I have realised that I have gaps in fundamental mathematics, probability and statistics and to be honest in everything I have ever learned. Recently I spoke with my friend who was asked to evaluate double integral in polar coordinates in an interview for quant position and I realised that I could not do it anymore. Reason is that when I was younger I did not have a structure for learning and many things just faded in my memory. Now I have all my notes in my PC: university material from Financial Mathematics, 3rd year modules from Economics and Statistics degree, code libraries and my personal latex notes on different topics(I will make them available some time in the future once they are complete). However, I have nothing on basic algebra, trigonometry, calculus, engineering mathematics, probability theory, measure theory, bayesian statistics... The list goes on an on. What I realised that I have to start from the very basics to have all basic structure in my head, then move forward. It is easy to make some assumptions when you are attending taught courses and your lecturer says: "you do not have time to go into proofs as they require knowledge in measure theory(or some other topic I have never seen or can not remember).
2014-03-22. [Beecher, Penna, Bittinger] Precalculus
First book in this review part is called "Basic algebra and trigonometry"(It exists with name "Precalculus" as well). It has 1100 pages that consist of examples, graphs and exercises that will ensure one's understanding about topics covered in the book. It is simple, coherent and introduces everything in a right manner and at a right pace. Previously I jumped into advanced notes on set theory, functions, mappings and measure theory and never finished. Now I see the reason. If one can not relate it to any prior knowledge then the link is missing being more difficult to remember and comprehend. The book I mentioned starts with simple algebra and introduces all at a right time.
Say function composition. When I met this notion when looking at condensed notes at intermediate level straight after definition numerous rules on inverse functions were given in a list. While I was able to comprehend all I felt that it will not be long till I forget it. Another demotivation was that I met this on the second topic in the introduction chapter on probability theory. To complete it all when seeing these mathematical notations for the first time is suicidal. Even though I can comprehend it and have studied it all in a bit different format, this is too exhausting. This book introduced it straight after definition of simple functions and provided numerous exercises in applications so I can practise few and make sure I will remember it when I next meet it.
To sum up, it is an essential book for anybody who is willing to start from basics and fill gaps in algebra and trigonometry (if has any). I have gone through, almost, all of it (skipping parts on partial fractions and some others) and starting with Fourier analysis.
2014-03-22. [Emanuel Derman] My Life as a Quant - Reflections on Physics and Finance
Few days ago I was having a conversation with my flatmate about quantitative finance versus physics. I was trying to explain to him why finance is more exciting and rewarding to model, but somehow failed and conclusion was that physics is probably superior due to its higher purpose and less related to person's financial benefits. Then I found the following quote in the end of the book and read it out loud for him once I got home: “…physicists turned quants don’t expect too much from their theories, though many economists naively do. Perhaps this is because physicists, raised on theories capable of superb divination, know the difference between a fundamental theory and a phenomenological toy, useful though the latter may be. Trained economists have never seen a really first-class model. It’s not that physics is “better,” but rather that finance is harder. In physics you’re playing against God, and He doesn’t change his laws very often. When you’ve checkmated Him, He’ll concede. In finance, you’re playing against God’s creatures, agents who value assets based on their ephemeral opinions.They don’t know when they’ve lost, so they keep trying.”
I was not planning to review any fiction, but this book deserves to be in any financial analyst's shelf. I will not elaborate too much, but will give some thoughts about my consequent actions that will follow due to reading this book.
I will respect pragmatic modelling approaches more as until now I was stochastic calculus modelling admirer and perceived "tree" models as inferior and too simplistic. I will talk to DPD of "Msc Mathematical Trading and Finance" course I did and will strongly advise him to include this book to pre-reading list for the course. I will mention and quote this book numerous times and this follows not from the fact that the author is famous practitioner and I blindly believe in all he says but rather that his book strongly reinforced my beliefs that I have already started developing being in early stage of transferring theory into practice.
