I'm not a practitioner, so read with some skepticism, but here's my list: * Calculus * Real Analysis * Statistical Mechanics * Probability I'm not sure I h

I'm not a practitioner, so read with some skepticism, but here's my list: * Calculus * Real Analysis * Statistical Mechanics * Probability I'm not sure I have any good recommendations for Calculus, but for real analysis, I would recommend "The Way of Analysis" by Strichartz [0]. I don't have good recommendations for books on statistical mechanics, as I haven't found a book that isn't entrenched in coming from a physics perspective and teaches the underlying methods and algorithms. The best I can recommend is "Complexity and Criticality" by Christensen and Moloney [1], but it's pretty far afield of statistical mechanics and the like. Simulating percolation, the Ising model and ricepiles uses a lot of the same methods as financial simulation (MCMC, etc.). For probability, I would recommend "Probability and Computing" by Mitzenmacher and Upfal [2], "Probability ..." by Durrett [3] and Feller Vol. 1 and 2 [4] [5] for reference. I also would recommend "Frequently asked questions in Quantitative Finance" by Wilmott [6]. Also know that there's a quantitative finance SO [7] that might be helpful. [0] https://www.amazon.com/Analysis-Revised-Jones-Bartlett-Mathematics/dp/0763714976 https://www.amazon.com/Analysis-Revised-Jones-Bartlett-Mathe... [1] https://www.amazon.com/COMPLEXITY-CRITICALITY-Imperial-College-Advanced/dp/186094504X https://www.amazon.com/COMPLEXITY-CRITICALITY-Imperial-Colle... [2] https://www.amazon.com/Probability-Computing-Randomization-Probabilistic-Techniques/dp/110715488X https://www.amazon.com/Probability-Computing-Randomization-P... [3] https://www.amazon.com/Probability-Theory-Examples-Durrett-Hardcover/dp/B008CM9LJY https://www.amazon.com/Probability-Theory-Examples-Durrett-H... [4] https://www.amazon.com/Introduction-Probability-Theory-Applications-Vol/dp/0471257087 https://www.amazon.com/Introduction-Probability-Theory-Appli... [5] https://www.amazon.com/Introduction-Probability-Theory-Applications-Vol/dp/0471257095 https://www.amazon.com/Introduction-Probability-Theory-Appli... [6] https://www.amazon.com/Frequently-Asked-Questions-Quantitative-Finance-ebook/dp/B003YJEZQE/132-9748153-1044354 https://www.amazon.com/Frequently-Asked-Questions-Quantitati... [7] https://quant.stackexchange.com/ https://quant.stackexchange.com/