Textbook for quantitative finance

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I'm looking for a book/pdf/guide to quantitative finance that contains all of the necessary mathematical prerequisites, as well as modern quantitative finance topics. Preferably something written at the advanced undergraduate/beginning graduate level.

Any recommendations are greatly appreciated. I cannot seem to find a comprehensive text that is written in a reasonably rigorous way (makes use of theorems from lin alg, probability, analysis, etc).

Thanks!

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