Economics - how much writing?Watch
Educate me. Thanks!
Which leads on to what type of maths: in general, calculus, mainly differentiation in particular. Integration will play into the probability and statistics parts of the course, which are also quite important; depending on options this will be at a minimum more applied statistics (in econometrics type modules) but depending where you go, there may be options to take more sophisticated probability and distribution theory type courses (e.g. LSE). Matrices will also probably be common, and you'll also do complex numbers and differential equations to some extent on most courses. You may have opportunities to go more into the pure maths side which underpins the higher economic theory you would do at e.g. masters and PhD level, which would be mainly real analysis (i.e. theory of calculus) and linear algebra (i.e. theory of matrices/vectors...and some other stuff).
This might potentially follow through to things like measure theory (a rigorous formulation of integration, which underpins high level probability theory), algebra generally (that is, groups rings and fields, although I have no idea how this is relevant to economics), further differential equations and then partial differential equations (used in modelling various systems, including the Black Scholes Equation in finance) and complex analysis (like real analysis but for complex valued functions; again I don't really see the relevance to economics). Also various aspects of probability and statistics, including notably stochastic processes (used in financial mathematics and actuarial science).
The further into economics you go, the more mathematical it gets. For example, most top US grad schools expect you to have real analysis and linear algebra either on entry or by the end of the first year of the PhD (in economics). Similar coverage is likely to be expected or developed in the UK, although they may be a little less strict if your area of research isn't as highly quantitative (in the US they tend to adopt a "one size fits all" approach to training in the earlier stages of PhDs). Masters level economics will certainly expect you to be very comfortable with calculus (inc multivariable calculus and basic differential equations, which you do in undergrad) and matrices/complex numbers (although not to the complex analysis/functions or formal linear algebra level).