Posts Tagged ‘operation’
Tuesday, December 29th, 2009
How to Construct a Cayley Table
Description
A detailed tutorial on how to construct a Cayley table. Step by step tutorial including several examples of how to construct a Cayley table for reference.
Overview
A Cayley table is a table that expresses the structure of a finite set. A Cayley table is set up by having the elements of the set across the first row, and numbers going in a numerical order of n + 1 starting at 1 down the first column. Sometimes the table is simply different ways the elements can be ordered. Other times is is a true table, where an operation is performed between two numbers in the space where they cross each other. However, a true Cayley table must be constructed using an identity skeleton. Once an identity skeleton for the finite set has been decided on, the Cayley table can be filled out using the identity skeleton. Since there is more than one possible identity skeleton for a finite set, you may have to go through a trial and error process until you find the right one.
Tags: addition, Cayley, chart, column, cross, discrete math, division, elements, error, finite, graph, identity, multiplication, operation, order, process, row, set, skeleton, subtraction, table, trial
Posted in Discrete Math | No Comments »
Friday, November 20th, 2009
How to Pick Variables
Description
A detailed tutorial on how to pick variables. Step by step tutorial including several examples of how to pick variables for reference.
Overview
Variables are letters picked to represent unknown values in expressions and equations. Usually they are lowercase, but they can be made uppercase. When trying to pick a variable, you must choose wisely. x is the most common variable, followed by n. x is picked because people associate it with the unknown, and n is picked because it stands for “number.” The variable should be easily recognizable – you should not use a variable that looks like another number or some symbol of a mathematical operation. You should check to see what is included in your equation – for instance, m stands for slope, so if you are doing an equation with slope you need to pick a different variable to avoid confusion. And you should always pick a variable that makes sense – the first letter of your subject matter usually works quite well.
Tags: a, algebra, b, c, choose, equation, expression, lowercase, m, mathematical, n!, number, operation, slope, symbol, unknown, uppercase, value, variable, variables, x, y, z
Posted in Algebra | No Comments »
Thursday, November 5th, 2009
Definition of an Operand
Description
A detailed tutorial on the definition of an operand. Step by step tutorial including several examples of an operand for reference.
Overview
An operand can be any number. However, a number is only called an operand when there is some kind of operation being performed on it. There are simple operands and complex operands. A simple operand is what people call an operand – just one number. A complex operand is an operand that consists of an operation inside it, and therefore has at least 2 operands inside the first operand.
Tags: addition, arithmetic, complex, division, exponents, multiplication, number, operand, operation, order, parenthesis, simple, subtraction
Posted in Arithmetic | No Comments »
Thursday, November 5th, 2009
Transpose of a Vector Explained
Description
A detailed tutorial on the transpose of a vector. Step by step tutorial including several examples of the transpose of a vector for reference.
Overview
The transpose of a vector is very similar to the transpose of a matrix, because even though the function the operation is being performed on changes, the operation itself doesn’t change. When you transpose a vector, it is just a way of saying the the column of your vector becomes a row, or the row of your vector becomes a column. Transposing vectors is not done very often, but it is still an important part of linear algebra.
Tags: algebra, angle, arrow, change, columns, flip, function, operation, ray, reflect, rows, transpose, vector
Posted in Algebra | No Comments »
Tuesday, October 27th, 2009
The Inverse of Relations
Description
A detailed tutorial on the inverse of relations. Step by step tutorial including several examples of the inverse of relations for reference.
Overview
Inverse is a term you should be familiar with. An inverse operation is one that undoes the original operation. But what is an inverse relation? When you take the inverse of a relation, you are switching the endpoints in every ordered pair in the original relation. For each ordered pair in the relation, instead of being written as (x, y) it will now be written as (y, x).
Tags: cartesian, coordinates, discrete math, endpoint, inverse, operation, ordered pair, relations, x, y
Posted in Discrete Math | No Comments »
Tuesday, October 27th, 2009
Cartesian Products in Set Theory
Description
A detailed tutorial of Cartesian products in set theory. Step by step tutorial including several examples of Cartesian products in set theory for reference.
Overview
A Cartesian product is an operation that can be performed in set theory. It is named not for the multiplication that occurs, but for the way the resulting set is written: it is written in ordered pairs, just like Cartesian coordinates. Two sets are said to be multiplied, such as A and B. Whichever set is written first in the operation has its first coordinate written with the second coordinate of the second set. This continues until all coordinates have been used at least once.
Tags: cartesian, coordinates, discrete math, element, multiplication, operation, ordered pair, product, set, subset, theory
Posted in Discrete Math | No Comments »
Friday, October 23rd, 2009
Introduction to Vector Space
Description
A detailed tutorial on vector space. Step by step tutorial including several examples of vector space and how to solve for vector space for reference.
Overview
Vector space is simply a structure in mathematics that is formed by a collection of vectors. Vector space can be calculated using vector addition and scalar multiplication. Vector space is very dependent on the definition of a vector. Some vectors are simply arrows on a fixed plane. But in general, the term vector just means there is an object for which two operations can be performed. The definition of vector space is defined in algebraic terms, as opposed to the geometric terms that can sometimes be applied.
Tags: addition, algebra, arrow, collection, definition, Geometry, multiplication, object, operation, plane, scalar, space, vector
Posted in Algebra | No Comments »
Thursday, October 8th, 2009
Introduction to Inverse Operations
Description
A detailed tutorial on the different inverse operations. Step by step tutorial including several examples of the different inverse operations for reference.
Overview
Inverse operations are operations that undo each other – for example, if you do something a problem, and then use the inverse operation, it should be like it never happened. Common inverse functions are addition and subtraction, multiplication and division, square roots and squaring, and logarithms and exponents.
Tags: addition, arithmetic, division, exponent, inverse, logarithm, Math, multiplication, operation, square roots, squaring, subtraction
Posted in Arithmetic | No Comments »
