# Mathematical Skills

Minimum level of mathematical skills required for the School of Maths MSc programmes.

You will need an aptitude for mathematics for our MSc programmes and should have done some mathematics as part of your university degree. The following is the level of mathematics you will require for the OR MSc programmes. If you are a student of one of the School's other programmes you may require a very much higher level of mathematics skills.

It is important that you have mastered the items in **bold **before starting the programme.

- Algebra:
**Rearranging and simplifying expressions****Equalities and inequalities**- Sequences: limits and series

- Matrices:
**Matrix operations: multiplication, transposition, inversion****Determinant of matrix, nonsingularity**

**Linear Algebra:****Solving systems of simultaneous linear equations****Scalar product, norms****Linear dependence**

**Functions of one variable:****Plotting graphs of functions****Linear, quadratic, logarithmic and exponential functions****Differentiation: critical points; classifying minimizers/maximizers****Taylor expansion****Integration: area under a curve**- Continuity
- Differentiability

- Functions of several variables:
**Differentiation, partial derivatives****Gradient, Hessian, necessary and sufficient conditions for a minimizer/maximizer****Taylor expansion**

**Convexity:****Convex sets****Convex and concave functions**

**Elements of Probability Theory:****Random variables: expected value, variance****Distributions: binomial, exponential, normal, Poisson**