# Introduction to Abstract and Linear Algebra

- Institution: IIT Kharagpur
- Department: Mathematics
- Teacher: Prof. Sourav Mukhopadhyay
- Level: Graduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111105112)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111105112)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

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

1. [Lecture 01 : Set Theory](https://invisiblenetwork.ai/learn/nptel/111105112/5740d3ec7b70) (YouTube)
2. [Lecture 02 : Set Operations](https://invisiblenetwork.ai/learn/nptel/111105112/8e0a5891b78c) (YouTube)
3. [Lecture 03 : Set Operations (contd.)](https://invisiblenetwork.ai/learn/nptel/111105112/48a93fbc2438) (YouTube)
4. [Lecture 04 : Set of sets](https://invisiblenetwork.ai/learn/nptel/111105112/d69e41219a78) (YouTube)
5. [Lecture 05 : Binary relation](https://invisiblenetwork.ai/learn/nptel/111105112/40a026d9a098) (YouTube)
6. [Lecture 06 : Equivalence relation](https://invisiblenetwork.ai/learn/nptel/111105112/37f63b3fbcda) (YouTube)
7. [Lecture 07 : Mapping](https://invisiblenetwork.ai/learn/nptel/111105112/9113195906f7) (YouTube)
8. [Lecture 08 : Permutation](https://invisiblenetwork.ai/learn/nptel/111105112/3b4c98e5fc57) (YouTube)
9. [Lecture 09 : Binary Composition](https://invisiblenetwork.ai/learn/nptel/111105112/fcb7b23ac6d6) (YouTube)
10. [Lecture 10 : Groupoid](https://invisiblenetwork.ai/learn/nptel/111105112/b871389cf874) (YouTube)
11. [Lecture 11 : Group](https://invisiblenetwork.ai/learn/nptel/111105112/f4bfea8b7576) (YouTube)
12. [Lecture 12 : Order of an element](https://invisiblenetwork.ai/learn/nptel/111105112/93a019725bee) (YouTube)
13. [Lecture 13 : Subgroup](https://invisiblenetwork.ai/learn/nptel/111105112/a6633d230954) (YouTube)
14. [Lecture 14 : Cyclic Group](https://invisiblenetwork.ai/learn/nptel/111105112/ec9f666a5b10) (YouTube)
15. [Lecture 15 : Subgroup Operations](https://invisiblenetwork.ai/learn/nptel/111105112/360dcb86cf66) (YouTube)
16. [Lecture 16 : Left Cosets](https://invisiblenetwork.ai/learn/nptel/111105112/c075b218125a) (YouTube)
17. [Lecture 17 : Right Cosets](https://invisiblenetwork.ai/learn/nptel/111105112/741a131496a0) (YouTube)
18. [Lecture 18 : Normal Subgroup](https://invisiblenetwork.ai/learn/nptel/111105112/0a46e31d8e64) (YouTube)
19. [Lecture 19 : Rings](https://invisiblenetwork.ai/learn/nptel/111105112/176eb23e2053) (YouTube)
20. [Lecture 20 : Field](https://invisiblenetwork.ai/learn/nptel/111105112/60f0a36d348f) (YouTube)
21. [Lecture 21 : Vector Spaces](https://invisiblenetwork.ai/learn/nptel/111105112/d68519f14843) (YouTube)
22. [Lecture 22 : Sub-Spaces](https://invisiblenetwork.ai/learn/nptel/111105112/dce8dbb953b3) (YouTube)
23. [Lecture 23 : Linear Span](https://invisiblenetwork.ai/learn/nptel/111105112/2068df9fd673) (YouTube)
24. [Lecture 24 : Basis of a Vector Space](https://invisiblenetwork.ai/learn/nptel/111105112/794e94e7409a) (YouTube)
25. [Lecture 25 : Dimension of a Vector space](https://invisiblenetwork.ai/learn/nptel/111105112/f3b37c8c6b9b) (YouTube)
26. [Lecture 26 : Complement of subspace](https://invisiblenetwork.ai/learn/nptel/111105112/622e0fa5a5c4) (YouTube)
27. [Lecture 27 : Linear Transformation](https://invisiblenetwork.ai/learn/nptel/111105112/7b42c411eaaf) (YouTube)
28. [Lecture 28 : Linear Transformation (cont...)](https://invisiblenetwork.ai/learn/nptel/111105112/8bfa19323934) (YouTube)
29. [Lecture 29 : More on linear mapping](https://invisiblenetwork.ai/learn/nptel/111105112/ecb6d8608388) (YouTube)
30. [Lecture 30 : Linear Space](https://invisiblenetwork.ai/learn/nptel/111105112/b58eb788c2cb) (YouTube)
31. [Lecture 31 : Rank of a matrix](https://invisiblenetwork.ai/learn/nptel/111105112/1f88f4d44b5b) (YouTube)
32. [Lecture 32 : Rank of a matrix (cont....)](https://invisiblenetwork.ai/learn/nptel/111105112/cbe0cd9f3cbc) (YouTube)
33. [Lecture 33 : System of linear equations](https://invisiblenetwork.ai/learn/nptel/111105112/40073b3938d2) (YouTube)
34. [Lecture 34 : Row rank and Column rank](https://invisiblenetwork.ai/learn/nptel/111105112/91bc929d417a) (YouTube)
35. [Lecture 35 : Eigen value of a matrix](https://invisiblenetwork.ai/learn/nptel/111105112/3a174457cb0b) (YouTube)
36. [Lecture 36 : Eigen Vector](https://invisiblenetwork.ai/learn/nptel/111105112/beb99328f92f) (YouTube)
37. [Lecture 37 : Geometric multiplicity](https://invisiblenetwork.ai/learn/nptel/111105112/25e62a1157e5) (YouTube)
38. [Lecture 38 : More on eigen value](https://invisiblenetwork.ai/learn/nptel/111105112/9a3d26f303de) (YouTube)
39. [Lecture 39 : Similar matrices](https://invisiblenetwork.ai/learn/nptel/111105112/06d12d130eaa) (YouTube)
40. [Lecture 40 : Diagonalisable](https://invisiblenetwork.ai/learn/nptel/111105112/5e3b27ef88b2) (YouTube)