictionВидео
Propositional Equivalences_ Logical EquivalenceВидео
(Optional) InclassExВидео
Propositional Equivalences_ The use of ≡,↔,=Видео
Propositional Equivalences_ De Morgan’s lawsВидео
(Optional) Propositional Equivalences_ Logical Equivalence Example1Видео
(Optional) Propositional Equivalences_ Logical Equivalence Example2Видео
(Optional) Propositional Equivalences_ Logical Equivalence Example3Видео
(Optional) Propositional Equivalences_ Logical Equivalence Example4Видео
Propositional Equivalences_ Revisit the Knight and Knave puzzleВидео
Quiz 1Задание
03Predicate Logic (First-order logic)25 материалов
Predicate-LogicЧтениеPredicate Logic OverviewВидеоPredicate Logic (First-order logic) - IntroВидеоPredicates_Definition & ExamplesВидеоQuantifiers_Universal Quantification & DomainВидео(Optional) Quantifiers_Example1ВидеоQuantifiers_Universal and Existential QuantifiersВидео(Optional) Quantifiers_Example2Видео(Optional) InclassExВидеоQuantifiers with Restricted domains_Restricted DomainsВидеоQuantifiers with Restricted Domains_ExplanationВидеоQuantifiers with Restricted Domains_Precedence of Quantifiers & Binding VariablesВидеоLogical Equivalences involving Quantifiers_Logical EquivalenceВидеоNegating Quantified Expressions_De Morgan's Laws for QuantifiersВидео(Optional) Negating Quantified Expressions_ExamplesВидеоNested Quantifiers_IntroВидеоNested Quantifiers_Order of QuantifiersВидеоNested Quantifiers_Quantifications of Two VariablesВидео(Optional) Nested Quantifiers_ExampleВидеоNested Quantifiers_Translating into EngВидеоNull Quantifications_IntroВидео(Optional) Null Quantifications_Example1Видео(Optional) Null Quantifications_Example2ВидеоFurther Example & Negating Nested QuantifiersВидеоQuiz 2Задание
04Inference30 материалов
InferenceЧтение🔴Inference OverviewВидеоInference IntroductionВидеоRules of Inference_IntroВидеоRules of Inference_ArgumentВидеоRules of Inference_Rules of Inference for Propositional LogicВидео(Optional) Rules of Inference_Rules of Inference for Propositional Logic_Example1 & 2Видео(Optional) Rules of Inference_Rules of Inference for Propositional Logic_Example3ВидеоRules of Inference_Rules of Inference for Propositional Logic_Invalid ArgumentВидеоRules of Inference_Rules of Inference for Predicate Logic_Intro & Example1Видео(Optional) Rules of Inference_Rules of Inference for Predicate Logic_Example2Видео(Optional) Rules of Inference_Rules of Inference for Predicate Logic_Example3ВидеоBasic Proof Techniques_Some Terminology_IntroВидеоBasic Proof Techniques_Some Terminology_AxiomaticВидеоBasic Proof Techniques_Some Terminology_Corollary & ConjectureВидео(Optional)Basic Proof Techniques_Direct Proof_Intro & Example1Видео(Optional) Basic Proof Techniques_Direct Proof_Example2 & 3ВидеоBasic Proof Techniques_Direct Proof_Limitation of Direct ProofsВидеоBasic Proof Techniques_Proof by ContrapositionВидео(Optional) Basic Proof Techniques_Proof by Contraposition_Example1Видео(Optional) Basic Proof Techniques_Proof by Contraposition_Example2ВидеоBasic Proof Techniques_Proof by ContradictionВидео(Optional) Basic Proof Techniques_Proof by Contradiction_Example1Видео(Optional) Basic Proof Techniques_Proof by Contradiction_Example2ВидеоBasic Proof Techniques_Proof by Contradiction_Proving Biconditional Statements & ExampleВидео(Optional) Basic Proof Techniques_Proof by Contradiction_Example3ВидеоSome comments on proofsВидеоTheorems and ProofsВидео(Optional) InclassExВидеоQuiz 3Задание
05Sets-Functions30 материалов
Sets-FunctionsЧтениеSets-Functions OverviewВидеоSets_Set & Set BuilderВидеоSets_Some Important SetsВидеоSets_Empty Set and Singleton SetВидеоSets_Set EqualityВидеоSets_SubsetВидеоSets_Proper Subset, Cardinality of Finite Sets & Power SetВидеоSets_Ordered TupleВидеоSets_Cartesian Product & RelationВидеоSets_Union & IntersectionВидеоSets_Union, Intersection, and CardinalityВидеоSets_Difference and ComplementВидеоSets_Set Identities and Logic EquivalencesВидеоFunctions_Function & ExamplesВидеоFunctions_Injective Function & Surjective FunctionВидеоFunctions_BijectionВидеоFunctions_Inverse Function & ExampleВидеоFunctions_Composition & ExampleВидео(Optional) InclassExВидеоCardinality of Sets_Hilbert’s Grand HotelВидеоCardinality of Sets_Cardinality of Infinite SetsВидео(Optional) Cardinality of Sets_Cardinality of Infinite Sets_ExampleВидеоCardinality of Sets_Q is countable & StringВидеоCardinality of Sets_R is uncountableВидеоCardinality of Sets_Compare infinite setsВидеоCardinality of Sets_The Contiuum Hypothesis & Schroder-Bernstein TheoremВидеоCardinality of Sets_S smaller than P(S)ВидеоCardinality of Sets_Uncomputable functionsВидеоQuiz 4Задание