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Discrete Mathematics for Computer Science and Engineering · LearnSpace
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Discrete Mathematics for Computer Science and Engineering

Курс от Birla Institute of Technology & Science, Pilani
Начальный≈ 44.1 чАнглийский
О курсеНавыкиПрограммаПреподаватели

О курсе

Welcome to the Discrete Mathematics course, your gateway to mastering the mathematical foundations essential for modern computing and data science. Designed for aspiring software engineers, computer scientists, data analysts, and cryptographers, this course is ideal for undergraduate students, professionals looking to enhance their analytical skills, and anyone interested in the theoretical underpinnings of computer science. You'll dive into discrete mathematical structures crucial for data structures, algorithms, operating systems, and cryptography. Explore key topics such as sets, relations, functions, graphs, combinatorics, and formal mathematical proofs, equipping you with the logical reasoning and problem-solving skills needed for sophisticated computer science applications. Unlock your potential with structured learning techniques that enhance your analytical thinking. This course is perfect for those aiming to pursue careers in artificial intelligence, cybersecurity, software development, and data science. With engaging lectures and hands-on exercises, you'll master the principles of discrete mathematics and prepare yourself for advanced computing challenges. Gain the confidence to tackle complex mathematical concepts and apply them in practical scenarios, paving the way for a successful and fulfilling career in engineering, computer science, and data analysis.

Навыки, которые вы освоите

CryptographyTheoretical Computer ScienceAlgorithmsApplied MathematicsMathematics and Mathematical ModelingData Management

Программа курса

10 модулей · 392 учебных материалов

01Proof Methods34 материалов

Let's Get Started

About Discrete MathematicsВидеоCourse Overview & Critical InformationЧтение

Basics of Logic

Overview: Proof MethodsВидеоPropositions, Truth Tables, and ConnectivesВидео

Учитесь у экспертов

Venkatakrishnan Ramaswamy

Assistant Professor

Dr. N.L. Bhanu Murthy

Professor

Discrete Mathematics for Computer Science and Engineering
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Обучение на Coursera

≈ 44.1 ч

10 модулей

Язык: Английский

Часть программы вашего университета
Propositions, Truth Tables, and Connectives: Real-World AnalogyЧтение
Propositions, Truth Tables, and ConnectivesЗадание
Conditional, Converse, Contrapositive, and InverseВидео
Conditional, Converse, Contrapositive, and Inverse: Real-World Analogy Чтение
Conditional, Converse, Contrapositive, and InverseЗадание
Logical EquivalencesВидео
Logical EquivalencesЧтение
Logical EquivalencesЗадание
Predicates and QuantifiersВидео
Predicates and QuantifiersЧтение
Predicates and QuantifiersЗадание
Negating Quantified Expressions and Nested QuantifiersВидео
Negating Quantified Expressions and Nested QuantifiersЧтение
Negating Quantified Expressions and Nested QuantifiersЗадание
Rules of InferenceВидео
Rules of InferenceЧтение
Rules of InferenceЗадание

Proof Methods

Proof TerminologyВидеоProof Terminology: Real-World AnalogyЧтениеPractice Quiz: Proof TerminologyЗаданиеDirect ProofВидеоPractice Quiz: Direct ProofЗаданиеIndirect ProofВидеоPractice Quiz: Indirect ProofЗаданиеTrivial and Vacuous ProofВидеоPractice Quiz: Trivial and Vacuous ProofЗаданиеAdditional Readings: Proof MethodsЧтение

Summary and Assessment

Wrap-Up: Proof MethodsВидеоKnights, Knaves, and Logical ReasoningDIALOGUETest Yourself: Proof MethodsЗадание
02More Proof Methods, Sequences, and Summations40 материалов

