Introduction
I, and I assume other students, often find learning experience enhanced when the context of the study, i.e. origin and the application, clearly visible. (e.g. Students like psychology class - it's about themselves) And it is with this intent of identifying the context of linear algebra I sought to compile articles and notes for the project.
I sought forth to identify an individual responsible for the invention of linear algebra, a progenitor of the principles of linear algebra as Newton was to Calculus (or was he?). I no longer think of doing so. Theorems and rules are attributed to single/group of mathematicians; linear algebra, I think, cannot. Rather, linear algebra appears to be a fundamental faculty in mathematics, and as I lend Professor Uli's words, "Linear algebra to mathematician is what addition and multiplication is to non-mathematicians." Perhaps as one cannot find a sole author of a particular language, one cannot find one for linear algebra.
In the search for application, few applications of matrix theory are readily noted, including its use in the Google's PageRank algorithm and alternate representation of geometry/graphs. But I'm rather unsatisfied with such selections. What I mean by the previous statement is that I may have used and will use the term linear algebra and mathematics indiscriminately in my deciding the applications of linear algebra because I do not understand both well. I doubt that my chosen applications of linear algebra will be an application of linear algebra and nothing else, and am afraid that if I take such singular position, I will not be satisfied. I don't plan on weighing too much of my time on the applications.
Then, what will I actually do if inventor of algebra is undefinable and the application of linear algebra is unidentifiable? I will compile brief biography of intriguing mathematicians who may have had some say in the advancement of linear algebra. I may also try to write few articles on linear algebra and its historical development. But most importantly, I seek to write about mathematics- from a very normal college student's point of view. That would be my very own context in learning linear algebra.
It is quite hard to make any statement regarding mathematics since I have only slightest idea of its nature, but I would like to attempt, for the sake of introducing what I think of mathematics: Perhaps the entire construct of mathematics may have begun with the sole purpose of application- to count the number of fruit, , share harvests, collect taxes. Mathematics was a reflection of the physical world into a numerical form that our logical minds can construe, and it was useful once the findings in this alternative universe was translated back into the language of the physical world. I think that mathematics has matured to the point where it has become more than a mirror image of the physical world, and reveals things that cannot be translated in the language of the physical world. It is complete.
I find this following quote intriguing:
"In adolescence, I hated life and was continually on the verge of suicide, from which, however, I was restrained by the desire to know more mathematics." - Bertrand Russell
I don't really appreciate the study of mathematics as he does; I think I only like the idea of appreciating mathematics as I read the works and stories of great mathematicians. However, I do generally like mathematics. And I will find it pleasant to like mathematics much more, and this project will be one of many attempts to appreciate mathematics.
