Abstract
This paper discusses the theory of matrices, how it was developed, how it changed, some of the applications for which it has been used, and other aspects of the issue. The writer notes how the underlying ideas are ancient and began with the Babylonians and Chinese and then resurfaced in the seventeenth century with the world of Cayley and others. Further the writer points out that the theory of matrices has led to uses in physics, chemistry, and economics as well as mathematics.

From the Paper
"Matrices are a means of visualizing mathematical concepts and relationships in graphic form. A matrix is a rectangular set of elements viewed as a single entity, identified by the number of rows and columns of which it is made. Matrices can be added or multiplied on the basis of an algebra of matrices, and one application of this sort of operation is seen in vector analysis and in the solving of systems of linear equations. The basis for the matrix is found in the Cartesian system of Rene Descartes, whose contribution to mathematics was in the development of analytical geometry, closely tied with the development of the Cartesian system of mapping on a grid or graph, for Descartes saw that a function or polynomial can be represented graphically by points."

Tags:algebra, matrices, theory

Abstract
This paper looks at the early history of the airplane, what innovations have been made since its conception, mistakes made as airplanes evolved, and what possible changes will be made in the airline industry in the future. This information is evaluated with regard to the impact airplanes have had on transportation and the transportation industry.

From the Paper
"At the end of the 1800's, several people were trying invent the airplane. In 1891, German engineer Otto Lilienthal started to experiment with hang gliders. He based his experiments on the conceptions of Sir George Cayley, who had extensively studied birds and their flight almost a hundred years earlier (invention.psychology.msstate.edu/). Cayley discovered "the lift function and the thrust function of bird wings were separate and distinct, and could be imitated by different systems on a fixed-wing craft (invention.psychology.msstate.edu/)." Lilienthal dealt with a fixed-wing glider at first, instead of a complete airplane. He made airline invention a respectable concept since he was a noted engineer. Prior to his involvement, inventors of airplanes were looked upon as crackpots and wild-eyed dreamers."

Tags:otto, lilienthal, sir, george, cayley, wright, brothers, aviation, transatlantic, propulsion, streamlining, radar