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Course11110511240 lectures

Introduction to Abstract and Linear Algebra

Prof. Sourav Mukhopadhyay · IIT Kharagpur

Start with lecture 1 At NPTEL

About

Abstract and Linear Algebra are applicable to every discipline, be it engineering and technology, economics or social sciences. It is essential for the students to get acquainted with the subject of Abstract and Linear Algebra at an early stage. The present course has been designed to introduce the subject to undergraduate/postgraduate students in science and engineering. The course contains a good introduction to each topic and an advance treatment of theory at a fairly understandable level to the students at this stage.

Intended audience: Mathematics

Lectures

Week 1 :

  1. Lecture 01 : Set Theory YouTube
  2. Lecture 02 : Set Operations YouTube
  3. Lecture 03 : Set Operations (contd.) YouTube
  4. Lecture 04 : Set of sets YouTube
  5. Lecture 05 : Binary relation YouTube

Week 2 :

  1. Lecture 06 : Equivalence relation YouTube
  2. Lecture 07 : Mapping YouTube
  3. Lecture 08 : Permutation YouTube
  4. Lecture 09 : Binary Composition YouTube
  5. Lecture 10 : Groupoid YouTube

Week 3 :

  1. Lecture 11 : Group YouTube
  2. Lecture 12 : Order of an element YouTube
  3. Lecture 13 : Subgroup YouTube
  4. Lecture 14 : Cyclic Group YouTube
  5. Lecture 15 : Subgroup Operations YouTube

Week 4 :

  1. Lecture 16 : Left Cosets YouTube
  2. Lecture 17 : Right Cosets YouTube
  3. Lecture 18 : Normal Subgroup YouTube
  4. Lecture 19 : Rings YouTube
  5. Lecture 20 : Field YouTube

Week 5 :

  1. Lecture 21 : Vector Spaces YouTube
  2. Lecture 22 : Sub-Spaces YouTube
  3. Lecture 23 : Linear Span YouTube
  4. Lecture 24 : Basis of a Vector Space YouTube
  5. Lecture 25 : Dimension of a Vector space YouTube

Week 6 :

  1. Lecture 26 : Complement of subspace YouTube
  2. Lecture 27 : Linear Transformation YouTube
  3. Lecture 28 : Linear Transformation (cont...) YouTube
  4. Lecture 29 : More on linear mapping YouTube
  5. Lecture 30 : Linear Space YouTube

Week 7 :

  1. Lecture 31 : Rank of a matrix YouTube
  2. Lecture 32 : Rank of a matrix (cont....) YouTube
  3. Lecture 33 : System of linear equations YouTube
  4. Lecture 34 : Row rank and Column rank YouTube
  5. Lecture 35 : Eigen value of a matrix YouTube

Week 8 :

  1. Lecture 36 : Eigen Vector YouTube
  2. Lecture 37 : Geometric multiplicity YouTube
  3. Lecture 38 : More on eigen value YouTube
  4. Lecture 39 : Similar matrices YouTube
  5. Lecture 40 : Diagonalisable YouTube

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Kharagpur
Department
Mathematics
Teacher
Prof. Sourav Mukhopadhyay
Level
Graduate
Language
English
Subjects
Mathematics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
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