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Series of lectures on mathematical analysis
Financial engineering courses and books are as follows:

Tsinghua University and Song's "Quantitative Analysis Method of Finance", this book is all about the core theory of finance, which is very thorough and helpful to clarify the thinking.

Hull's "option futures and other derivatives", the first financial project, is known as the Wall Street Bible. It's helpful to have a staff member on Wall Street, whether studying or working.