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NOC:Introduction to Abstract and Linear Algebra
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NOC:Introduction to Abstract and Linear Algebra
by Prof Sourav Mukhopadhyay

In algebra, which is a broad division of mathematics, abstract algebra (occasionally called modern algebra) is the study of algebraic structures. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras. The term abstract algebra was coined in the early 20th century to distinguish this area of study from th...

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About This Course

In algebra, which is a broad division of mathematics, abstract algebra (occasionally called modern algebra) is the study of algebraic structures. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras. The term abstract algebra was coined in the early 20th century to distinguish this area of study from th...

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Course Curriculum
8 Sections | 40 Lecture | 19h 50min total length
Expand all sections
NOC:Introduction to Abstract and Linear Algebra

MODULE 1

| 02h 25min total length
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    Lecture 05: Binary relation

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    Lecture 04: Set of sets

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    Lecture 03: Set Operations (contd.)

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    Lecture 02: Set Operations

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    Lecture 01: Set Theory

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NOC:Introduction to Abstract and Linear Algebra

MODULE 2

| 02h 16min total length
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    Lecture 06: Equivalence relation

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    Lecture 07: Mapping

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    Lecture 09: Binary Composition

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    Lecture 08: Permutation

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    Lecture 10: Groupoid

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NOC:Introduction to Abstract and Linear Algebra

MODULE 3

| 02h 21min total length
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    Lecture 15 : Subgroup Operations

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    Lecture 14 : Cyclic Group

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    Lecture 13 : Subgroup

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    Lecture 12 : Order of an element

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    Lecture 11 : Group

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NOC:Introduction to Abstract and Linear Algebra

MODULE 4

| 02h 28min total length
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    Lecture 16 : Left Cosets

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    Lecture 17 : Right Cosets

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    Lecture 18 : Normal Subgroup

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    Lecture 19 : Rings

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    Lecture 20 : Field

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NOC:Introduction to Abstract and Linear Algebra

MODULE 5

| 02h 54min total length
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    Lecture 25 : Dimension of a Vector space

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    Lecture 24 : Basis of a Vector Space

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    Lecture 23 : Linear Span

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    Lecture 22 : Sub-Spaces

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    Lecture 21 : Vector Spaces

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NOC:Introduction to Abstract and Linear Algebra

MODULE 6

| 02h 43min total length
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    Lecture 30: Linear Space

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    Lecture 29: More on linear mapping

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    Lecture 2: Linear Transformation (cont...)

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    Lecture 27: Linear Transformation

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    Lecture 26: Complement of subspace

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NOC:Introduction to Abstract and Linear Algebra

MODULE 7

| 02h 20min total length
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    Lecture 35: Eigen value of a matrix

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    Lecture 34: Row rank and Column rank

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    Lecture 33: System of linear equations

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    Lecture 32: Rank of a matrix (cont....)

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    Lecture 31: Rank of a matrix

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NOC:Introduction to Abstract and Linear Algebra

MODULE 8

| 02h 19min total length
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    Lecture 40 : Diagonalisable

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    Lecture 39 : Similar matrices

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    Lecture 38 : More on eigen value

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    Lecture 37 : Geometric multiplicity

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    Lecture 36 : Eigen Vector

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