# Discrete Mathematics - IIITB

- Institution: IIIT Bangalore
- Department: Computer Science and Engineering
- Teacher: Prof. Ashish Choudhury
- Level: Undergraduate
- Language: English
- Subjects: Computer science, Engineering
- Source: [NPTEL](https://nptel.ac.in/courses/106108227)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/106108227)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

Discrete mathematics is the study of mathematical structures that are discrete in the sense that they assume only distinct, separate values, rather than in a range of values. It deals with the mathematical objects that are widely used in all most all fields of computer science, such as programming languages, data structures and algorithms, cryptography, operating systems, compilers, computer networks, artificial intelligence, image processing, computer vision, natural language processing, etc. The subject enables the students to formulate problems precisely, solve the problems, apply formal proof techniques and explain their reasoning clearly.

Intended audience: The course is intended for any student from the computer science discipline

## Lectures

1. [Introduction to Mathematical Logic](https://invisiblenetwork.ai/learn/nptel/106108227/ddfebb902209) (YouTube)
2. [Logical Equivalence](https://invisiblenetwork.ai/learn/nptel/106108227/1a161929ace4) (YouTube)
3. [SAT Problem](https://invisiblenetwork.ai/learn/nptel/106108227/79363c2d4c76) (YouTube)
4. [Rules of Inference](https://invisiblenetwork.ai/learn/nptel/106108227/a54b977d7006) (YouTube)
5. [Resolution](https://invisiblenetwork.ai/learn/nptel/106108227/e6f831a350d5) (YouTube)
6. [Tutorial 1: Part I](https://invisiblenetwork.ai/learn/nptel/106108227/864dc3c47c33) (YouTube)
7. [Tutorial 1: Part II](https://invisiblenetwork.ai/learn/nptel/106108227/4a7d676eadc5) (YouTube)
8. [Predicate Logic](https://invisiblenetwork.ai/learn/nptel/106108227/a586e3e465e3) (YouTube)
9. [Rules of Inferences in Predicate Logic](https://invisiblenetwork.ai/learn/nptel/106108227/c5a4a22d3666) (YouTube)
10. [Proof Strategies I](https://invisiblenetwork.ai/learn/nptel/106108227/21c7c463386a) (YouTube)
11. [Proof Strategies II](https://invisiblenetwork.ai/learn/nptel/106108227/80daee9061b6) (YouTube)
12. [Induction](https://invisiblenetwork.ai/learn/nptel/106108227/487434fcee7e) (YouTube)
13. [Tutorial 2: Part I](https://invisiblenetwork.ai/learn/nptel/106108227/a573189f2ad9) (YouTube)
14. [Tutorial 2: Part II](https://invisiblenetwork.ai/learn/nptel/106108227/076700071ab9) (YouTube)
15. [Sets](https://invisiblenetwork.ai/learn/nptel/106108227/c806513bfcf9) (YouTube)
16. [Relations](https://invisiblenetwork.ai/learn/nptel/106108227/2601417cb2d3) (YouTube)
17. [Operations on Relations](https://invisiblenetwork.ai/learn/nptel/106108227/0705b95f5c5c) (YouTube)
18. [Transitive Closure of Relations](https://invisiblenetwork.ai/learn/nptel/106108227/0276ba409e29) (YouTube)
19. [Warshall’s Algorithm for Computing Transitive Closure](https://invisiblenetwork.ai/learn/nptel/106108227/768cc87413eb) (YouTube)
20. [Tutorial 3](https://invisiblenetwork.ai/learn/nptel/106108227/eb464e4ddf7c) (YouTube)
21. [Equivalence Relation](https://invisiblenetwork.ai/learn/nptel/106108227/f2a6788e8616) (YouTube)
22. [Equivalence Relations and Partitions](https://invisiblenetwork.ai/learn/nptel/106108227/ca77edcd5378) (YouTube)
23. [Partial Ordering](https://invisiblenetwork.ai/learn/nptel/106108227/f8ccd6f66d2d) (YouTube)
24. [Functions](https://invisiblenetwork.ai/learn/nptel/106108227/78bac06977a8) (YouTube)
25. [Tutorial 4: Part I](https://invisiblenetwork.ai/learn/nptel/106108227/7128dac53a6f) (YouTube)
26. [Tutorial 4: Part II](https://invisiblenetwork.ai/learn/nptel/106108227/fa7c1e136e57) (YouTube)
27. [Countable and Uncountable Sets](https://invisiblenetwork.ai/learn/nptel/106108227/fedf57e523da) (YouTube)
28. [Examples of Countably Infinite Sets](https://invisiblenetwork.ai/learn/nptel/106108227/0d682fdbee71) (YouTube)
29. [Cantor’s Diagonalization Argument](https://invisiblenetwork.ai/learn/nptel/106108227/851da2b04166) (YouTube)
30. [Uncomputable Functions](https://invisiblenetwork.ai/learn/nptel/106108227/1c1e4eab73c7) (YouTube)
31. [Tutorial 5](https://invisiblenetwork.ai/learn/nptel/106108227/49a63543097d) (YouTube)
32. [Basic Rules of Counting](https://invisiblenetwork.ai/learn/nptel/106108227/1aa824eb29f7) (YouTube)
