Building a Quantitative Finance Math Foundation

# Pre-requisite math books, to the pre-requisite math needed to become a front desk quant


# Pre-requisite math books, to the pre-requisite math needed to become a front desk quant












This question is about the pre-requisites to the pre-requisite math needed to become a front desk quant. I have done research online and I found that there are a lot of recommended books as a pre-requisite to become a quant. A great answer has been given by Daneel Olivaw in this thread. Some of them are

- Options, Futures and Other Derivatives -- John Hull

- Stochastic Calculus for Finance I: The Binomial Asset Pricing Model -- Steven Shreve

- Stochastic Calculus for Finance II: Continuous-Time Models -- Steven Shreve

- Stochastic Differential Equations -- Bernt Oksendal

- Analysis of Financial Time Series -- Ruey S. Tsay

However, it seems like I'd need background in basic math to be able to study any of the above. The pre-requisite math has pre-requisites! This brings me to my question. Which books are pre-requisites to the pre-requisite math needed to become a quant?

Specifically, it would be great if you can comment on the following list as to whether you think I'd need it or not, to be able to study the advanced math needed to become a quant.

- Principles of Mathematical Analysis -- Walter Rudin

- Probability and Measure -- Patrick Billingsley

- Real and Complex Analysis -- Walter Rudin

- Linear Algebra Done Right -- Sheldon Axler

- Ordinary Differential Equations -- Arnold

- Partial Differential Equations -- Lawrence Evans

Please let me know about your opinion about the pre-requisites to the pre-requisite math needed to become a quant. Specifically, I would greatly appreciate if you can just modify the above list for me.

## Answer by oliversm (score 12, accepted)

https://quant.stackexchange.com/a/54512

## Really you need a degree

Reading any one book from the above will not set you up. Furthermore, you will find yourself trapped in a cycle, where really none of the books you suggested can be read in isolation. Taking for example a book on PDEs, you will quickly find you need a lot of knowledge of linear algebra if you want to approximate any of these. For linear algebra you need some functional analysis, so on and so forth. It may sound daunting, but really you need to be reading up on all of these topics incrementally and simultaneously, which is exactly what is done on a degree in maths or physics (or similar). You really do need a wide and far reaching body of knowledge, and this is why most introductions to mathematical finance are only found in postgraduate masters degrees, albeit some undergraduates will give a very light introduction which is typically void of any stochastic calculus.

## Don't read books, read lecture notes

As a solution to this, I suggest you would be much better off reading undergraduate lecture notes. This has the advantage that they tell you most of the stuff you would need to know for a first year student (or also second year material), and then nothing beyond that. Textbooks will go into far too much material if you plan to read them cover to cover, and hence you have little idea of when to stop reading a textbook. (Use textbooks to supplement lecture notes). For the core of finance you need an array of items, namely (and in order of should be learnt and suggested undergraduate year material in parentheses) linear algebra(2), ODEs(1), PDEs(2), probability theory(1), statistics(1), SDEs, financial modelling.