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Browse this excellent & concise book, which starts with a few practical problems to test your math background; if you pass, it'll take from Forwards, to Bermudan Swaptions in only about 150 pages!
Blyth, S.J. (2013), “An Introduction to Quantitative Finance”
Fun factoid - Blyth was the former head of Harvard's Endowment and Stats prof. He taught Stat-123 which was a jr level class at Harvard. He'd put on IR options trades via Bloomberg chat in the middle of his lectures in real time!
Anyway now it's the key to unlocking vast riches through a career as an AI researcher too, seems like a good skill to have.
Often a way to do this (which I personally dislike, but it's also objectively "fine" teaching and can be done very well) relies on "manipulation of symbols" rather than "manipulation of mathematical objects". This is a bit like like learning programming in a language that has macros but no functions. Usually, this includes teaching a set of rules ("allowed manipulations") that allows proving a contradiction, the remedy being that you just don't, perhaps by relying on your "intuition" and knowledge of the problem domain (as opposed to just the math), which only comes with experience and isn't taught systematically.
The style of teaching that I find just intolerable pretends to be doing formal math, keeps telling you that rigor is important, floods you with definitions and terms, and then just does the "macro style of math" anyway, while skipping rigorous theorem statements (let alone proofs) entirely. Unfortunately, I find this article comes pretty close to this style.