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 From time to time people email me asking how to get started as a quant. While there are a number of fields that comprise the quant discipline and no list can be all-inclusive, if you are going to be interviewing for a quant position, you may wish to be conversant in the following areas: 

• Finance and Financial Engineering, including complex financial derivatives and valuations, volatility surfaces and smiles, replication, arbitrage and equilibrium pricing models, CAPM, APT, Fama-French models and possibly risk management concepts depending on the area you’ll be supporting.

• Statistics and Probability, at a fairly deep level with a good knowledge of distributions, maximum likelihood theory and perhaps empirical distribution fitting, tests for normality and fitting of joint distribution using tools such as copulas, how to perform out of sample tests, properties and expectation of random variables, correlation and covariance and so on.

• Strong mathematics skills in areas including stochastic calculus, including martingales, markov processes (quick! What is the difference between a martingale and a markov process?), Ito’s lemma and so forth as well as ordinary calculus, differential equations, numerical methods, linear algebra and possibly a little computational complexity, algorithm analysis and optimization.

• Econometrics – properties of ARCH, GARCH, detecting the order of an AR/MA process and so on, stationary and non-stationary variance and how to test and correct for the same if need be, transformations, random walks, unit root tests and so forth.

• Knowledge of several computer packages, operating systems and languages including SAS, S-Plus, R, Matlab; expertise in a programming language such as C++, C# and/or Java, and experience with a non-Windows operating systems such as Unix.

• Detailed knowledge of capital markets may be required, including understanding of credit derivatives, mortgage securities, fixed income and detailed knowledge of various interest rate models, depending on where you will be interviewing.

• Understanding of simulation techniques such as generating simulations from various distributions and inverse transform theory, details of the Monte Carlo method and how simulation is used to value various financial instruments (also when you need to simulate as opposed to using other methods), possibly including variance reduction methods; random and pseudo-random number generation techniques, the pros and cons of various techniques, extreme value theory and so forth.

This should get you started.  Good luck, and if you have questions, just post them in the comments section.