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Description
Introduction to Abstract and Linear Algebra. Instructor: Dr. Sourav Mukhopadhyay, Department of Mathematics, IIT Kharagpur. 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. (from nptel.ac.in)
Course Curriculum
- Lecture 01 – Set Theory Unlimited
- Lecture 02 – Set Operations Unlimited
- Lecture 03 – Set Operations (cont.) Unlimited
- Lecture 04 – Set of Sets Unlimited
- Lecture 05 – Binary Relation Unlimited
- Lecture 06 – Equivalence Relation Unlimited
- Lecture 07 – Mapping Unlimited
- Lecture 08 – Permutation Unlimited
- Lecture 09 – Binary Composition Unlimited
- Lecture 10 – Groupoid Unlimited
- Lecture 11 – Group Unlimited
- Lecture 12 – Order of an Element Unlimited
- Lecture 13 – Subgroup Unlimited
- Lecture 14 – Cyclic Group Unlimited
- Lecture 15 – Subgroup Operations Unlimited
- Lecture 16 – Left Cosets Unlimited
- Lecture 17 – Right Cosets Unlimited
- Lecture 18 – Normal Subgroup Unlimited
- Lecture 19 – Rings Unlimited
- Lecture 20 – Field Unlimited
- Lecture 21 – Vector Spaces Unlimited
- Lecture 22 – Subspaces Unlimited
- Lecture 23 – Linear Span Unlimited
- Lecture 24 – Basis of a Vector Space Unlimited
- Lecture 25 – Dimension of a Vector Space Unlimited
- Lecture 26 – Complement of Subspace Unlimited
- Lecture 27 – Linear Transformation Unlimited
- Lecture 28 – Linear Transformation (cont.) Unlimited
- Lecture 29 – More on Linear Mapping Unlimited
- Lecture 30 – Linear Space Unlimited
- Lecture 31 – Rank of a Matrix Unlimited
- Lecture 32 – Rank of a Matrix (cont.) Unlimited
- Lecture 33 – System of Linear Equations Unlimited
- Lecture 34 – Row Rank and Column Rank Unlimited
- Lecture 35 – Eigenvalue of a Matrix Unlimited
- Lecture 36 – Eigenvector Unlimited
- Lecture 37 – Geometric Multiplicity Unlimited
- Lecture 38 – More on Eigenvalue Unlimited
- Lecture 39 – Similar Matrices Unlimited
- Lecture 40 – Diagonalisable Unlimited
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