The formulation, analysis and interpretation of mathematical models in various areas of application. Possible topics include population modelling,...
Discrete-time financial models and riskless asset pricing. Notion of arbitrage, martingale measure, and complete and incomplete markets. Fundamental...
Solution techniques using computational methods in matrix, differential and integral equations. Statistical simulation, Fourier and other transform...
Linear programming algorithms, duality theory and post-optimum sensitivity analysis. Integer programming. Deterministic and stochastic dynamic...
Prerequisites Permission of the department. Notes Irregular course
Geometry of curves and surfaces, curvature, geodesics, first and second fundamental forms, the Gauss Theorema Egregium and the Gauss-Bonnet theorem....
Cayley-Hamilton Theorem; real and complex inner product spaces; Spectral Theorem; bilinear and quadratic forms; canonical forms. Prerequisites...
Monoids and groups, subgroups, quotient groups and group homomorphisms: groups acting on sets, conjugacy and the class equation; the Sylow theorems;...
Sigma-algebras of sets; set functions; outer measures, measurable sets and Lebesgue measure; Riemann and Lebesgue integrals; convergence in measure.
Conditional expectations, sigma-algebras, and filtrations; martingales and stopping times; Gaussian processes and Brownian motion; stochastic...
Hyperbolic, parabolic and elliptic differential equations; boundary value problems of applied mathematics including such partial differential...
Topological spaces: bases and subbases of topologies; closures and interiors; subspaces, continuity; the quotient topology; product spaces; the...
Continuous-time financial models and riskless asset pricing. Black-Scholes theory. Arbitrage free pricing of European, American, and exotic options....
Numerical methods used in financial engineering and risk management, including numerical solutions of ordinarily differential equations, finite...
Rings; subrings, quotient rings and ring homomorphisms; ideal theory; polynomial rings; integral domains and divisor theory; fields and field...
A detailed study of a topic under faculty supervision including the submission of a formal report.
Prerequisites Permission of the department.† Notes Irregular course
An introduction to modelling tools used in modern applications of mathematics, with examples from the applied sciences and finance. The course will...
Completion of an appropriate individual project under faculty supervision, including submission of a final report and presentation in a department...
Markov Chains in discrete and continuous time; birth-death processes; renewal theory; renewal-reward theory; Markov processes; stationary processes;...