Posts Tagged ‘complete’
Thursday, November 5th, 2009
How to Use Parametrization
Description
A detailed tutorial on how to use parametrization. Step by step tutorial including several examples of how to use parametrization for reference.
Overview
Parametrization can be used in many different branches of math, including algebra and calculus. Parametrization involves setting up parameters necessary for the complete or relevent specification of a geometric object. This means it is only used when calculating a shape or part of a shape, because that is what a geometric object is. Sometimes, this is nothing more than identifying the parameters. Other times it becomes an involved mathematical process that is used to find out what the parameters are.
Tags: Calculus, complete, decide, deciding, define, defining, differential equations, geometric, identify, identifying, parameter, parametrization, relevent, set, setting, shape, specification, vector
Posted in Differential Equations | No Comments »
Tuesday, October 27th, 2009
Introduction to Hilbert Space
Description
A detailed tutorial on on the application of Hilbert space. Step by step tutorial including several examples of Hilbert space for reference.
Overview
A Hilbert space is commonly used in vector algebra and calculus to generalize the notion of Euclidean space. It is an abstract vector space possessing the structure of an inner product that allows length and angle to be measured. Hilbert spaces are also complete, which is a property that allows enough limits in the space for calculus to be used accurately.
Tags: abstract, algebra, angle, Calculus, complete, Hilbert, inner, length, limit, product, space, structure, vector
Posted in Algebra | No Comments »
Thursday, October 22nd, 2009
Inductive Sets in Set Theory
Description
A detailed tutorial on inductive sets in set theory. Step by step tutorial including several examples of inductive sets in set theory for reference.
Overview
An inductive set is a continuous set of natural numbers that follows a basic pattern of n + 1. This means that for all numbers in the set, that number plus the number one must also be included in the set.The set does not need to include all natural numbers – that is, the set may start at any natural number provided it is greater than or equal to one. However, the set must continue to infinity or it cannot be considered an inductive set.
Tags: -1, addition, complete, continuous, discrete math, element, equal, greater, induction, inductive, infinity, mathematical, natural, numbers, one, pattern, principle, set, subset, theory
Posted in Discrete Math | No Comments »
Friday, September 25th, 2009
The Heine-Borel Theorem Explained
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.
Tags: biconditional, bounded, closed, compact, complete, discrete math, Eduard Heine, Emile Borel, equivalent, Euclidian space, finite subcover, Heine-Borel Theorem, Math, metric, spaces, subset, totally
Posted in Discrete Math | No Comments »
