Undergraduate courses

'qualifying course'

Introduction to the Mathematics of Finance and demography

The Theory of Interest; Simple and Compound, Effective and Nominal Rates of Interest; Discounting and the Rate of Discount; Equations of Value; Annuity Theory; Analysis of the Annuity; Sinking Funds; The Force of Interest; Introduction to the Mathematics of Finance; Fixed Interest Securities; Life Table Theory; Elementary Demography.

'qualifying course'

This course comprises of the following:
Probability; conditional probability; Bayes theorem; random variables; distributions and their properties; generating functions; bivariate distributions; marginal and conditional distributions; transformations of random variables; order statistics; introduction to sampling; introduction to sums of random variables and sampling distributions.
Sums of random variables; sampling distributions; law of large numbers; Chebychev’s inequality; Central limit Theorem; point estimation; interval estimation; hypothesis testing; ANOVA ; Chi-squared tests; sufficient statistics; theory of hypothesis testing; Monte Carlo simulation; review of matrix theory; multivariate normal distribution; introduction to multiple regression.

'qualifying course'

Risk Theory

Loss distributions; parameter estimation and inference; deductibles; reinsurance; inflation; risk models; compound distributions; panjer’s recursive formula; probability of ruin; integro-differential equation; adjustment coefficient; Lundberg’s inequality; optimisation of reinsurance arrangements; reserving models; no claim discount systems; Bayesians statistics; credibility theory.

Non -Parametric Statistics

An introduction to some of the most commonly used non-parametric techniques. Items include: order statistics and their applications, the sign test and its variations; rank tests; tests for the measure of association; tests of randomness; discussion of the treatment of ties and the Kolmogorov-Smirnov test for one and two samples.

Stochastic Processes

This course is an introduction to stochastic processes, which are mathematical models for systems that evolve randomly over time or space. The course is composed of three parts. The first part exposes some general facts about stochastic processes and their properties while the two last parts focus on discrete state space Markov processes.

Regression Analysis

Multiple regressions includes theory as well as aspects of assessing model fit, such as residual analysis, outlier diagnostics and problems of model interpretation due to multicollinearity.

Time Series Analysis

The time series section covers the theory and application of exponential smoothing, Box Jenkins time series methods, including model building and model checks. An introduction to Spectral Analysis: Time series in the frequency domain.

Generalised linear Models

The rest of the module deals with applied likelihood methods generalised linear models and categorical data analysis (Logistic Regression, Poisson Regression, Negative Binomial Regression, ZIP and ZAP Models). It also includes a section on the design of experiments including background and an overview, the concept of blocking and randomisation and some designs of experiments.