More Proof Methods and Fallacies

More Proof Methods and Fallacies ВидеоProof by ContradictionВидеоProof by Contradiction: Real-World AnalogyЧтениеProof by ContradictionЗаданиеConstructive Existence ProofВидеоAdditional Readings: Constructive Existence ProofЧтениеPractice Quiz: Constructive Existence ProofЗаданиеNonconstructive Existence ProofВидеоAdditional Readings: Nonconstructive Existence ProofЧтениеPractice Quiz: Nonconstructive Existence ProofЗаданиеProof by CasesВидеоProof by Cases: Real-World AnalogyЧтениеProof by CasesЗаданиеCounterexamples and Common FallaciesВидеоAdditional Readings: Counterexamples and Common FallaciesЧтениеCounterexamples and Common FallaciesЗадание

Mathematical Induction

Introduction to InductionВидеоEssential Reading: Introduction to InductionЧтениеPractice Quiz: Introduction to InductionЗаданиеWriting Proofs Using Mathematical InductionВидеоWriting Proofs Using Mathematical Induction: Real-World AnalogyЧтениеPractice Quiz: Writing Proofs Using Mathematical InductionЗадание

Sequences and Summations

Introduction to Sequences and SummationsВидеоEssential Reading: Introduction to Sequences and SummationsЧтениеPractice Quiz: Introduction to Sequences and SummationsЗаданиеArithmetic and Harmonic ProgressionВидеоEssential Reading: Arithmetic and Harmonic ProgressionЧтениеPractice Quiz: Arithmetic and Harmonic ProgressionЗадание

Summary and Assessment

Wrap-Up: Proof Methods, Sequences, and SummationsВидеоProof Methods, Sequences, and SummationsЧтениеTest Yourself: Sequences and SummationsЗадание
03Sets and Functions47 материалов

Sets and Set Operations

Introduction to the ModuleВидеоFundamentals of Set TheoryВидеоEssential Reading: Fundamentals of Set TheoryЧтениеPractice Quiz: Fundamentals of Set TheoryЗаданиеSubsets and Equality of SetsВидеоEssential Reading: Subsets and Equality of SetsЧтениеPractice Quiz: Subsets and Equality of SetsЗаданиеNull Set and Power SetВидеоEssential Reading: Null Set and Power SetЧтениеPractice Quiz: Null Set and Power SetЗаданиеCardinality and Cartesian ProductsВидеоEssential Reading: Cardinality and Cartesian ProductsЧтениеPractice Quiz: Cardinality and Cartesian ProductsЗаданиеSet Operations: Part 1ВидеоEssential Reading: Set Operations: Part 1ЧтениеPractice Quiz: Set Operations: Part 1ЗаданиеSet Operations: Part 2ВидеоEssential Reading: Set Operations—Part 2ЧтениеPractice Quiz: Set Operations: Part 2ЗаданиеSet Identities: Part 1ВидеоEssential Reading: Set Identities—Part 1ЧтениеPractice Quiz: Set Identities: Part 1ЗаданиеSet Identities: Part 2ВидеоEssential Reading: Set Identities—Part 2ЧтениеPractice Quiz: Set Identities: Part 2ЗаданиеComputer Representation of SetsВидеоEssential Reading: Computer Representation of SetsЧтениеPractice Quiz: Computer Representation of SetsЗадание

Functions

Introduction to FunctionsВидеоEssential Reading: Introduction to FunctionsЧтениеPractice Quiz: Introduction to FunctionsЗаданиеFloor and Ceil FunctionsВидеоEssential Reading: Floor and Ceil FunctionsЧтениеPractice Quiz: Floor and Ceil FunctionsЗадание

Summary

Module Wrap-Up: Sets and FunctionsВидео
04 Relations and Countable Sets45 материалов

Countable and Uncountable Sets

Introduction to Countable Sets ВидеоEssential Reading: Introduction to Countable SetsЧтениеPractice Quiz: Introduction to Countable Sets ЗаданиеUncountable SetsВидеоEssential Reading: Uncountable SetsЧтениеPractice Quiz: Uncountable SetsЗаданиеCountability of Sets: ExamplesВидеоEssential Reading: Countability of Sets: ExamplesЧтениеPractice Quiz: Countability of Sets: ExamplesЗадание

