Math From Scratch

By W. Blaine Dowler

What's Math From Scratch about?

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.)

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Math From Scratch episodes:

07.01.2014
Introducing Basis Vectors
We start to lay down the requirements of basis vectors.
06.01.2014
Matrix Solutions to Polynomial Equations
We play with matrices and polynomials, looking for solutions to polynomials equations that come in matrix form.
05.01.2014
Introducing Matrices
Preliminary work with a two dimensional analogue for vectors.
04.01.2014
n-tuples, Vectors and beyond
Moving beyond the constraints of the number line.
03.01.2014
Fundamental Theorem of Algebra: An Introduction
Conceptually introducing, though not yet proving, the Fundamental Theorem of Algebra.
02.01.2014
Complex Numbers and New Algebras
Examining the real number axioms and rejecting one of the list.
01.01.2014
Dropping the Axiom of Inequality
Examining the real number axioms and rejecting one of the list.
12.01.2013
Finding Quartic Roots
Finding the roots of quartic polynomials
11.01.2013
Finding Cubic Polynomial Roots
Finding the roots of cubic polynomials
10.01.2013
Finding Polynomial Roots
Finding the roots of linear and quadratic polynomials
09.01.2013
Defining Polynomials
Covering the rigorous definition of traditional polynomials
08.01.2013
Order of Operations and Isolating Variables
Covering the key elements of the order of algebraic operations and isolating variables
07.01.2013
Constants, Variables and Parameters
Defining three basic, critical and frequently neglected terms in algebra.
06.01.2013
Defining the Real Numbers
Defining the real numbers.
05.01.2013
Limits
Defining limits and leading into complete sets.
04.01.2013
Constructing an Impossible Number
Examining the non-terminating, non-repeating decimal numbers and their implications.
03.01.2013
Decimal Representation
Introducing decimal representations in base 10, and converting to and from fraction and decimal notations.
02.01.2013
Rational Exponents
Introducing rational numbers in the context of exponents
01.01.2013
Infinite Sequences and Series
Introducing infinite sequences and series, and some of the related problems that arise.
12.01.2012
Finite Sequences and Series
Introducing finite sequences and finite series
11.01.2012
Infinite Processes
10.01.2012
Defining the Rational Numbers
Defining the rational numbers, which include any and all numbers which can be written as fractions.
09.01.2012
The Field Axioms
This lesson begins with the construction of the most common algebraic structure.
06.01.2012
The RSA Encryption Algorithm
The RSA encryption algorithm is an incredibly important part of the encryption puzzle. This is how it works.
05.01.2012
Totients
Totients are an incredibly important piece of the RSA encryption puzzle
04.01.2012
Chinese Remainder Theorem
Covering one of the key thoerems in modern algebra
03.01.2012
Linear Diophantine Equations
Solving Linear Diophantine Equations
02.01.2012
The Euclidean Algorithm
Introducing the Euclidean Algorithm
01.01.2012
Modular Arithmetic
Introducing modular arithmetic and modular rings
12.01.2011
Divisibility Rules
Compiling the divisibility rules in base 10
11.01.2011
The Fundamental Theorem of Arithmetic
Introducing sets of numbers, linear diophantine equations and the fundamental theorem of arithmetic
10.01.2011
Defining Division With Remainder
Introducing the division algorithms
09.10.2011
Metric Spaces Other Than Canada
Introducing metric spaces, absolute value and the number line
08.20.2011
Bases Other Than 10
Examining popular nonstandard bases, including binary, octal and hexadecimal
07.30.2011
All Your Bases Are Belong to Us
Dealing with base 10 and the bases representation theorem
07.09.2011
One Algebra to Rule Them All: Ring Theory
Introducing and manipulating the axioms of ring theory
06.18.2011
Cosets and Cardinality
Covering factors, cosets, cardinality and Lagrange's Theorem
05.28.2011
Mappings
Detailing and defining mappings and functions
05.07.2011
In Her Majesty's Secret Subgroup
Dealing with and defining subgroups
04.16.2011
Your Locker Does NOT Have a Combination
Introducing permutations and combinations
03.26.2011
Structuring Symmetry - Applications of Group Theory
Basic applications of group theory
03.05.2011
The Group Axioms
Establishing the axioms of an algebraic group, one of the simplest yet widely applicable algebraic systems.
02.12.2011
Defining Whole Numbers
Formally defining the counting numbers, as well as addition and multiplication
01.22.2011
Set Theory
Introducing sets and assembling the basics of mathematics.
01.01.2011
Relations
Defining relations

What's Math From Scratch about?

Download our free app to listen on your phone

Math From Scratch episodes:

Introducing Basis Vectors

Matrix Solutions to Polynomial Equations

Introducing Matrices

n-tuples, Vectors and beyond

Fundamental Theorem of Algebra: An Introduction

Complex Numbers and New Algebras

Dropping the Axiom of Inequality

Finding Quartic Roots

Finding Cubic Polynomial Roots

Finding Polynomial Roots

Defining Polynomials

Order of Operations and Isolating Variables

Constants, Variables and Parameters

Defining the Real Numbers

Limits

Constructing an Impossible Number

Decimal Representation

Rational Exponents

Infinite Sequences and Series

Finite Sequences and Series

Infinite Processes

Defining the Rational Numbers

The Field Axioms

The RSA Encryption Algorithm

Totients

Chinese Remainder Theorem

Linear Diophantine Equations

The Euclidean Algorithm

Modular Arithmetic

Divisibility Rules

The Fundamental Theorem of Arithmetic

Defining Division With Remainder

Metric Spaces Other Than Canada

Bases Other Than 10

All Your Bases Are Belong to Us

One Algebra to Rule Them All: Ring Theory

Cosets and Cardinality

Mappings

In Her Majesty's Secret Subgroup

Your Locker Does NOT Have a Combination

Structuring Symmetry - Applications of Group Theory

The Group Axioms

Defining Whole Numbers

Set Theory

Relations