Course module

समुच्चय, रैखिक और अमूर्त बीजगणित / Sets, Linear and Abstract Algebra — UPESSC PGT (प्रवक्ता) Mathematics 2026

Sets-relations-functions, matrices और vector spaces; group theory Discrete Mathematics में, rings-fields-modules Abstract Algebra में; उच्च समीकरण अलग home में। / Set foundations, linear algebra, groups, rings, fields and theory of equations.

Explore the module outline and lessons below. Enroll free to begin studying here.

Return to /learn/UPESSC-PGT-2026-MATHEMATICS/math-algebra after enrolling
Lessons
71
Duration
—
PYQs
0
Practice
224

Syllabus index

Lessons in this module

Set Theory

Sets, Representation of Sets and Hierarchy of numbers

  1. Sets, Representation of Sets and Hierarchy of numbersPdf

Finite, Infinite, Countable, and Uncountable Sets

  1. Finite, Infinite, Countable, and Uncountable SetsPdf

Null, Universal, Subsets, Proper Subsets

  1. Null, Universal, Subsets, Proper SubsetsPdf

Power Set and its Cardinality

  1. Power Set and its CardinalityPdf

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

  1. Set Operations – Union, Intersection, Set Difference, Symmetric Difference, and ComplementPdf

Relations

Cartesian Product, Relation, Inverse & Complement

  1. Cartesian Product, Relation, Inverse & ComplementPdf

Reflexive Irreflexive Relation – Count, and Properties

  1. Reflexive Irreflexive Relation – Count, and PropertiesPdf

Symmetric Anti-Symmetric Asymmetric Relation and Properties

  1. Symmetric Anti-Symmetric Asymmetric Relation and PropertiesPdf

Transitive Relation – Definition, Count, and Properties

  1. Transitive Relation – Definition, Count, and PropertiesPdf

Equivalence Relation, Equivalence Classes, Partitions of a Set

  1. Equivalence Relation, Equivalence Classes, Partitions of a SetPdf

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

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

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

  1. Hasse Diagram, Greatest Element, Least Element, Upper Bound, Lower BoundPdf

Functions

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

  1. Definition of a Function – Domain, Co-domain, Range, and Count of Possible FunctionsPdf

Composition of Functions – Definition, Properties, and Examples

  1. Composition of Functions – Definition, Properties, and ExamplesPdf

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

  1. One-to-One (Injective) Function – Definition, Count, and PropertiesPdf

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

  1. Onto (Surjective) Function – Definition, Count, and PropertiesPdf

Bijective Function – Definition, Count, and Properties

  1. Bijective Function – Definition, Count, and PropertiesPdf

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

  1. Inverse of a Function – Definition, Existence Conditions, and ExamplesPdf

Algebra

Factorization & Simplification

  1. [Notes] Some Example QuestionsPdf

Linear Algebra

Matrix Addition and Multiplication

  1. [Notes] Matrix Addition & MultiplicationPdf

Elementary Row and Column Operations

  1. [Notes] Elementary Row & Column OperationsPdf

Group Theory

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

  1. Closure-Algebraic Structure, Associative-SemiGroup, Identity-MonoidPdf

Inverse Property and Group

  1. Inverse Property and GroupPdf

Commutative Property and Abelian Groups

  1. Commutative Property and Abelian GroupsPdf

Classification of Finite and Infinite Groups

  1. Classification of Finite and Infinite GroupsPdf

Explore the course

Next moduleअनुक्रम, श्रेणी और वास्तविक विश्लेषण / Sequences, Series and Real Analysis
View course details
Loading lesson…