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

  1. Options, Futures and Other Derivatives -- John Hull
  2. Stochastic Calculus for Finance I: The Binomial Asset Pricing Model -- Steven Shreve
  3. Stochastic Calculus for Finance II: Continuous-Time Models -- Steven Shreve
  4. Stochastic Differential Equations -- Bernt Oksendal
  5. 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.

  1. Principles of Mathematical Analysis -- Walter Rudin
  2. Probability and Measure -- Patrick Billingsley
  3. Real and Complex Analysis -- Walter Rudin
  4. Linear Algebra Done Right -- Sheldon Axler
  5. Ordinary Differential Equations -- Arnold
  6. 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.

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    $\begingroup$ All are good to know. IMHO 2 (Probability & measure) is most important, (1 or 3, your choice) is useful to get there. Selected parts from 6 (the more basic stuff) are useful. The others less important. Your initial goal should be "to learn Probability from a mathematically sophisticated point of view" so you can read the Shreve and Oksendal books. $\endgroup$ – noob2 May 29 at 10:39
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    $\begingroup$ Reading books is indeed essential, but linearly moving through the concepts can take a very long time, which is hard when one does not feel the subject! As an alternative, one can try problem driven/agile approach-i.e., pick a problem that is of interest to you, e.g., pricing some equity exotics or interest rates product, and try to model it- read relevant texts, code it, and read about the underlying concepts/terminology as you encounter them. In 3 to 6 months time you will have a fairly good idea of what is needed. And whatever you might have missed will be revealed by the next problem! $\endgroup$ – Magic is in the chain May 29 at 11:30
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    $\begingroup$ It could be helpful if you could add your current level of proficiency. I.e. if you need to learn probability too, Shreve is definitely a wrong way to start :) $\endgroup$ – LazyCat May 29 at 16:37
  • $\begingroup$ @LazyCat I have a PhD in EE ... I was a mixed signal analog engineer but now, I have quit and I want to become a quant. I have been trained in basic real analysis, basic probability (not measure theoretic but the dumbed down version of it), linear algebra, ODEs and PDEs. I need to learn rigorous probability before I can graduate to the books on the first list. Please do let me know if you have any suggestions. $\endgroup$ – TryingHardToBecomeAGoodPrSlvr May 29 at 18:56

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.

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    $\begingroup$ I agree wholeheartedly with this answer. On a related note, learn python. $\endgroup$ – RWP - Down by the Bay May 29 at 13:34
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    $\begingroup$ It might help to watch lectures on Youtube as well if that suits your style of learning. $\endgroup$ – Bob Jansen May 29 at 15:42
  • $\begingroup$ @RWP-DownbytheBay I had read about that somewhere. At some point, I will be taking courses by Ernie Chan one of which is based on Python based backtesting methods. But that will be after I am done with the groundwork with all the above courses and learning basic Python programming for numerical algorithms. $\endgroup$ – TryingHardToBecomeAGoodPrSlvr May 29 at 18:58

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