A long term series of PDF format lessons, building mathematics from scratch.  New lessons are posted the first day of the month ten months of the year (January - June and September - December.)

We start to lay down the requirements of basis vectors.

Introducing Basis Vectors

We play with matrices and polynomials, looking for solutions to polynomials equations that come in matrix form.

Matrix Solutions to Polynomial Equations

Preliminary work with a two dimensional analogue for vectors.

Introducing Matrices

Moving beyond the constraints of the number line.

n-tuples, Vectors and beyond

Conceptually introducing, though not yet proving, the Fundamental Theorem of Algebra.

Fundamental Theorem of Algebra: An Introduction

Examining the real number axioms and rejecting one of the list.

Complex Numbers and New Algebras

Dropping the Axiom of Inequality

Finding Quartic Roots

Finding Cubic Polynomial Roots

Finding the roots of linear and quadratic polynomials