Math 431: Rough Draft of Notes: Course Notes

The title of this course is Geometry for Computer Applications. This course contains material which is not covered in any one particular course. Most briefly, the goal of the course is to develop algebraic data types for computer graphics. — If we take points, lines, lengths, angles, areas, etc. as the basic building blocks of graphics, then an over arching theme is to discover ways in which to represent geometric objects in a computer. Additionally, we aim to develop ways in which to represent in a computer the manner in which these geometric objects transform. It should be said plainly that this is a math course, however hardware and software consideration are certainly involved in the investigations. In particular, the practical use of abstract objects for implementation in a computer is taken as our loadstar. Furthermore we will engage in programing with mathematica. (Some mathematica programs may be as routine as elementary calculations while others may be as exciting as creating dynamical visualizations of exotic geometric structures! 1 Surveying the literature one quickly understands a primary challenge this pursuit is that the prospect of narration is insurmountable. This can be partially explained in that there are many perspectives and directions in which to approach such deep and broad and central subjects as geometry and computer engineering. Furthermore the nature of mathematical ideas ever build on one on another, in manifold directions. Aside from size and scope, another obstacle is that mathematical texts often lack much warmth of feeling. — It might not be that all agree on this point, however it is confessed here rather than debated what makes good mathematical exposition; instead, by conceding we simultaneously emphasize the essential truth that a serious student must take ownership in learning process. What remains is that there is a cost involved in learning. In this course suggestions will be made about ways in which to think about formal arguments and abstractions and references will be given to pursue notions further. In addition, we will be developing course notes to be used as primary