Relations and Their Properties

Introduction to RelationsВидеоEssential Reading: Introduction to RelationsЧтениеPractice Quiz: Introduction to RelationsЗаданиеInverse and Complementary RelationsВидеоEssential Reading: Inverse and Complementary RelationsЧтениеPractice Quiz: Inverse and Complementary RelationsЗадание

Summary and Assessment

Module Wrap-Up: Relations and Countable SetsВидеоStudy Guide for QuizzesЧтениеTest Yourself: Sets, Functions, and RelationsЗадание
05Equivalence and Partial Ordered Relations 44 материалов

Equivalence Relations

Introduction to Equivalence RelationsВидеоIntroduction to Equivalence RelationsЧтениеPractice Quiz: Introduction to Equivalence RelationsЗаданиеExamples of Equivalence RelationsВидеоExamples of Equivalence RelationsЧтениеPractice Quiz: Examples of Equivalence RelationsЗаданиеPartitions of a SetВидеоPartitions of a SetЧтениеPractice Quiz: Partitions of a SetЗаданиеEquivalent Classes and Partitions: Part 1ВидеоEquivalent Classes and Partitions: Part 1ЧтениеPractice Quiz: Equivalent Classes and Partitions: Part 1ЗаданиеEquivalent Classes and Partitions: Part 2ВидеоEquivalent Classes and Partitions: Part 2ЧтениеPractice Quiz: Equivalent Classes and Partitions: Part 2ЗаданиеEquivalent Classes and Partitions: Part 3ВидеоEquivalent Classes and Partitions: Part 3ЧтениеPractice Quiz: Equivalent Classes and Partitions: Part 3ЗаданиеEquivalence Relation for Partition of a SetВидеоEquivalence Relation for Partition of a SetЧтениеPractice Quiz: Equivalence Relation for Partition of a SetЗадание

Partial Orderings

Introduction to Partial Order RelationsВидеоIntroduction to Partial Order RelationsЧтениеPractice Quiz: Introduction to Partial Order RelationsЗаданиеTotally Ordered SetsВидеоTotally Ordered SetsЧтениеPractice Quiz: Totally Ordered SetsЗадание

Summary and Assessment

Module Wrap-Up Video: Equivalence and Partial Ordered RelationsВидеоTest Yourself: Equivalence and Partial Ordered RelationsЗадание
06Counting Techniques45 материалов

Basics of Counting

Introduction to Combinatorics and CountingВидеоIntroduction to Combinatorics and CountingЧтениеPractice Quiz: Introduction to Combinatorics and CountingЗаданиеThe Extended Product Rule ВидеоThe Extended Product Rule ЧтениеPractice Quiz: The Extended Product Rule ЗаданиеCounting Subsets of a Finite Set ВидеоCounting Subsets of a Finite Set ЧтениеPractice Quiz: Counting Subsets of a Finite Set ЗаданиеThe Sum RuleВидеоThe Sum RuleЧтениеPractice Quiz: The Sum RuleЗаданиеThe Sum and Product Rule: An ExampleВидеоThe Sum and Product Rule: An ExampleЧтениеPractice Quiz: The Sum and Product Rule: An ExampleЗаданиеThe Inclusion-Exclusion PrincipleВидеоThe Inclusion-Exclusion PrincipleЧтениеPractice Quiz: The Inclusion-Exclusion PrincipleЗадание

The Pigeonhole Principle, Permutations, and Combinations

The Pigeonhole Principle: Part 1ВидеоThe Pigeonhole Principle: Part 1ЧтениеPractice Quiz: The Pigeonhole Principle: Part 1ЗаданиеThe Pigeonhole Principle: Part 2ВидеоThe Pigeonhole Principle: Part 2ЧтениеPractice Quiz: The Pigeonhole Principle: Part 2Задание

Summary and Assessment

Module Wrap-Up Video: Counting TechniquesВидеоStudy Guide for QuizzesЧтениеTest Yourself: Counting TechniquesЗадание
07Recursive Functions and Recurrence Relations43 материалов

