Book Title: An Introduction to Forcing (for people who don't care about foundations.)
Synopsis: Forcing is one of the most amazing techniques in use today, and it offers amazing insight into how objects in mathematics can be constructed. The aim of this book would be to focus on the tools and methods of Forcing, and provide examples of constructions which highlight the intrinsic beauty that can be found hiding under the surface of a forcing argument. Moreover, it would highlight the practical applications of, and sense of naturalness the "Forcing Perspective" brings to inductive mathematical constructions (which might be outside the domain of set-theoretic interest.)
Reason For Wanting to Write It: When I first learned about Forcing, the first thing that struck me was "Why the hell has no one ever told me about this? What the hell!? This is AWESOME!" That sense of awe has stayed with me throughout my very short "career." So the book would be a way for me to share this view with other mathematicians who don't really care all that much about "set theory", "category theory", or "foundations" (just like I did before I learned about independence proofs, etc.) Moreover, the aim would not be to convert them to some relativist view of mathematics, but to just show them how directly linking the logical structure of an object with its construction can open new doors, and add much needed perspective to any field.
When Would It Get Written: Honestly, not now, and not in the near future, maybe 10 10/20 years. The reason for this is, I just don't know enough yet, I'm still a student. That being said, I must admit, I am most likely not the first person anyone would pick to write such a book. However, if I was ever presented with the opportunity I would take it in a heartbeat. To me the importance of the ideas and perspective for mathematics as a whole out weigh the possible huge list of errors and corrections that would follow such a book (if written by me that is).
PS: if there are any spelling or grammar errors, feel free to fix them.
