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Abstract

Graph Theory is the study of mathematical graphs used to model the relationships between a network of vertices and edges. After Euler published his work on the Konigsberg Bridge Problem, the basic concepts behind his work expanded and graph theory is used in modern mathematical research, chemical and biological science and computer engineering. This project provides a simple demonstration of the uses of modern graph theory by formulating a “plan of travel” between five major international cities: Los Angeles, New York City, London, Paris and Tokyo. The process was twofold: to find a route with the lowest cost and a route with the shortest distance. The procedure included the utilization of the four major algorithms in graph theory (Nearest Neighbor, Sorted Edges, Brute Force Method, and Kruskal’s method) to create a “plan of travel” that would model the more sophisticated technology used by computer systems like MapQuest. This project concluded by finding the route with the lowest cost (LA-Tokyo-Paris-London-NYC-LA) and the route with the smallest distance (LA-Tokyo-Paris-London-NYC-LA

برای مشاهده ی ادامه ی مطلب برین به سایت زیر: 

http://education.uncc.edu/cmste/summer%20ventures/2010%20Practical%20Applications%20of%20Advanced%20Math/Kevin%20Cheung.pdf

سلام،امیدوارم از متن زیر راجع به معرفی نظریه جدید کدگذاری خوشتون بیاد!

In the beginning ...

Coding theory originated with the advent of computers. Early

computers were huge mechanical monsters whose reliability was

low compared to the computers of today. Based, as they were, on

banks of mechanical relays, if a single relay failed to close the

entire calculation was in error. The engineers of the day devised

ways to detect faulty relays so that they could be replaced. While

R.W. Hamming was working for Bell Labs, out of frustration

with the behemoth he was working with, the thought occurred that

if the machine was capable of knowing it was in error, wasn't it

also possible for the machine to correct that error. Setting to work

on this problem Hamming devised a way of encoding information

so that if an error was detected it could also be corrected. Based in

part on this work, Claude Shannon developed the theoretical

.framework for the science of coding theory

برای ادامه ی مطلب از سایت زیر بازدید فرمایید.

http://www-math.cudenver.edu/~wcherowi/courses/m5410/codingintro.pdf