33. [Permutation and Combination](https://invisiblenetwork.ai/learn/nptel/106108227/99fc30677b70) (YouTube)
34. [Counting Using Recurrence Equations](https://invisiblenetwork.ai/learn/nptel/106108227/cbc6d1f4d703) (YouTube)
35. [Solving Linear Homogeneous Recurrence Equations – Part I](https://invisiblenetwork.ai/learn/nptel/106108227/a4c349d1292c) (YouTube)
36. [Solving Linear Homogeneous Recurrence Equations – Part II](https://invisiblenetwork.ai/learn/nptel/106108227/1f281f2c60fc) (YouTube)
37. [Tutorial 6: Part I](https://invisiblenetwork.ai/learn/nptel/106108227/4fe2d8c2b442) (YouTube)
38. [Tutorial 6: Part II](https://invisiblenetwork.ai/learn/nptel/106108227/5ba69c7b321b) (YouTube)
39. [Solving Linear Non-Homogeneous Recurrence Equations](https://invisiblenetwork.ai/learn/nptel/106108227/db431e3212b4) (YouTube)
40. [Catalan Numbers](https://invisiblenetwork.ai/learn/nptel/106108227/c0fea10bc018) (YouTube)
41. [Catalan Numbers – Derivation of Closed Form Formula](https://invisiblenetwork.ai/learn/nptel/106108227/e26acf717a88) (YouTube)
42. [Counting Using Principle of Inclusion-Exclusion](https://invisiblenetwork.ai/learn/nptel/106108227/cd4eab84ecdd) (YouTube)
43. [Tutorial 7](https://invisiblenetwork.ai/learn/nptel/106108227/4b2b64d1cfae) (YouTube)
44. [Graph Theory Basics](https://invisiblenetwork.ai/learn/nptel/106108227/3e285edaf254) (YouTube)
45. [Matching](https://invisiblenetwork.ai/learn/nptel/106108227/ec0e5f87abbf) (YouTube)
46. [Proof of Hall’s Marriage Theorem](https://invisiblenetwork.ai/learn/nptel/106108227/eecf35cead2c) (YouTube)
47. [Various Operations on Graphs](https://invisiblenetwork.ai/learn/nptel/106108227/8e1114457789) (YouTube)
48. [Vertex and Edge Connectivity](https://invisiblenetwork.ai/learn/nptel/106108227/5046c89d1f11) (YouTube)
49. [Tutorial 8](https://invisiblenetwork.ai/learn/nptel/106108227/532eedf9cc27) (YouTube)
50. [Euler Path and Euler Circuit](https://invisiblenetwork.ai/learn/nptel/106108227/2c6850097665) (YouTube)
51. [Hamiltonian Circuit](https://invisiblenetwork.ai/learn/nptel/106108227/781eb1266246) (YouTube)
52. [Vertex and Edge Coloring](https://invisiblenetwork.ai/learn/nptel/106108227/45a268b418f0) (YouTube)
53. [Tutorial 9: Part I](https://invisiblenetwork.ai/learn/nptel/106108227/d00bf5c7a6b7) (YouTube)
54. [Tutorial 9: Part II](https://invisiblenetwork.ai/learn/nptel/106108227/03bdeb280c22) (YouTube)
55. [Modular Arithmetic](https://invisiblenetwork.ai/learn/nptel/106108227/2dac01419e0a) (YouTube)
56. [Prime Numbers and GCD](https://invisiblenetwork.ai/learn/nptel/106108227/1418bb062051) (YouTube)
57. [Properties of GCD and Bézout’s Theorem](https://invisiblenetwork.ai/learn/nptel/106108227/c1e0884929c9) (YouTube)
58. [Linear Congruence Equations and Chinese Remainder Theorem](https://invisiblenetwork.ai/learn/nptel/106108227/9a5bd0db1d72) (YouTube)
59. [Uniqueness Proof of the CRT](https://invisiblenetwork.ai/learn/nptel/106108227/7d723db04712) (YouTube)
60. [Fermat’s Little Theorem, Primality Testing and Carmichael Numbers](https://invisiblenetwork.ai/learn/nptel/106108227/1a657d0abfe5) (YouTube)
61. [Group Theory](https://invisiblenetwork.ai/learn/nptel/106108227/55984c78323e) (YouTube)
62. [Cyclic Groups](https://invisiblenetwork.ai/learn/nptel/106108227/94e73b359b88) (YouTube)
63. [Subgroups](https://invisiblenetwork.ai/learn/nptel/106108227/ddb3aae87cd9) (YouTube)
64. [Discrete Logarithm and Cryptographic Applications](https://invisiblenetwork.ai/learn/nptel/106108227/8fb837d28e93) (YouTube)
65. [More Applications of Groups](https://invisiblenetwork.ai/learn/nptel/106108227/e1a4379fe502) (YouTube)
66. [Rings, Fields and Polynomials](https://invisiblenetwork.ai/learn/nptel/106108227/d37d76d7e9d3) (YouTube)
67. [Polynomials Over Fields and Properties](https://invisiblenetwork.ai/learn/nptel/106108227/c980aab10c72) (YouTube)
68. [Finite Fields and Properties I](https://invisiblenetwork.ai/learn/nptel/106108227/3b642bac4290) (YouTube)
69. [Finite Fields and Properties II](https://invisiblenetwork.ai/learn/nptel/106108227/fa6f6f7517c4) (YouTube)
70. [Primitive Element of a Finite Field](https://invisiblenetwork.ai/learn/nptel/106108227/cfffeabe93f5) (YouTube)
71. [Applications of Finite Fields](https://invisiblenetwork.ai/learn/nptel/106108227/43124a430f2a) (YouTube)
72. [Goodbye and Farewell](https://invisiblenetwork.ai/learn/nptel/106108227/ada9b14c9316) (YouTube)