Course module

Discrete Mathematics — Bihar Polytechnic Lecturer (Computer Science)

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Lessons: 291
Duration: 20 hr
PYQs: 0
Practice: 482

Syllabus index

Lessons in this module

291 linked lessons

Permutation, Combination and Probability / क्रमचय, संचय एवं प्रायिकता

गणना के मूल सिद्धांत / Fundamental Principles of Counting

क्रमचय / Permutations

संचय एवं वस्तुओं का वितरण / Combinations and Distribution of Objects

कबूतरखाना सिद्धांत एवं समावेशन-अपवर्जन / Pigeonhole Principle and Inclusion–Exclusion

Set Theory

Sets, Representation of Sets and Hierarchy of numbers

Finite, Infinite, Countable, and Uncountable Sets

Null, Universal, Subsets, Proper Subsets

Power Set and its Cardinality

Set Operations – Union, Intersection, Set Difference, Symmetric Difference, and Complement

Relations

Cartesian Product, Relation, Inverse & Complement

Reflexive Irreflexive Relation – Count, and Properties

Symmetric Anti-Symmetric Asymmetric Relation and Properties

Transitive Relation – Definition, Count, and Properties

Equivalence Relation, Equivalence Classes, Partitions of a Set

Partial Order Relation – Properties, Partially Ordered Set (Poset), and Total Order Relation

Hasse Diagram, Greatest Element, Least Element, Upper Bound, Lower Bound

Lattice – Definition, Formation, and Examples of Join and Meet Operations

Bounded, Unbounded, Distributive, Complemented Lattices and Boolean Algebr

Functions

Definition of a Function – Domain, Co-domain, Range, and Count of Possible Functions

Composition of Functions – Definition, Properties, and Examples

One-to-One (Injective) Function – Definition, Count, and Properties

Onto (Surjective) Function – Definition, Count, and Properties

Bijective Function – Definition, Count, and Properties

Inverse of a Function – Definition, Existence Conditions, and Examples

Propositional and Predicate Logic

Introduction to Propositions, Laws of Contradiction and Excluded Middle

Types of Propositions – Atomic and Compound

Logical Operators – Negation, Conjunction, and Disjunction

Implication and Bi-Conditional Operators in Logic

Types of Logical Cases – Tautology, Contradiction, Contingency, Satisfiability, and Validity

Introduction to First Order Predicate Logic

Quantifiers – Universal and Existential

Graph Theory

Introduction to Graphs – Definitions, Terminology (Loops, Parallel Edges, Adjacent Vertices)

Types of Graphs – Finite, Infinite, Null, Trivial, Complete

Bipartite, Cycle, Regular, and Complement of a Graph

Number of Graphs – Counting of Simple, Undirected, Unlabeled

Degree of Vertex – Isolated and Pendant Vertices, Handshaking Lemma, and Degree Sequence

Minimum and Maximum Degree – Relationships, Degree Constraints, and Havel-Hakimi Theorem

Graph Traversal – Walk, Path, Trail, Circuit, and Connected Graphs

Euler and Hamiltonian Graphs – Definitions, Conditions, and Examples

Planar Graphs – Kuratowski’s Theorems, Homorphism and examples

Euler Formula – Planar Graph Formula, Applications, and Derived Relations

Graph Coloring – Vertex Coloring, Edge Coloring, Chromatic Number, and Coloring Theorems

Trees – Definitions, Properties, Eccentricity, Diameter, Radius, and Center

Spanning Tree and Spanning Forest – Definition, Construction, and Applications

Cut Set and Connectivity – Edge Connectivity, Vertex Connectivity, and Cut Set Concepts

Graph Isomorphism – Definition, Detection, and Problem Solving

Graph Matching – Maximal, Maximum, Perfect Matching, and Related Concepts

Graph Covering – Line and Vertex Covering, Independent Set, and Minimal/Maximal Variants

