If you are a complete beginner to the world of quantitative finance, I suggest you take a look at my newbies guide first, then come back here.
The following topics are discussed on QuantStart:
Algorithmic trading is a rapidly growing area, both in the quant fund industry and in the retail trader space. To become a successful algorithmic trader requires a solid background in many topics.
This is the place to start if you are looking for guidance on how to accelerate your quant career. I've discussed changing careers, PhDs, MFEs and as well as the different types of quant roles.
The following lists of books will get you up to speed on how to become a quant. I've broken them down into Maths Finance, C++, Python and Interview Guides. If you want to see in depth book reviews, check out the section below.
The areas of quantitative finance and data science both make heavy use of statistical inference and machine learning.
The binomial model is a great way to introduce options pricing. Although the method is rarely used computationally, it provides good intuition on how options pricing works.
You can't do quantitative finance without stochastic calculus. The following articles discuss the relevant stochastic calculus you need to understand the famous Black-Scholes equation derivation.
The Black-Scholes equation is a partial differential equation (PDE). In order to solve it you can use numerical discretisation techniques such as Finite Difference Methods. The following articles walk you through the basic techniques.
As with stochastic calculus, you really cannot avoid learning C++ for pricing derivatives! Love it or hate it, it is essential. Although the following articles won't teach you how to program from scratch, I will point out intermediate to advanced features that you can impress interviewers with when you apply for that banking role!
If you are more interested in becoming a quantitative trader in a hedge fund, then Python is something you definitely need to know. End-to-end trading systems are now being built entirely in Python, so I've written some articles to help you get started.
I've reviewed some of my favourite Quant Finance books below. If you are interested in any of the following titles then please take a look.