Cartesian coordinates represent a point in space by describing how far it is from each axis.

Coefficient and augmented matrices are used to store the coefficlents of systems of linear equations.

A straight line can be represented by the equation y = mx + b, where m is the gradient and b is the point it intersects the y axis. Includes code in Python.

Equivalent systems are systems which share the same solution set.

The gradient is the change in y relative to a change in x. It can be calculated by dividing the change in y by the change in x. Includes code in Python.

Linear equations are equations in which every variable is linear, i.e. not exponential or polynomial.

Strictly triangular systems of linear equations are easy to solve, and can be generated from systems that are not strictly triangular.

Summation notation uses the greek letter 'sigma' to signify that a set of values should be summed. Includes code in Python.

Systems of linear equations are a set of linear equations that work together. Includes example code in Python.

We can find the derivative of almost all functions by applying simple rules.

A derivative is a function that describes the gradient of another function.

A functions minima and maxima are the points where it's gradient is 0. We can use its derivative to find them.

An iterated function recursively calls itself a number of times. It is used to model chaotic and dynamic systems.

How to calculate the area of a parallelogram using it's base and height. Includes example code in Python.

How to calculate the area of a trapezium using it's bases and height. Includes example code in Python.

How to calculate the area of a triangle using it's base and height. Includes example code in Python.

How to calculate the area of a triangle from coordinates. Includes example code in Python.

The pythagorean theorem can be used to find the length of the hypotinuse given the length of the other two sides. Includes example code written in Python

A diagonal matrix is a type of symmetric matrix in which every element is set to 0 apart from the main diagonal.

The dot product is a method of multiplying two vectors and receiving a number as the result. includes example code in Python.

The dot product is a method of multiplying a row and column vector and receiving a number as the result. includes example code in Python.

How to refer to elements in a matrix, with example code in Python and LaTeX

An identity matrix is a matrix in which all elements along the main diagonal are equal to 1 and all other elements are 0. includes example code in python

A matrix is a rectangular group of numbers (or symbols) with a given number of rows and columns. Includes example code in Python and Latex.

Matrices can be added to produce new matrices, this is only possible if the order of the matrices is the same. Includes example code in Python.

Matrix Multiplication, or matrix product, is a method of multiplying two matrices to produce a third matrix. Includes example code in Python.

When transposing a matrix, each row in the original matrix is used as a column in the transposed matrix. includes example code written in python.

Position vectors are vectors that represent fixed locations in space. They represent the vector needed to get from the origin to a specific location.

Row and Column vectors are special types of matrices which have only one column or row. includes example code in Python.

To multiply a matrix by a number (scalar), you multiply each element by that number. Includes example code in Python.

A symmetric matrix is a matrix whose transpose is equal to itself.

Introduction to creating, using, and combining transformation matrices to transform vectors in two and three dimensions.

Vectors can be added to produce new vectors, this is only possible if the vectors have the same number of elements. Includes example code in Python.

The Vector Outer Product is a method of multiplying two vectors and receiving a matrix as the result. Includes example code in Python.

To scale a vector by a number, you multiply each component of the vector by that number. Includes example code in Python.

Vectors are mathematical objects which represent change. They are the complement to coordinates, which represent fixed points. Includes example code in Python.

Mathematical models describe relationships between inputs and outputs and can be used for predictions.

An introduction to the sequence 2n + 1 and its recursive midpoint property, including example code in Python.

Given the two numbers: x and y, we can say that x divides y if there is third number z which forms the equality x * z = y. includes example code in Python.

An overview of the properties of divisibility. Includes example code in Python.

A function is a mapping from elements in one set to elements in a second set. Includes example code in Python.

An introduction to the set of integers and the set of real numbers. Includes example code in Python.

Functions can be classified by how they map elements between the domain and codomain. Three types of mappings are: Injections, Surjections, and Bijections.

If f is a function, then its inverse function g is defined as the reverse of the mapping created by f.

An ordered pair is not a type of set. An ordered pair may contain duplicate elements, and its order is important. Includes example code in Python.

A set is a collection of elements, it is unordered, and every element is unique. Includes example code in Python

An introduction to the notation for sets of ordered pairs of integers and real numbers.

The mean is a method of finding the average of a list of numbers. It is calculated by the sum divided by the count. Includes example code in Python.

Determine the error between two sets using the Mean Absolute Error. Includes example code in Python.

Determine the error between two sets using the Root Mean Squared Error. Includes example code in Python.

sin, cos, and tan describe relationships between the angles and sides of a right angled triangle. Includes example code in Python.

A proof of the mathematical identity that sin^2x + cos^2x = 1