# Math Foundation

- Institution: IIT Hyderabad
- Department: Mathematics
- Teacher: Prof. Sukumar D
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111106003)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111106003)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

This is an introductory course to the UG students across the disciplines which needs mathematical maturity. The course is carved out by considering the necessary notions and concepts that are needed for understanding, appreciating and enjoying mathematics. It is also observed that, the clarity and confidence on these foundational concepts, empowers avoiding mis-understating or difficult in understanding. Broadly the following topics or covered: Logic (mathematical statement), Sets (both understanding and describing), Functions (interaction and interconnection among the sets both qualitatively and quantitatively), Relation on sets (mainly equivalence relation and partial orders). Proof techniques, geometric intuition, writing skills will be acquired on the way systematically. Learning them and digesting them slowly gives confidence in self-learning as well as in self-correcting.

Intended audience: Anyone want to pursue Mathematics

Prerequisites: No pre-requisite. Class 12 or equivalent.

## Lectures

1. [Mathematical Statements](https://invisiblenetwork.ai/learn/nptel/111106003/222e3647f8ba) (YouTube)
2. [Negation of statements](https://invisiblenetwork.ai/learn/nptel/111106003/e772de53cafd) (YouTube)
3. [Universal and existential quantifiers](https://invisiblenetwork.ai/learn/nptel/111106003/536d217c87e4) (YouTube)
4. [Negation rules to quantified statements](https://invisiblenetwork.ai/learn/nptel/111106003/1daa1320eeb4) (YouTube)
5. [Nested quantifiers and their negation rules](https://invisiblenetwork.ai/learn/nptel/111106003/234e69ba85ef) (YouTube)
6. [Review of statements, negation, and quantifiers](https://invisiblenetwork.ai/learn/nptel/111106003/43f35e90e6db) (YouTube)
7. [Compound Statements](https://invisiblenetwork.ai/learn/nptel/111106003/9389a1b3938d) (YouTube)
8. [Compound Statements with Quantifiers](https://invisiblenetwork.ai/learn/nptel/111106003/5a28a913769b) (YouTube)
9. [Implications and their negation](https://invisiblenetwork.ai/learn/nptel/111106003/e014b090dbd9) (YouTube)
10. [Converse and Related Implications](https://invisiblenetwork.ai/learn/nptel/111106003/0291e80384e3) (YouTube)
11. [Biconditionals (If and Only If)](https://invisiblenetwork.ai/learn/nptel/111106003/8932d87dee64) (YouTube)
12. [Contrapositive and Week 2 Review](https://invisiblenetwork.ai/learn/nptel/111106003/48848d55919d) (YouTube)
13. [Proofs in Mathematics](https://invisiblenetwork.ai/learn/nptel/111106003/4996f9116851) (YouTube)
14. [Direct Proof Method](https://invisiblenetwork.ai/learn/nptel/111106003/fcd7e3371770) (YouTube)
15. [Contrapositive Proof](https://invisiblenetwork.ai/learn/nptel/111106003/1c12fd85c4a8) (YouTube)
16. [Proof by Contradiction](https://invisiblenetwork.ai/learn/nptel/111106003/bc36a392d33a) (YouTube)
17. [Proving Equivalence](https://invisiblenetwork.ai/learn/nptel/111106003/eeec02720d0d) (YouTube)
18. [Induction & Counterexamples](https://invisiblenetwork.ai/learn/nptel/111106003/147a55209274) (YouTube)
19. [Basic Set Terminology](https://invisiblenetwork.ai/learn/nptel/111106003/f52a818ab341) (YouTube)
20. [Empty Set, Subsets and Power Sets](https://invisiblenetwork.ai/learn/nptel/111106003/562d34b93cb4) (YouTube)
21. [Equality of Sets](https://invisiblenetwork.ai/learn/nptel/111106003/4237501579df) (YouTube)
22. [Describing Sets and Proving Equality](https://invisiblenetwork.ai/learn/nptel/111106003/e645276c8430) (YouTube)
23. [Union and Intersection](https://invisiblenetwork.ai/learn/nptel/111106003/95208ef51f50) (YouTube)
24. [Complement and Difference](https://invisiblenetwork.ai/learn/nptel/111106003/f45735ba9570) (YouTube)
25. [Family of Sets](https://invisiblenetwork.ai/learn/nptel/111106003/6dea39761667) (YouTube)
26. [Union of a Family](https://invisiblenetwork.ai/learn/nptel/111106003/738695b81790) (YouTube)
27. [Intersection of a Family](https://invisiblenetwork.ai/learn/nptel/111106003/e0c659aaa184) (YouTube)
28. [Disjoint and Pairwise Disjoint Families](https://invisiblenetwork.ai/learn/nptel/111106003/eb23e65f3aab) (YouTube)
29. [Cartesian Product](https://invisiblenetwork.ai/learn/nptel/111106003/6c7aae6d6b6e) (YouTube)
30. [Worked Examples and Review](https://invisiblenetwork.ai/learn/nptel/111106003/3539e13652cb) (YouTube)
31. [Functions: Definition and Examples](https://invisiblenetwork.ai/learn/nptel/111106003/7f91ba09b480) (YouTube)
