# Algebra 1: Foundations

- Institution: IIT Palakkad
- Department: Mathematics
- Teacher: Prof. Jaikrishnan J
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111106763)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111106763)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

This is part 1 of a series of courses on Algebra at the undergraduate level. The first course is the foundational course. We will spend half of the course on fundamentals which are often skirted in college courses. The aim of the first six weeks is to have a thorough understanding of the basic objects that form the backbone of modern algebra. Along the way, we will also introduce the notion of proof in an elementary setting. The latter six weeks is an introduction to linear algebra culminating in an elementary proof of the existence of the Jordan form given by Terence Tao. Throughout the course we will sprinkle interesting tidbits about history.

Intended audience: Bachelor’s students in the sciences and engineering

Prerequisites: High school mathematics

## Lectures

1. [The nature of pure mathematics](https://invisiblenetwork.ai/learn/nptel/111106763/a19e5157def3) (YouTube)
2. [Basic set theory](https://invisiblenetwork.ai/learn/nptel/111106763/3b07b9b71310) (YouTube)
3. [Basic logic](https://invisiblenetwork.ai/learn/nptel/111106763/6031b1b8f09d) (YouTube)
4. [Proofs](https://invisiblenetwork.ai/learn/nptel/111106763/a988a490caf4) (YouTube)
5. [More about proofs](https://invisiblenetwork.ai/learn/nptel/111106763/df23299c251b) (YouTube)
6. [Set theoretic identities](https://invisiblenetwork.ai/learn/nptel/111106763/e52e519cc33b) (YouTube)
7. [Functions](https://invisiblenetwork.ai/learn/nptel/111106763/f5d2f952c8f6) (YouTube)
8. [Equivalence relations](https://invisiblenetwork.ai/learn/nptel/111106763/90c8d0a71978) (YouTube)
9. [Quotients](https://invisiblenetwork.ai/learn/nptel/111106763/0f5e7d14379d) (YouTube)
10. [More functions](https://invisiblenetwork.ai/learn/nptel/111106763/bd6814aabe56) (YouTube)
11. [Binary operations](https://invisiblenetwork.ai/learn/nptel/111106763/d2932ca68b2c) (YouTube)
12. [Groups](https://invisiblenetwork.ai/learn/nptel/111106763/248fa6731ca3) (YouTube)
13. [Rings and integral domains](https://invisiblenetwork.ai/learn/nptel/111106763/ebf30e0cd550) (YouTube)
14. [Peeking under the carpet](https://invisiblenetwork.ai/learn/nptel/111106763/94572ef0b8d2) (YouTube)
15. [The Integers](https://invisiblenetwork.ai/learn/nptel/111106763/01289f1eb948) (YouTube)
16. [Induction](https://invisiblenetwork.ai/learn/nptel/111106763/f1c4898b7407) (YouTube)
17. [Applications of Induction.](https://invisiblenetwork.ai/learn/nptel/111106763/5aa559dedb18) (YouTube)
18. [Uniqueness of Integers.](https://invisiblenetwork.ai/learn/nptel/111106763/d7d46a3bd07c) (YouTube)
19. [Cardinality of sets](https://invisiblenetwork.ai/learn/nptel/111106763/98d203b1c116) (YouTube)
20. [Division in the Integers](https://invisiblenetwork.ai/learn/nptel/111106763/4d292dc1a9c7) (YouTube)
21. [Congruences](https://invisiblenetwork.ai/learn/nptel/111106763/53f7861a9297) (YouTube)
22. [Basic number theory](https://invisiblenetwork.ai/learn/nptel/111106763/54f6892ba7c0) (YouTube)
23. [Fields](https://invisiblenetwork.ai/learn/nptel/111106763/f3233f7a11a2) (YouTube)
24. [Real numbers](https://invisiblenetwork.ai/learn/nptel/111106763/776abb2ec5d0) (YouTube)
25. [Complex numbers](https://invisiblenetwork.ai/learn/nptel/111106763/7a8dff6ca790) (YouTube)
26. [Polynomials](https://invisiblenetwork.ai/learn/nptel/111106763/50c039964279) (YouTube)
27. [System of Linear Equations](https://invisiblenetwork.ai/learn/nptel/111106763/1548eae0acb9) (YouTube)
28. [Gaussian elimination](https://invisiblenetwork.ai/learn/nptel/111106763/a172dc1bec11) (YouTube)
29. [Matrix Algebra](https://invisiblenetwork.ai/learn/nptel/111106763/7eaed6857418) (YouTube)
30. [Square systems.](https://invisiblenetwork.ai/learn/nptel/111106763/2bd5f2f9bebe) (YouTube)
31. [The set of solutions](https://invisiblenetwork.ai/learn/nptel/111106763/4d89af465f30) (YouTube)
32. [Vector spaces](https://invisiblenetwork.ai/learn/nptel/111106763/f4decb3946a6) (YouTube)
33. [Direct sums of subspaces](https://invisiblenetwork.ai/learn/nptel/111106763/e6c2a8491919) (YouTube)
34. [Spans and linear independence](https://invisiblenetwork.ai/learn/nptel/111106763/28cca44ad1a1) (YouTube)
35. [Basis](https://invisiblenetwork.ai/learn/nptel/111106763/1938d901ab84) (YouTube)
36. [Linear Maps](https://invisiblenetwork.ai/learn/nptel/111106763/301d3276efaf) (YouTube)
37. [The Rank--Nullity theorem](https://invisiblenetwork.ai/learn/nptel/111106763/fb75bd5ddb5a) (YouTube)
38. [Matrices and Linear transformations](https://invisiblenetwork.ai/learn/nptel/111106763/4c5d8fc652df) (YouTube)
39. [Change of basis](https://invisiblenetwork.ai/learn/nptel/111106763/bac98b3ad4ca) (YouTube)
40. [Eigenvalues](https://invisiblenetwork.ai/learn/nptel/111106763/059505a223fa) (YouTube)
41. [Minimal Polynomial](https://invisiblenetwork.ai/learn/nptel/111106763/8cc1b85710e0) (YouTube)
42. [Applications of the minimal polynomial](https://invisiblenetwork.ai/learn/nptel/111106763/e22697f36b1f) (YouTube)
43. [Triangular Form](https://invisiblenetwork.ai/learn/nptel/111106763/658a467c8e30) (YouTube)
44. [Jordan Form](https://invisiblenetwork.ai/learn/nptel/111106763/14ac0a881c39) (YouTube)
45. [Examples of Canonical Forms](https://invisiblenetwork.ai/learn/nptel/111106763/3a90497dd184) (YouTube)