Understanding english syntax mathematically—which demands strictness—is what I want to achieve. However, a wide range of choices I can make upon selecting a book covering related fields makes me puzzled in that I have no idea what is the right way—what are the extensively-adopted steps—to study english syntax in scientific approach. In particular, syntactic theory seems to cover most of my interests but it turns out to be too general to study english syntax only. As calculus is considered one of the prerequisites for mathematical analysis, I wish to know what are the prerequisites for learning english syntax and what are considered classic textbooks covering english syntax and its prerequisites.
There is no mathematics of English for you to learn, unfortunately, but for someone with an analytic bent, I think a careful study of McCawley's The Syntactic Phenomena of English, doing the exercises, would be fun and useful.
I second Lawler's recommendation of logic as the most relevant formal discipline for the study of language, and, specifically, I suggest Hans Reichenbach's text Elements of Synbolic Logic (available on line!). Reichenbach had lots of interest to say about English.
In my opinion, the most relevant area of mathematics is that connected with the Chomsky Hierarchy and context free languages.