Course module

Paper 2 | Discrete Mathematical StructureMPPSC Assistant Professor Computer Science Paper 2 2026

Lessons: 216
Duration: 17 hr 33 min
PYQs: 298
Practice: 1309

12% of this course's PYQ weight is covered in this module.

Syllabus index

Lessons in this module

216 linked lessons

Digital Systems & Boolean Basics

Digital Fundamentals & Boolean Algebra

Boolean Expression

Boolean Minimization

K-Map Structure & PIs

Function Equivalence

Logic Circuit Analysis

Adv. Laws & Optimization

Set Theory

Sets, Representation of Sets and Hierarchy of numbers

Finite, Infinite, Countable, and Uncountable Sets

Finite, Infinite, Countable, Uncountable SetDrm Video

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

Equivalence RelationDrm Video

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

Partial Order RelationDrm Video

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

Compostion of FunctionsDrm Video

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

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

Bijective Function – Definition, Count, and Properties

Bijective FunctionDrm Video

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

Inverse of a FunctionDrm Video

Graph Theory

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

Basic Terminology of GraphDrm Video

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

Connected GraphDrm Video

Euler and Hamiltonian Graphs – Definitions, Conditions, and Examples

Planar Graphs – Kuratowski’s Theorems, Homorphism and examples

Planner GraphDrm Video

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

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

Propositional and Predicate Logic

Introduction to Propositions, Laws of Contradiction and Excluded Middle

Types of Propositions – Atomic and Compound

Compound PropositionDrm Video

Logical Operators – Negation, Conjunction, and Disjunction

Implication and Bi-Conditional Operators in Logic

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

Type of casesDrm Video

Introduction to First Order Predicate Logic

First order Predicate LogicDrm Video

Quantifiers – Universal and Existential

Practice Problems on Quantifiers and Predicate Logic

Practice QuestionsDrm Video

Functional Completeness

Functionality Complete SetDrm Video

Questions and Practice Problems on Propositions

Proposition Questions notesPdf

Multi-Topic Content (Cross-Concept Material)

Gate 1992Drm Video

Probability

Basic Concepts and Terminology

Classical Problems (Cards, Dice, Coins, Digits, Number, Objects)

Probability Using Venn Diagrams & Set Theory

Module lessons

Lessons

MPPSC-Unit Test-Discrete Mathematical StructureTest

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