First of all, we consider a quantitative part of economics rather than the qualitative one.
* Econometrics, namely "economic measurement", is on a base of mathematical economics and economic theory, purposed at providing emphirical contents and verification to the economic theories (on relationships par exemple).
issues: regression analysis
* Mathematical economics, which can be regarded as the "theoretical" counterpart of econometrics, explores the mathematical -- mostly statistical -- aspects of real economic systems / worlds.
issues: arbitrage
Now let's get on the fly:
* Elements: Statistical decision theory (including bay�sienne), Gaussien linear model, classic methods of estimation, ...
* Choice of model: parametric relation, non-parametric relation, variable selection, test, ...
* Monte-Carlo methods in finance
* Simulation
* Stochastic processes
...
