Friday, December 18th, 2009
An Overview of Topology
Description
A detailed tutorial on the mathematical study of topology. Step by step tutorial including several examples of topology for reference.
Overview
Topology is a study in mathematics that deals with space and spatial properties of objects. There are several different types of topology. The most common topics, called subtopics, are point-set topology, algebraic topology, geometric topology, and low dimensional topology. Topology may be a familiar sounding name to you – doubtless you have heard of a “topographical map,” used in science classes. However, the way the topographic map is created is with the study of math known as topology.
Tags: algebra, algebraic, dimensional, geometric, low, map, point, point-set, set, study, subtopic, topic, topological, topology
Posted in Algebra | No Comments »
Thursday, November 5th, 2009
Introduction to Linear Transformations
Description
A detailed tutorial on linear transformations. Step by step tutorial including several examples of linear transformations for reference.
Overview
A linear transformation takes place between two vector spaces. For two vector spaces V and W, there is a map T such that T(v_1 + v_2) = T(v_1) + T(v_2) for any vectors v_1 and v_2 in V, and T(a v) = a T(v) for any scalar a. Examples of linear transformation are often obtained through matrix multiplication. Linear transformations can also be injective or surjective
Tags: algebra, injective, linear, map, matrix, multiplication, scalar, space, surjective, transformation, vector
Posted in Algebra | No Comments »
Friday, September 25th, 2009
Four-Color Theorem Explained
Description
A detailed tutorial on the four-color theorem. Step by step tutorial including several examples of the four-color theorem for reference.
Overview
The four-color theorem is a concept in math that states that given any seperation of a plane into seperate regions, the regions can be colored in using at the most four colors so that no two adjacent regions have the same color. These planes are called maps, and in fact a real map is an example of one. In order for two regions to be adjacent, they must share a side. If they share a point they are not considered adjacent.
Tags: adjacent, color, four, four color map theorem, four-color, four-color theorem, Geometry, map, Math, planes, point, regions, seperate, side, theorem
Posted in Geometry | No Comments »