Recursive Definitions and Structural Induction

Introduction to Recursive DefinitionsВидеоIntroduction to Recursive DefinitionsЧтениеPractice Quiz: Introduction to Recursive DefinitionsЗаданиеRecursively Defined Functions: Part 1ВидеоRecursively Defined Functions: Part 1ЧтениеPractice Quiz: Recursively Defined Functions: Part 1ЗаданиеRecursively Defined Functions: Part 2ВидеоRecursively Defined Functions: Part 2ЧтениеPractice Quiz: Recursively Defined Functions: Part 2ЗаданиеRecursively Defined SetsВидеоRecursively Defined SetsЧтениеPractice Quiz: Recursively Defined SetsЗаданиеStructural InductionВидеоStructural InductionЧтениеPractice Quiz: Structural InductionЗаданиеExamples of Proofs Using Structural Induction: Part 1ВидеоExamples of Proofs Using Structural Induction: Part 1ЧтениеPractice Quiz: Examples of Proofs Using Structural Induction: Part 1ЗаданиеExamples of Proofs Using Structural Induction: Part 2ВидеоExamples of Proofs Using Structural Induction: Part 2ЧтениеPractice Quiz: Examples of Proofs Using Structural Induction: Part 2Задание

Recurrence Relations

Introduction to Recurrence RelationsВидеоIntroduction to Recurrence RelationsЧтениеPractice Quiz: Introduction to Recurrence RelationsЗаданиеExamples of Recurrence Relations: Part 1ВидеоExamples of Recurrence Relations: Part 1ЧтениеPractice Quiz: Examples of Recurrence Relations: Part 1 Задание

Summary

Module Wrap–Up: Recursive Functions and Recurrence RelationsВидео
08Introduction to Graphs36 материалов

Graphs and Their Computer Representations

Introduction to Modeling Real-World Settings with GraphsВидеоIntroduction to Modeling Real-World Settings with GraphsЧтениеPractice Quiz: Introduction to Modeling Real-World Settings with GraphsЗаданиеDefinitions of GraphsВидеоDefinitions of GraphsЧтениеPractice Quiz: Definitions of GraphsЗаданиеUndirected Graphs TerminologyВидеоUndirected Graphs TerminologyЧтениеPractice Quiz: Undirected Graphs TerminologyЗаданиеDirected Graphs TerminologyВидеоDirected Graphs TerminologyЧтениеPractice Quiz: Directed Graphs TerminologyЗаданиеSubgraphsВидеоSubgraphsЧтениеPractice Quiz: SubgraphsЗаданиеRepresenting Graphs: Adjacency ListsВидеоRepresenting Graphs: Adjacency ListsЧтениеPractice Quiz: Representing Graphs: Adjacency ListsЗаданиеRepresenting Graphs: Adjacency Matrices and Incidence Matrices ВидеоRepresenting Graphs: Adjacency Matrices and Incidence Matrices ЧтениеPractice Quiz: Representing Graphs: Adjacency Matrices and Incidence Matrices ЗаданиеSome Special Simple Graphs ВидеоSome Special Simple Graphs ЧтениеPractice Quiz: Some Special Simple Graphs Задание

Bipartite Graphs and Graph Isomorphism

Bipartite GraphsВидеоBipartite GraphsЧтениеPractice Quiz: Bipartite GraphsЗаданиеMatchingsВидеоMatchingsЧтениеPractice Quiz: MatchingsЗаданиеIsomorphism of Graphs

Summary and Assessment

Module Wrap–Up: Introduction to GraphsВидеоStudy Guide for QuizzesЧтениеTest Yourself: Recursive Functions, Recurrence Relations and Graph TheoryЗадание
09Advanced Topics on Graphs, Paths, and Connectivity22 материалов

