NOC:Algebra 1: Foundations

Lecture 1 - The nature of pure mathematics

Lecture 2 - Basic set theory

Lecture 3 - Basic logic

Lecture 4 - Proofs

Lecture 5 - More about proofs

Lecture 6 - Set theoretic identities

Lecture 7 - Functions

Lecture 8 - Equivalence relations

Lecture 9 - Quotients

Lecture 10 - More functions

Lecture 11 - Binary operations

Lecture 12 - Groups

Lecture 13 - Rings and integral domains

Lecture 14 - Peeking under the carpet

Lecture 15 - The Integers

Lecture 16 - Induction

Lecture 17 - Applications of Induction

Lecture 18 - Uniqueness of Integers

Lecture 19 - Cardinality of sets

Lecture 20 - Division in the Integers

Lecture 21 - Congruences

Lecture 22 - Basic number theory

Lecture 23 - Fields

Lecture 24 - Real numbers

Lecture 25 - Complex numbers

Lecture 26 - Polynomials

Lecture 27 - System of Linear Equations

Lecture 28 - Gaussian elimination

Lecture 29 - Matrix Algebra

Lecture 30 - Square systems

Lecture 31 - The set of solutions

Lecture 32 - Vector spaces

Lecture 33 - Direct sums of subspaces

Lecture 34 - Spans and linear independence

Lecture 35 - Basis

Lecture 36 - Linear Maps

Lecture 37 - The Rank--Nullity theorem

Lecture 38 - Matrices and Linear transformations

Lecture 39 - Change of basis

Lecture 40 - Eigenvalues

Lecture 41 - Minimal Polynomial

Lecture 42 - Applications of the minimal polynomial

Lecture 43 - Triangular Form

Lecture 44 - Jordan Form

Lecture 45 - Examples of Canonical Forms