| My background as a mathematician likely biases this answer. Someone who has experienced life outside of academia will likely have different advice. The mathematics you will likely want to know includes: - Multivariate Calculus/Matrix Stuff/Linear Algebra - Real Analysis - Probability - Measure Theory? - Statistics 101 If you successfully took proofs-based mathematics courses in undergraduate and you've grokked "mathematical maturity" then learning these subjects is just a matter of time. These subjects for the basics tools for dealing with classical statistics. I'm not currently engaged in research but there seems to be a few major trends in the talks I've attended. - It appears that the Frequestist approach to finite dimensional models with small sample sizes is largely resolved. - The introduction of high powered computing gave new life to the analytically intractible Bayesian approach and has renewed interest in how to to Monte Carlo simulation more efficiently. - There has been a lot of work studying situation where the number of parameters is infinite or at least significantly larger than the number of samples. Eg, determining 10,000 genes from each of five people with cancer and five without and trying to identify which gene causes cancer. - Perhaps this is more machine learning but there has also been interest in how to deal with unstructured data. Traditionally the random variables have been numbers so you can say things like "Assume a citizens height is normally distributed with mean x and variance y." It's a bit more tricky to meaningfully put a distribution on the set of all email texts, or the set of all network structures etc. - There also appears to be interest (on blogs at least) about data visualisation. The point of mentioning all of these is to point out that there are a number of options available to you. Some are more pure mathsy and other more computer sciencey. Different topics will require different mathematical backgrounds. |