Connectivity, Euler, and Hamilton Graphs

Basics of Graph Connectivity: Paths, Cycles, and Simple PathsВидеоBasics of Graph Connectivity: Paths, Cycles, and Simple PathsЧтениеPractice Quiz: Basics of Graph Connectivity: Paths, Cycles, and Simple PathsЗаданиеConnectedness in Undirected GraphsВидеоConnectedness in Undirected GraphsЧтениеPractice Quiz: Connectedness in Undirected GraphsЗаданиеConnectedness in Directed GraphsВидеоConnectedness in Directed GraphsЧтениеPractice Quiz: Connectedness in Directed GraphsЗаданиеEuler Paths and CircuitsВидеоEuler Paths and CircuitsЧтениеPractice Quiz: Euler Paths and CircuitsЗаданиеHamilton Paths and CircuitsВидеоHamilton Paths and CircuitsЧтениеPractice Quiz: Hamilton Paths and CircuitsЗадание

Planar Graphs and Graph Coloring

Planar Graphs and Euler’s FormulaВидеоPlanar Graphs and Euler’s FormulaЧтениеPractice Quiz: Planar Graphs and Euler’s FormulaЗаданиеGraph ColoringВидеоGraph ColoringЧтениеPractice Quiz: Graph ColoringЗадание

Summary

Module Wrap–Up: Advanced Topics on Graphs, Paths, and Connectivity Видео
10Trees and Basic Algebraic Structures36 материалов

Trees and Spanning Trees

Modeling Real-World Settings as Trees​ ВидеоAdditional Readings: Modelling Real-World Settings as TreesЧтениеPractice Quiz: Modeling Real-World Settings as Trees​ЗаданиеTrees and Rooted TreesВидеоEssential Reading: Trees and Rooted TreesЧтениеPractice Quiz: Trees and Rooted TreesЗаданиеProperties of TreesВидеоEssential Reading: Properties of TreesЧтениеPractice Quiz: Properties of TreesЗаданиеSpanning TreesВидеоEssential Reading: Spanning TreesЧтениеPractice Quiz: Spanning TreesЗаданиеFinding Minimum Spanning Trees with Prim's AlgorithmВидеоEssential Reading: Finding Minimum Spanning Trees with Prim's AlgorithmЧтениеPractice Quiz: Finding Minimum Spanning Trees with Prim's AlgorithmЗаданиеFinding Minimum Spanning Trees with Kruskal's AlgorithmВидеоEssential Reading: Finding Minimum Spanning Trees with Kruskal’s AlgorithmЧтениеPractice Quiz: Finding Minimum Spanning Trees with Kruskal's AlgorithmЗадание

Basic Algebraic Structures

Abstraction and Abstract AlgebraВидеоEssential Reading: Abstraction and Abstract AlgebraЧтениеPractice Quiz: Abstraction and Abstract AlgebraЗаданиеSemi-Groups and MonoidsВидеоEssential Reading: Semi-Groups and MonoidsЧтениеPractice Quiz: Semi-Groups and MonoidsЗадание

