I am looking for a well-written, theoretically rigorous textbook that contains all the mathematics necessary to transition smoothly to a graduate course in mathematical finance.
I am graduating with a BSc in Economics from a quantitatively rigorous program but continuing my studies in mathematical finance will require a strong mathematical background. While for the program an economics undergrad is formally sufficient it is originally intended for math undergraduates.
I am now looking for a book that ideally would contain everything from highest level pre-undergraduate mathematics up until first year content of a pure mathematics undergraduate degree course; in the subjects of calculus, linear algebra, probability theory, and set theory.
For some of the more fundamental concepts it would be important that they are explored quite formally; I have the impression that the way I learned many of the basic concepts before my undergrad has been somewhat simplistic.
I am looking for the kind of book that is a "classic," that can be referred to to refresh fundamental and intermediate concepts. Something that's in every math students bookshelf.
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