I ought to give some background for this. Starting my senior year of high school, I began to investigate interesting problems that showed up in my Calculus II class. I was encouraged by my teacher (special thanks to Mr. Turkington!) to work on these problems and I eventually decided to start writing up my results. I eventually began to investigate problems of my own, and I had eventually investigated over 20 different topics ranging from calculus to number theory. In all, I had written over 550 pages worth of mathematical research (not all of it was necessarily new, but I had worked on the projects independently).Â
Consequently, I decided it would be nice to consolidate all of these documents into a "book" (it is more of an "anthology" of various mathematical subjects rather than a cohesive book). In the process, I significantly improved the formatting and edited the documents. Thus far, it is somewhere around the halfway stage of completion and 700 pages long, including the unedited chapters. I do not think this is publishable in the traditional sense, not least because of the conversational tone and the fact that much of the work is not particularly interesting to mathematics as a whole. That said, I have worked on more formal publications for the truly publishable results, in particular my work on Pascal's triangle. I still think much of the material is intellectually stimulating, so I have included it below. I have also included the rest of the chapters that I have not yet edited into the new version.
H. Rajesh, Consolidated Math Doc. In prep. [PDF]