Posts Tagged ‘direct’
Tuesday, December 29th, 2009
How to Identify a Disconnected Graph
Description
A detailed tutorial on how to identify disconnected graphs. Step by step tutorial including several examples of disconnected graphs for reference.
Overview
A disconnected graph is a graph where not every single vertex is connected to all other vertices. Typically, graphs will have paths from all vertices, but if there is not a direct path from each and every vertex, then it is considered to be a disconnected graph. Some common shapes that are seen that are disconnected graphs are stars, rectangles, and hexagons. The opposite of a disconnected graph is a connected graph.
Tags: closed, connected, direct, disconnected, discrete math, edge, graph, hexagon, open, opposite, path, rectangle, shape, star, triangle, vertex, vertices, walk
Posted in Discrete Math | No Comments »
Tuesday, December 29th, 2009
How to Identify a Connected Graph
Description
A detailed tutorial on how to identify connected graphs. Step by step tutorial including several examples of connected graphs for reference.
Overview
A connected graph is a graph where every single vertex is connected to every other vertex. This does not mean to simply have a clear path from one vertex to another – it means there needs to be a direct path, or an edge, between two vertices. A triangle is a commonly seen shape that is a connected graph. The opposite of a connected graph is a disconnected graph.
Tags: closed, connected, direct, disconnected, discrete math, edge, graph, hexagon, open, opposite, path, rectangle, shape, star, triangle, vertex, vertices, walk
Posted in Discrete Math | No Comments »
Thursday, November 5th, 2009
Overview of the Dominated Convergence Theorem
Description
A detailed tutorial on the dominated convergence theorem. Step by step tutorial including several examples of the dominated convergence theorem for reference.
Overview
Unlike the monotone convergence theorem, the dominated convergence theorem only has one form. The official name of the theorem is Lebesgue’s Dominated Convergence Theorem, but most people just call it the dominated convergence theorem. It is considered to be a special version of the Fatou-Lebesque theorem, so Fatou’s lemma is used in direct proofs of this theorem. This theorem is also closely related to the bounded convergence theorem.
Tags: bounded proof, Calculus, convergence, direct, dominated, Fatou, form, Lebesque, lemma, monotone, special, theorem, version
Posted in Calculus | No Comments »
Thursday, October 29th, 2009
Definition of a Terminal Point
Description
A detailed tutorial on the definition of a terminal point. Step by step tutorial including several examples of terminal points for reference.
Overview
A terminal point is just a way of saying the ending point. The terminal point of a line or a figure is the point where it ends. The term terminal point is used often when talking about vectors – they end at the terminal point. The terminal point is referred as the head of the vector.
Tags: arithmetic, arrow, direct, ending, figure, head, initial, line, point, ray, segment, starting, tail, terminal, vector
Posted in Arithmetic | No Comments »
Thursday, October 29th, 2009
Definition of an Initial Point
Description
A detailed tutorial on the definition of an initial point. Step by step tutorial including several examples of initial points for reference.
Overview
An initial point is just a way of saying the starting point. The initial point of a line or a figure is the point where it begin. The term initial point is used often when talking about vectors – they start at the initial point. The initial point is referred as the tail of the vector.
Tags: arithmetic, arrow, direct, ending, figure, head, initial, line, point, ray, segment, starting, tail, terminal, vector
Posted in Arithmetic | No Comments »
Thursday, October 29th, 2009
Overview of Symmetric Relations
Description
A detailed tutorial on the property of symmetric relations. Step by step tutorial including several examples of symmetric relations for reference.
Overview
A symmetric relation can be mathematically defined as for all x, y, and z belonging to A, if x R y and y R z, then x R z. In this statement, A is a set, and R is a relation of that set. An empty set is considered to be symmetric. Since a symmetric relation is defined by a conditional sentence, a proof for the symmetric property of relations would be written as a direct proof.
Tags: conditional, direct, discrete math, empty, equal, equivalence, married, odd, proof, property, r, relation, set, symmetric, x, y
Posted in Discrete Math | No Comments »
Thursday, October 29th, 2009
Overview of Transitive Relations
Description
A detailed tutorial on the property of transitive relations. Step by step tutorial including several examples of transitive relations for reference.
Overview
A transitive relation can be mathematically defined as for all x and y belonging to A, if x R y, then y R x. In this statement, A is a set, and R is a relation of that set. An empty set is considered to be transitive. Since a transitive relation is defined by a conditional sentence, a proof for the transitive property of relations would be written as a direct proof.
Tags: conditional, direct, discrete math, divides, empty, equal, equivalence, great, greater, implies, proof, property, r, relation, set, subset, transitive, x, y, z
Posted in Discrete Math | No Comments »
Thursday, October 8th, 2009
Inverse Variation Explained
Description
A detailed tutorial on inverse variation. Step by step tutorial including several examples of inverse variation and what inverse variation is for reference.
Overview
Inverse variation states that two variables are inversely proportional if one of the variables is directly proportional with the multiplicative inverse of the other, or equivilently if their product is a constant. Inverse variation can be expressed mathematically as y = k / x, where x and y are the variables and k is a nonzero constant
Tags: constant, direct, division, inverse, k, Math, multiplicative inverse, non-zero, proportionality, reciprocal, statistics, variable, variation, x, y
Posted in Statistics | No Comments »
Thursday, October 8th, 2009
Direct Variation Explained
Description
A detailed tutorial on direct variation. Step by step tutorial including several examples of direct variation and what direct variation is for reference.
Overview
Direct variation states that given two variables x and y, y is directly proportional to x if there is a non-zero constant k such that y = k * x. The variable k is referred to as the proportionality constant or the constant of proportionality.
Tags: constant, direct, inverse, k, Math, non-zero, proportionality, statistics, variable, variation, x, y
Posted in Statistics | No Comments »
Thursday, October 8th, 2009
Combined Variation Explained
Description
A detailed tutorial on combined variation. Step by step tutorial including several examples of combined variation and what combined variation is for reference.
Overview
Combined variation refers to using both direct variation and inverse variation at the same time. Combined variation can be expressed as y = (k * x) / (z^2). Typically when both direct and inverse variation are being used, the same variable will variate directly at one point and inversely at another.
Tags: combine, combined variation, direct, inverse, k, Math, point, statistics, variable, variation, x, y, z
Posted in Statistics | No Comments »
