This module aims to develop an understanding of topics in group theory, vector calculus and multivariable calculus, of the formulation of problems involving these topics and an appreciation of applications in these areas. The module continues to develop key mathematical and numerical skills needed by a mathematical scientist.

This module aims to develop and support key mathematical, learning and professional skills needed by a mathematical scientist. It aims to consolidate and extend students' knowledge of functions and calculus that forms the basis of much of the mathematical content of the rest of the degree.

Content covers a range of current topics in OR. Indicative technical content includes data envelopment analysis, location theory, meta-heuristics, applications of mathematical programming, linear and non-linear modelling using a dedicated software package such as LINGO.

Topics include:

- Interest: Compounding, discounting and the time value of money, period compounded and continuously compounded interest rates; Discounted Cash Flow, NPV, IRR and effective interest rates, mortgages, annuities and sinking funds.
- Bonds: Coupons, rates and yields; valuation methods, maturities, duration and convexity.
- Portfolio Theory: Markowitz portfolio theory; expected return and variance of returns; market portfolio; the efficient frontier.
- Asset pricing models: The Capital Asset Pricing Model and the Fama and French three-factor model
- Derivatives: Continuous time The stochastic model of share prices, The Black Scholes Equation
- Options in practice: The binomial lattice Monte Carlo methods

Topics include:

- Vector Calculus: Grad, Div, Curl
- Line integrals, Greenâ€™s theorem in the plane
- Multiple integration: double and triple integrals
- Probability and Statistics: Binomial, Poisson and Normal distributions, confidence intervals

This module aims to provide the student with the appropriate basic mathematical background required for study in a branch of Engineering or Building.