Fourier series; Vector calculus; Laplace transforms; Fourier transforms;  Special functions.

Differential equations and classifications - first order differential equations; the existence and uniqueness theorem; second and higher order linear differential equations; power series solutions; Legendre

 polynomials, Bessel functions; numerical methods.

Introduction to actuarial science; measurement of interest; solutions of  problems in interest, basic annuities; more general annuities, yield rates, amortization schedules and sinking funds, bonds and other securities, practical applications.

The course will consist of a mixture of lectures and practical work (which will be assessed by the student’s completion of practical assignments to be submitted); Computer practical sessions in which the statistical package R, will be used to analyse the data. This will be the basis on which continuous assessment will be conducted. The lectures will focus on statistical modelling, including selection of appropriate models, the analysis and interpretation of results and diagnostics. Exploratory and graphical techniques will be considered, as well as formal statistical procedures.

This course will enable the students to perform a range of nonparametric methods and robust procedures that do not assume that the sample data are from pre-specified families of distribution.

In this course, we take a more fundamental approach to estimation and quantifying the accuracy of estimates. There will also be some graphical interpretation with some examples and exercises making use of the statistical computer package R.

This is a compulsory level II course which is an important foundation course in actuarial science. Candidates should master the fundamental concepts of actuarial and financial mathematics and its simple applications. This course allows the candidate to begin preparation for the professional examinations (the Society of Actuaries Actuarial Models examination, Exam 3 of the Casualty Actuarial Society, and the Faculty/Institute of Actuaries Contingencies examination).

This is a compulsory level II course which is an important foundation course in actuarial science and finance. Candidates should master the fundamental concepts of financial mathematics and its simple applications. This course allows the candidate to begin preparation for the professional Financial Mathematics examinations (the Society of Actuaries course FM and the faculty/Institute of Actuaries CT1 exam) as well as the Quantitative Methods section of the CFA level I exam.

In this course students will be introduced to different forms of optimization problems and the various approaches that are available to solve such problems. The course will conclude with defining and solving non-linear programming problems. The course contains numerous definitions, theorems, lemmas and proofs. Examples will be interspersed throughout.

The purpose of this course is to introduce students to the methods and techniques of some key areas of mathematical models in Operations Research. This course analyzes the mathematical modeling that can be applied in solving the problems in industry, business, science and technology, management, decision support and other areas and disciplines.