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First, my notation. $K$ is the strike price, $S$ is the stock price, $r$ is the continuously compounded risk-free rate, $T$ is time at expiration, $t$ is time at issue, $\sigma$ is volatility, $\delta$ is continuously compounded dividend rate. The Black-Scholes formula for a European call is $C = Se^{-\delta (T-t)} N(d_1) - Ke^{-r(T-t)} N(d_2)$ $d_1 = ... 4 All the topics you've mentioned are wonderful and shouldn't be eschewed by reading some finance-oriented review book. I recommend these instead. Linear algebra: Hoffman and Kunze and Halmos Set theory: Halmos Measure theory: Rudin and Tao 3 I would recommend the books from Steven Shreve. Here is a link to some one of his older online pdf's (1997 but nevertheless true) so you can check if that fits the bill. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.137.6951&rep=rep1&type=pdf 3 Many of the strategies are motivated by objective functions (contour integrals) in the complex plane and the elements of complex linear spaces, so I'd recommend at least for an applied understanding: Saff, E. B., and Snider, A. D. Fundamentals of Complex Analysis with Applications to Engineering, Science and Mathematics. In addition to Saff and Snider, I ... 1 The following paper gives a simple derivation of the BSM (via a simple integration approach instead of the classical PDE approach) and the Greeks plus some intuition for each: Derivation and Comparative Statics of the Black-Scholes Call and Put Option Pricing Formulas by Garven, J. You find the derivation of the Greeks in chapter 4 (called "comparative ... 1 Crouhy, Mark and Galai's book Risk Management is about all aspects of risk management for investment banks, including credit risk of course. If you need to focus on one book, it is this one. 1 IMHO, I suggest you to read: Sironi, Andrea, and Andrea Resti. Risk management and shareholders' value in banking: from risk measurement models to capital allocation policies. Vol. 417. John Wiley & Sons, 2007. I studied that during the university for my risk management classes and I still find it enlightening and informative. The mathematics ... 1 I have heard good things about Epps but haven't read it. Hull is aimed at less technical people and can get a bit turgid. I have my list of recommended books with discussion at http://www.markjoshi.com/RecommendedBooks.html 1 You can find the solution here: http://www.wiley.com/legacy/wileychi/pwiqf2/supp/c02.pdf For all solutions see my answer here: http://quant.stackexchange.com/a/16061/12 1 Let's think about it like this:$V(E,T) = \int_E^{\infty} (x-E)^{+} \rho (x) dx$Then$\frac{\partial C}{\partial E} = \int^\infty_E \rho(x) dx$and$\frac{\partial^2 C}{\partial K^2} = \rho(K)\$ Ill leave you to interpret these quantities. Hint, what is the defintion of the value of a contingent claim?