MathIsimple
Part I

Foundations

Before diving into vector spaces and linear transformations, we establish the essential algebraic foundations. These prerequisites ensure you have the mathematical maturity to appreciate the abstract beauty of linear algebra.

4
Courses
10-14
Hours Total
Foundation
Level
What You'll Learn

Algebraic Structures

Understand groups, rings, and fields—the building blocks for defining vector spaces

Complex Number Theory

Master complex arithmetic and understand why ℂ is algebraically closed

Equivalence Relations

Learn how to partition sets and construct quotient structures

Gaussian Elimination

Develop systematic methods for solving systems of linear equations

Courses in This Part

LA-1.1
Algebraic Structures
Available
Groups, rings, and fields—the algebraic foundations that underpin vector spaces and linear maps
3-4 hours
Binary Operations
Groups & Subgroups
Rings
Fields
Field Axioms
LA-1.2
Complex Numbers
Available
The algebraic construction of ℂ, polar form, Euler's formula, and roots of unity
2-3 hours
Algebraic Construction
Polar Form
Euler's Formula
De Moivre's Theorem
Roots of Unity
LA-1.3
Equivalence Relations
Available
Relations, equivalence classes, partitions, and quotient structures
2-3 hours
Relations
Reflexivity, Symmetry, Transitivity
Equivalence Classes
Partitions
Quotient Sets
LA-1.4
Gaussian Elimination
Available
Row operations, echelon forms, and systematic solution of linear systems
3-4 hours
Elementary Row Operations
Row Echelon Form
Reduced Row Echelon Form
Solving Linear Systems
LU Decomposition