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Programme: BScHons Mathematics of Finance

Faculty of Natural and Agricultural Sciences
Minimum duration of study: 1 year
Total credits: 135

Programme information

Renewal of registration

  1. Subject to exceptions approved by the Dean, on the recommendation of the head of department, and in the case of distance education where the Dean formulates the stipulations that will apply, a student may not sit for an examination for the honours degree more than twice in the same module.
  2. A student for an honours degree must complete his or her study, in the case of full-time students, within two years and, in the case of after-hours students, within three years of first registering for the degree and, in the case of distance education students, within the period stipulated by the Dean. Under special circumstances, the Dean, on the recommendation of the head of department, may give approval for a limited extension of this period.

In calculating marks, General Regulation G.12.2 applies.

Apart from the prescribed coursework, a research project is an integral part of the study.

Admission requirements

An appropriate BSc or equivalent Bachelor's degree with a minimum of 60% for all Mathematics/Applied mathematics modules at third-year level. In the selection procedure the candidate's complete undergraduate academic record will be considered. In particular, it is required that the candidate has completed real analysis at third-year level and linear algebra on second-year level each with a mark of at least 60% (UP modules WTW 310 and WTW 211 / WTW 221).

Promotion to next study year

The progress of all honours candidates is monitored biannually by the postgraduate coordinator/head of department. A candidate’s study may be terminated if the progress is unsatisfactory or if the candidate is unable to finish his/her studies during the prescribed period.

Pass with distinction

The BScHons degree is awarded with distinction to a candidate who obtains a weighted average of at least 75% in all the prescribed modules and a minimum of 65% in any one module.

Minimum credits: 135

Minimum credits:  135

Core credits:         120

Elective credits:      15

Other programme-specific information:

WTW 732 and WTW 762 are presented as weekly lectures together with some extra block lectures.

Core modules

WTW 710 Functional analysis 710 Credits: 15.00

Module content:

An introduction to the basic mathematical objects of linear functional analysis will be presented. These include metric spaces, Hilbert spaces and Banach spaces. Subspaces, linear operators and functionals will be discussed in detail. The fundamental theorems for normed spaces: The Hahn-Banach theorem, Banach-Steinhaus theorem, open mapping theorem and closed graph theorem. Hilbert space theory: Riesz' theorem, the basics of projections and orthonormal sets.

WTW 732 Mathematical models of financial engineering 732 Credits: 15.00

Module content:

Introduction to markets and instruments. Futures and options trading strategies, exotic options, arbitrage relationships, binomial option pricing method, mean variance hedging, volatility and the Greeks, volatility smiles, Black-Scholes PDE and solutions, derivative disasters.

WTW 733 Numerical analysis 733 Credits: 15.00

Module content:

An analysis as well as an implementation (including computer programs) of methods are covered. Numerical linear algebra: Direct and iterative methods for linear systems and matrix eigenvalue problems: Iterative methods for nonlinear systems of equations. Finite difference method for partial differential equations: Linear elliptic, parabolic, hyperbolic and eigenvalue problems. Introduction to nonlinear problems. Numerical stability, error estimates and convergence are dealt with.

WTW 734 Measure theory and probability 734 Credits: 15.00

Module content:

Measure and integration theory: The Caratheodory extension procedure for measures defined on a ring, measurable functions, integration with respect to a measure on a ?-ring, in particular the Lebesgue integral, convergence theorems and Fubini's theorem.
Probability theory: Measure theoretic modelling, random variables, expectation values and independence, the Borel-Cantelli lemmas, the law of large numbers. L¹-theory, L²-theory and the geometry of Hilbert space, Fourier series and the Fourier transform as an operator on L², applications of Fourier analysis to random walks, the central limit theorem.

WTW 762 Mathematical models of financial engineering 762 Credits: 15.00

Module content:

Exotic options, arbitrage relationships, Black-Scholes PDE and solutions, hedging and the Miller-Modigliani theory, static hedging, numerical methods, interest rate derivatives, BDT model, Vasicek and Hull-White models, complete markets, stochastic differential equations, equivalent Martingale measures.

WTW 764 Stochastic calculus 764 Credits: 15.00

Module content:

Mathematical modelling of Random walk. Conditional expectation and Martingales. Brownian motion and other Lévy processes. Stochastic integration. Ito's Lemma. Stochastic differential equations. Application to finance.

WTW 792 Project 792 Credits: 30.00

Module content:

Consult Department.

WTW 795 Project 795 Credits: 30.00

Module content:

Consult Department.

Elective modules

LMO 710 Linear models 710 Credits: 15.00

Module content:

Projection matrices and sums of squares of linear sets. Estimation and the Gauss-Markov theorem. Generalised t- and F- tests.

LMO 720 Linear models 720 Credits: 15.00

Module content:

The singular normal distribution. Distributions of quadratic forms. The general linear model. Multiple comparisons. Analysis of covariance. Generalised linear models. Analysis of categorical data.

MVA 710 Multivariate analysis 710 Credits: 15.00

Module content:

Matrix algebra. Some multivariate measures. Visualising multivariate data.  Multivariate distributions. Samples from multivariate normal populations. The Wishart distribution. Hotelling’s T ² statistic. Inferences about mean vectors.

MVA 720 Multivariate analysis 720 Credits: 15.00

Module content:

The matrix normal distribution, correlation structures and inference of covariance matrices. Discriminant analysis. Principal component analysis. The biplot. Multidimensional scaling. Exploratory factor analysis. Confirmatory Factor analysis and structural equation models.

WTW 750 Mathematical optimisation 750 Credits: 15.00

Module content:

Classical optimisation:  Necessary and sufficient conditions for local minima.  Equality constraints and Lagrange multipliers.  Inequality constraints and the Kuhn-Tucker conditions.  Application of saddle point theorems to the solutions of the dual problem.  One-dimensional search techniques.  Gradient methods for unconstrained optimisation.  Quadratically terminating search algorithms.  The conjugate gradient method.  Fletcher-Reeves.  Second order variable metric methods:  DFP and BFCS.  Boundary following and penalty function methods for constrained problems.   Modern multiplier methods and sequential quadratic programming methods.  Practical design optimisation project.

WTW 763 Finite element method 763 Credits: 15.00

Module content:

An analysis as well as an implementation (including computer programs) of methods is covered. Introduction to the theory of Sobolev spaces. Variational and weak formulation of elliptic, parabolic, hyperbolic and eigenvalue problems. Finite element approximation of problems in variational form, interpolation theory in Sobolev spaces, convergence and error estimates.

WTW 772 Mathematical methods and models 772 Credits: 15.00

Module content:

This module aims at using advanced undergraduate mathematics and rigorously applying mathematical methods to concrete problems in various areas of natural science and engineering.
The module will be taught by several lecturers from UP, industry and public sector. The content of the module may vary from year to year and is determined by relevant focus areas within the Department. The list of areas from which topics to be covered will be selected, includes: Systems of differential equations; dynamical systems; discrete structures; Fourier analysis; methods of optimisation; numerical methods; mathematical models in biology, finance, physics, etc.

WTW 776 Partial differential equations of mathematical physics 776 Credits: 15.00

Module content:

Field-theoretic and material models of mathematical physics. The Friedrichs-Sobolev spaces. Energy methods and Hilbert spaces, weak solutions – existence and uniqueness. Separation of variables, Laplace transform, eigenvalue problems and eigenfunction expansions. The regularity theorems for elliptic forms (without proofs) and their applications. Weak solutions for the heat/diffusion and related equations.