Summary and Assessment

Wrap–Up: Trees and Basic Algebraic StructuresВидеоGraphs, Trees and Algebraic StructuresЧтениеTest Yourself: Graphs, Trees and Algebraic StructuresЗадание
Strong InductionВидео
Essential Reading: Strong InductionЧтение
Practice Quiz: Strong InductionЗадание
Writing Proofs Using Strong InductionВидео
Essential Reading: Writing Proofs Using Strong InductionЧтение
Practice Quiz: Writing Proofs Using Strong InductionЗадание
Geometric ProgressionВидео
Essential Reading: Geometric ProgressionЧтение
Practice Quiz: Geometric ProgressionЗадание
Injective and Surjective FunctionsВидео
Essential Reading: Injective and Surjective FunctionsЧтение
Practice Quiz: Injective and Surjective FunctionsЗадание
Bijective FunctionsВидео
Essential Reading: Bijective FunctionsЧтение
Practice Quiz: Bijective FunctionsЗадание
Function Operators: Part 1Видео
Essential Reading: Function Operators—Part 1Чтение
Practice Quiz: Function Operators: Part 1Задание
Function Operators: Part 2Видео
Essential Reading: Function Operators—Part 2Чтение
Practice Quiz: Function Operators: Part 2Задание
Properties of Relations: Part 1Видео
Essential Reading: Properties of Relations: Part 1Чтение
Practice Quiz: Properties of Relations: Part 1Задание
Properties of Relations: Part 2Видео
Essential Reading: Properties of Relations: Part 2Чтение
Practice Quiz: Properties of Relations: Part 2Задание
Composite RelationsВидео
Essential Reading: Composite RelationsЧтение
Practice Quiz: Composite RelationsЗадание
n-ary RelationsВидео
Essential Reading: n-ary RelationsЧтение
Practice Quiz: n-ary RelationsЗадание
Representation of RelationsВидео
Essential Reading: Representations of RelationsЧтение
Practice Quiz: Representation of RelationsЗадание
Closure of RelationsВидео
Essential Reading: Closure of RelationsЧтение
Practice Quiz: Closure of RelationsЗадание
Applications of Relations: Part 1Видео
Essential Reading: Application of Relations: Part 1Чтение
Practice Quiz: Applications of Relations: Part 1Задание
Applications of Relations: Part 2Видео
Essential Reading: Application of Relations: Part 2Чтение
Practice Quiz: Applications of Relations: Part 2Задание
Applications of Relations: Part 3Видео
Essential Reading: Application of Relations: Part 3Чтение
Practice Quiz: Applications of Relations: Part 3Задание
Hasse DiagramВидео
Hasse DiagramЧтение
Practice Quiz: Hasse DiagramЗадание
Maximal and Minimal ElementsВидео
Maximal and Minimal ElementsЧтение
Practice Quiz: Maximal and Minimal ElementsЗадание
Upper and Lower Bounds: Part 1Видео
Upper and Lower Bounds: Part 1Чтение
Practice Quiz: Upper and Lower Bounds: Part 1Задание
Upper and Lower Bounds: Part 2Видео
Upper and Lower Bounds: Part 2Чтение
Practice Quiz: Upper and Lower Bounds: Part 2Задание
LatticeВидео
LatticeЧтение
Practice Quiz: LatticeЗадание
Generalized Pigeonhole Principle: Part 1Видео
Generalized Pigeonhole Principle: Part 1Чтение
Practice Quiz: Generalized Pigeonhole Principle: Part 1Задание
Generalized Pigeonhole Principle: Part 2Видео
Generalized Pigeonhole Principle: Part 2Чтение
Practice Quiz: Generalized Pigeonhole Principle: Part 2Задание
Permutations: Part 1Видео
Permutations: Part 1Чтение
Practice Quiz: Permutations: Part 1Задание
Permutations: Part 2Видео
Permutations: Part 2Чтение
Practice Quiz: Permutations: Part 2Задание
Combinations: Part 1Видео
Combinations: Part 1Чтение
Practice Quiz: Combinations: Part 1Задание
Combinations: Part 2Видео
Combinations: Part 2Чтение
Practice Quiz: Combinations: Part 2Задание
Examples of Recurrence Relations: Part 2Видео
Examples of Recurrence Relations: Part 2Чтение
Practice Quiz: Examples of Recurrence Relations: Part 2Задание
Examples of Recurrence Relations: Part 3Видео
Examples of Recurrence Relations: Part 3Чтение
Practice Quiz: Examples of Recurrence Relations: Part 3 Задание
Linear Recurrence RelationsВидео
Linear Recurrence RelationsЧтение
Practice Quiz: Linear Recurrence RelationsЗадание
Solving Linear Recurrence Relations: Part 1Видео
Solving Linear Recurrence Relations: Part 1Чтение
Practice Quiz: Solving Linear Recurrence Relations: Part 1Задание
Solving Linear Recurrence Relations: Part 2Видео
Solving Linear Recurrence Relations: Part 2Чтение
Practice Quiz: Solving Linear Recurrence Relations: Part 2Задание
Видео
Isomorphism of GraphsЧтение
Practice Quiz: Isomorphism of GraphsЗадание
GroupsВидео
Essential Reading: GroupsЧтение
Practice Quiz: GroupsЗадание
SubgroupsВидео
Essential Reading: SubgroupsЧтение
Practice Quiz: SubgroupsЗадание
RingsВидео
Essential Reading: RingsЧтение
Practice Quiz: RingsЗадание