Description
A detailed tutorial on mass-energy equivalence. Step by step tutorial including several examples of mass-energy equivalence for reference.
Overview
Mass-energy equivalence is the concept that the mass of a body is the measure of its energy content. This is often expressed by a formula written by Einstein, who is also the one that proposed the idea of mass-energy equivalence. This formula is 
Description
A detailed tutorial on the transpose of a matrix. Step by step tutorial including several examples of the transpose of a matrix for reference.
Overview
When you transpose a matrix, it is simply a way of saying that you write the matrix in a different way – this creates a new matrix. There are three ways you can transpose a matrix. The first way is to write the rows of your matrix as columns instead. The second way is to write the columns of your matrix as rows instead. And the third way is to reflect your matrix by its main diagonal. All of these actions accomplish the same thing, so it does not matter which method you use. When people talk about transposing something, they are usually referring to matrices.
Description
A detailed tutorial on square matrices and how to identify them. Step by step tutorial including several examples of square matrices for reference.
Overview
A square matrix is a simple matrix in the shape of a square. It has the same number of rows and columns. Square matrices are called nxn matrces. The most common values for n are 2 and 3. Two columns and rows is the smallest amount of rows and columns a square matrix can have – matrices with only one value are not considered to be square.
Description
A detailed tutorial on logical equivalence. Step by step tutorial with several examples of what logical equivalence is and how to identify it for reference.
Overview
In the study of discrete math, it is said that two statements are logically equivalent if and only if their truth tables match. This means that for every possible combination of the antecedent and the consequent, these two statements must have exactly the same answer in order to be logically equivalent. There is only a true or false answer to this question, there is no “possibly” or “maybe”.
Description
A detailed tutorial of the Heine-Borel theorem. Step by step tutorial including several examples of the Heine-Borel theorem for reference.
Overview
The Heine-Borel theorem is a concept in math that has to do with metric spaces. It states that for a subset S of Euclidian space R^n, the following two statements are equivalent: S is closed and bounded, and every open cover of S has a finite subcover, that is, S is compact. A more simple way of writing this theorem is that a subset of metric space is compact if and only if it is complete and totally bounded. Written in that form it is a biconditional statement.
