With the rise of deep learning and quantum computing, there has literally never been a better time to learn linear algebra.

Linear algebra is central to almost all areas of mathematics. For instance, linear algebra is fundamental in modern presentations of geometry, including for defining basic objects such as lines, planes and rotations. Also, functional analysis may be basically viewed as the application of linear algebra to spaces of functions. Linear algebra is also used in most sciences and engineering areas, because it allows modeling many natural phenomena, and efficiently computing with such models.

Lesson Plan

• (0:00) Systems of Linear Equations (1 of 3)
• (16:20) System of Linear Equations (2 of 3)
• (27:55) Systems of Linear Equations (3 of 3)
• (47:18) Row Reduction and Echelon Forms (1 of 2)
• (54:49) Row Reduction and Echelon Forms (2 of 2)
• (1:4:10) Vector Equations (1 of 2)
• (1:14:05) Vector Equations (2 of 2)
• (1:24:54) The Matrix Equation Ax = b (1 of 2)
• (1:39:21) The Matrix Equation Ax = b (2 of 2)
• (1:44:48) Solution Sets of Linear Systems
• (1:57:49) Linear Independence
• (2:11:20) Linear Transformations (1 of 2)
• (2:25:10) Linear Transformations (2 of 2)
• (2:39:19) Matrix Operations
• (2:56:24) Matrix Inverse
• (3:12:17) Invertible Matrix Properties
• (3:24:24) Determinants (1 of 2)
• (3:44:40) Determinants (2 of 2)
• (4:04:28) Cramer’s Rule
• (4:18:20) Vector Spaces and Subspaces (1 of 2)
• (4:48:30) Vector Spaces and Subspaces
• (5:13:13) Null Spaces, Column Spaces, and Linear Transformations
• (5:33:25) Basis of a Vector Space
• (5:59:43) Coordinate Systems in a Vector Space
• (6:15:41) Dimension of a Vector Space
• (6:26:35) Rank of a Matrix
• (6:50:09) Markov Chains
• (7:09:23) Eigenvalues and Eigenvectors
• (7:32:03) Matrix Diagonalization
• (7:49:08) Inner Product, Vector Length, Orthogonality

Learn Algebra in this full college course. Algebraic concepts are often used in programming.

This course was created by Dr. Linda Green, a lecturer at the University of North Carolina at Chapel Hill. Check out her YouTube channel: https://www.youtube.com/channel/UCkyLJh6hQS1TlhUZxOMjTFw

Chapters:

• (0:00:00) Exponent Rules
• (0:10:14) Simplifying using Exponent Rules
• (0:31:46) Factoring
• (0:45:08) Factoring – Additional Examples
• (0:55:37) Rational Expressions
• (1:15:22) Rational Equations
• (1:37:01) Absolute Value Equations
• (1:42:23) Interval Notation
• (1:49:35) Absolute Value Inequalities
• (1:56:55) Compound Linear Inequalities
• (2:05:59) Polynomial and Rational Inequalities
• (2:16:20) Distance Formula
• (2:20:59) Midpoint Formula
• (2:23:30) Circles: Graphs and Equations
• (2:33:06) Lines: Graphs and Equations
• (2:41:35) Parallel and Perpendicular Lines
• (2:49:05) Functions
• (3:00:53) Toolkit Functions
• (3:08:00) Transformations of Functions
• (3:20:29) Introduction to Quadratic Functions
• (3:33:02) Standard Form and Vertex Form for Quadratic Functions
• (3:37:18) Justification of the Vertex Formula
• (3:41:11) Polynomials
• (3:49:06) Exponential Functions
• (3:56:53) Exponential Function Applications
• (4:08:38) Exponential Functions Interpretations
• (4:18:17) Compound Interest
• (4:29:33) Logarithms: Introduction
• (4:38:15) Log Functions and Their Graphs
• (4:48:59) Combining Logs and Exponents
• (4:53:38) Log Rules
• (5:02:10) Solving Exponential Equations Using Logs
• (5:10:20) Solving Log Equations
• (5:19:27) Doubling Time and Half Life
• (5:35:34) Systems of Linear Equations
• (5:47:36) Distance, Rate, and Time Problems
• (5:53:20) Mixture Problems
• (5:59:48) Rational Functions and Graphs
• (6:13:13) Combining Functions
• (6:17:10) Composition of Functions
• (6:29:32) Inverse Functions

Just because computers can perform calculations quickly doesn’t mean that they are perfect.