Lessons in this module

Permutation, Combination and Probability / क्रमचय, संचय एवं प्रायिकता

गणना के मूल सिद्धांत / Fundamental Principles of Counting

क्रमचय / Permutations

संचय एवं वस्तुओं का वितरण / Combinations and Distribution of Objects

कबूतरखाना सिद्धांत एवं समावेशन-अपवर्जन / Pigeonhole Principle and Inclusion–Exclusion

Set Theory

Sets, Representation of Sets and Hierarchy of numbers

Finite, Infinite, Countable, and Uncountable Sets

Null, Universal, Subsets, Proper Subsets

Power Set and its Cardinality

Set Operations – Union, Intersection, Set Difference, Symmetric Difference, and Complement

Relations

Cartesian Product, Relation, Inverse & Complement

Reflexive Irreflexive Relation – Count, and Properties

Symmetric Anti-Symmetric Asymmetric Relation and Properties

Transitive Relation – Definition, Count, and Properties

Equivalence Relation, Equivalence Classes, Partitions of a Set

Partial Order Relation – Properties, Partially Ordered Set (Poset), and Total Order Relation

Hasse Diagram, Greatest Element, Least Element, Upper Bound, Lower Bound

Lattice – Definition, Formation, and Examples of Join and Meet Operations

Bounded, Unbounded, Distributive, Complemented Lattices and Boolean Algebr

Functions

Definition of a Function – Domain, Co-domain, Range, and Count of Possible Functions

Composition of Functions – Definition, Properties, and Examples

One-to-One (Injective) Function – Definition, Count, and Properties

Onto (Surjective) Function – Definition, Count, and Properties

Bijective Function – Definition, Count, and Properties

Inverse of a Function – Definition, Existence Conditions, and Examples

Propositional and Predicate Logic

Introduction to Propositions, Laws of Contradiction and Excluded Middle

Types of Propositions – Atomic and Compound

Logical Operators – Negation, Conjunction, and Disjunction

Implication and Bi-Conditional Operators in Logic

Types of Logical Cases – Tautology, Contradiction, Contingency, Satisfiability, and Validity

Introduction to First Order Predicate Logic

Quantifiers – Universal and Existential

Graph Theory

Introduction to Graphs – Definitions, Terminology (Loops, Parallel Edges, Adjacent Vertices)

Types of Graphs – Finite, Infinite, Null, Trivial, Complete

Bipartite, Cycle, Regular, and Complement of a Graph

Number of Graphs – Counting of Simple, Undirected, Unlabeled

Degree of Vertex – Isolated and Pendant Vertices, Handshaking Lemma, and Degree Sequence

Minimum and Maximum Degree – Relationships, Degree Constraints, and Havel-Hakimi Theorem

Graph Traversal – Walk, Path, Trail, Circuit, and Connected Graphs

Euler and Hamiltonian Graphs – Definitions, Conditions, and Examples

Planar Graphs – Kuratowski’s Theorems, Homorphism and examples

Euler Formula – Planar Graph Formula, Applications, and Derived Relations

Graph Coloring – Vertex Coloring, Edge Coloring, Chromatic Number, and Coloring Theorems

Trees – Definitions, Properties, Eccentricity, Diameter, Radius, and Center

Spanning Tree and Spanning Forest – Definition, Construction, and Applications

Cut Set and Connectivity – Edge Connectivity, Vertex Connectivity, and Cut Set Concepts

Graph Isomorphism – Definition, Detection, and Problem Solving

Graph Matching – Maximal, Maximum, Perfect Matching, and Related Concepts

Graph Covering – Line and Vertex Covering, Independent Set, and Minimal/Maximal Variants

Group Theory

Closure-Algebraic Structure, Associative-SemiGroup, Identity-Monoid

Inverse Property and Group

Commutative Property and Abelian Groups

Classification of Finite and Infinite Groups

Subgroup Definition, Examples, and Verification Techniques

Determining the Order of Elements within Groups

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