32. [Functions: More Examples](https://invisiblenetwork.ai/learn/nptel/111106003/427317ecdfcb) (YouTube)
33. [Injective Functions](https://invisiblenetwork.ai/learn/nptel/111106003/bf6a9e25a98b) (YouTube)
34. [Onto Functions](https://invisiblenetwork.ai/learn/nptel/111106003/db33740fc853) (YouTube)
35. [Bijections](https://invisiblenetwork.ai/learn/nptel/111106003/153e180d6826) (YouTube)
36. [Review: Functions](https://invisiblenetwork.ai/learn/nptel/111106003/d8d279102a6e) (YouTube)
37. [Functions: Graphical View](https://invisiblenetwork.ai/learn/nptel/111106003/e537a1f6160e) (YouTube)
38. [Composition of Functions](https://invisiblenetwork.ai/learn/nptel/111106003/35b66058abe4) (YouTube)
39. [Inverse Functions](https://invisiblenetwork.ai/learn/nptel/111106003/56d9005afc2b) (YouTube)
40. [Graph of the Inverse Function](https://invisiblenetwork.ai/learn/nptel/111106003/f886c576009d) (YouTube)
41. [Bijections between Intervals](https://invisiblenetwork.ai/learn/nptel/111106003/b2d393748f5c) (YouTube)
42. [Review: Composition and Inverses (W6 + W7)](https://invisiblenetwork.ai/learn/nptel/111106003/2d21c6c4a2d4) (YouTube)
43. [Cantor’s Theorem](https://invisiblenetwork.ai/learn/nptel/111106003/ee2bc9eee85c) (YouTube)
44. [Image of Subsets under Functions — 1](https://invisiblenetwork.ai/learn/nptel/111106003/ddbcce825343) (YouTube)
45. [Image of Subsets under Functions — 2](https://invisiblenetwork.ai/learn/nptel/111106003/0eadef2979de) (YouTube)
46. [Inverse Image of Subsets under Functions](https://invisiblenetwork.ai/learn/nptel/111106003/3ca8cb09d86c) (YouTube)
47. [Inverse Image of Subsets under Functions - 2](https://invisiblenetwork.ai/learn/nptel/111106003/584de1b91347) (YouTube)
48. [Review: Images and Inverse Images](https://invisiblenetwork.ai/learn/nptel/111106003/1b6aff14aba3) (YouTube)
49. [Relations: Definition and Examples](https://invisiblenetwork.ai/learn/nptel/111106003/a281acdbd8e1) (YouTube)
50. [Properties of Relations I - The Four Properties](https://invisiblenetwork.ai/learn/nptel/111106003/864b088884fc) (YouTube)
51. [Properties of Relations II - More Examples, Digraphs, and Matrices](https://invisiblenetwork.ai/learn/nptel/111106003/ac771f307a33) (YouTube)
52. [Equivalence Relations](https://invisiblenetwork.ai/learn/nptel/111106003/ec276106cf3d) (YouTube)
53. [Equivalence Classes and Partitions](https://invisiblenetwork.ai/learn/nptel/111106003/22c5dd85041b) (YouTube)
54. [Equivalence Classes and Partitions](https://invisiblenetwork.ai/learn/nptel/111106003/e855cfeef2a2) (YouTube)
55. [The Induction Principle](https://invisiblenetwork.ai/learn/nptel/111106003/b90d76691f65) (YouTube)
56. [The Strong Induction Principle](https://invisiblenetwork.ai/learn/nptel/111106003/e10037674bb9) (YouTube)
57. [The Well-Ordering Principle and the Division Algorithm](https://invisiblenetwork.ai/learn/nptel/111106003/6866ecfadaa9) (YouTube)
58. [Equivalence of the Three Principles](https://invisiblenetwork.ai/learn/nptel/111106003/82e31cd1c782) (YouTube)
59. [Worked Examples: gcd and Bezout](https://invisiblenetwork.ai/learn/nptel/111106003/4d1c86ad859b) (YouTube)
60. [Review: Pitfalls and the Whole Picture](https://invisiblenetwork.ai/learn/nptel/111106003/b5cfbffb0b1b) (YouTube)
61. [Cardinality: Comparing Sizes via Bijections](https://invisiblenetwork.ai/learn/nptel/111106003/5290648b96c9) (YouTube)
62. [The Schroder-Bernstein Theorem](https://invisiblenetwork.ai/learn/nptel/111106003/dc46807d92df) (YouTube)
63. [Knaster-Tarski and the Proof of Schroder-Bernstein](https://invisiblenetwork.ai/learn/nptel/111106003/3a6711e1030a) (YouTube)
64. [Finite Sets and the Pigeonhole Principle](https://invisiblenetwork.ai/learn/nptel/111106003/0a44581584de) (YouTube)
65. [Countable and Uncountable Sets](https://invisiblenetwork.ai/learn/nptel/111106003/266007c73256) (YouTube)
66. [Comparing Cardinality](https://invisiblenetwork.ai/learn/nptel/111106003/8477001e3971) (YouTube)
67. [Order Relations: Definition and Examples](https://invisiblenetwork.ai/learn/nptel/111106003/b19004a52492) (YouTube)
68. [Restriction, Chains, and Bounds](https://invisiblenetwork.ai/learn/nptel/111106003/cc17464a3d68) (YouTube)
69. [Maximum, Minimum, Maximal, Minimal, and LUB/GLB](https://invisiblenetwork.ai/learn/nptel/111106003/33f3733bb2d4) (YouTube)
70. [Hasse Diagrams and Intervals](https://invisiblenetwork.ai/learn/nptel/111106003/4222939d4c57) (YouTube)
71. [Well-Ordering, Zorn's Lemma, and the Axiom of Choice](https://invisiblenetwork.ai/learn/nptel/111106003/23adb3961a01) (YouTube)
72. [The Product of a Family](https://invisiblenetwork.ai/learn/nptel/111106003/f5ea93d5f299) (YouTube)