BSc Hons Mathematics & Statistics (Donghua University)

Here, we’ll present basic algebraic structures, with particular emphaisis on those relating to finite dimensional linear spaces and deepen your understanding of linear mappings. We’ll also describe inner product spaces and bilinear forms.

We'll show you analytical methods for solving ordinary and partial differential equations, so you'll develop an understanding along with technical skills in this area.

This module will:

• review the concepts of probability distributions and how to work with these
• present approaches to parameter estimation, focusing on maximum likelihood estimation, bootstrap estimation, and properties of estimators
• demonstrate hypothesis testing procedures, including classical likelihood ratio tests and computer-based methods for testing parameter values, and goodness-of-fit tests
• introduce and provide understanding of the least squares multiple regression model, general linear model, transformations and variable selection procedures
• illustrate the use of R functions for regression and interpretation of R output

This module will:

• convey the generalisation of the mechanics of single-particle systems to many-particle systems
• define the central ideas of a continuum description of material behaviour and explain relevant constraints
• ground students in the basic principles governing three-dimensional motions of rigid bodies
• convey how the ideas of continuum theory are applied to static and inviscid fluids

This module will introduce functions of a complex variable and define concepts like continuity, differentiability, analyticity, line integration and singular points. It’ll examine the important properties of such functions and consider some applications of them. For example, conformal mappings and the evaluation of real integrals using the Residue Theorem. We’ll also show you Fourier and Laplace transform methods for solving linear ordinary differential equations and convolution type integral equations.

You’ll learn about the basic concepts of random phenomena evolving in time, from two complementary points of view: modelling and data-driven analysis. We'll present the underlying ideas of simple stochastic processes, time series models, and the associated probability theory with statistical techniques. In addition to this, we'll cover how to apply the methods to financial and economic systems, including modelling, data analysis and forecasting.

We'll introduce you to the basic theory and applications of:

• metric spaces
• normed vector spaces and Banach spaces
• inner product spaces and Hilbert spaces
• bounded linear operators on normed linear spaces

This module will teach you to use numerical algorithms to approximate the solution of problems that can't be solved with pen and paper. It'll develop your skills in performing detailed analysis of the performance of numerical methods and will continue to develop your skills in the implementation of numerical algorithms using R.

This module will provide you with experience of the skills required to undertake project work and to communicate the findings in written and oral form. You’ll use a variety of sources like books, journals and the internet.

Here, we’ll give you an introduction to ideas in mathematics and statistics that can be used to model real systems. There will be an emphasis on the valuation of financial derivatives. You’ll also learn about deterministic analysis (calculus, differential equations) and stochastic analysis (Brownian motion, birth and death processes). In both cases, in addition to theoretical analysis, appropriate computational algorithms are presented. The first half of the class focuses on general modelling and simulation tools, and the second half looks at the specific application of valuing financial derivatives. This will include the celebrated Black-Scholes theory.

This module will present the main results in Functional Analysis and give an introduction to linear operators on Banach and Hilbert spaces. You'll also study applications to integral and differential equations.

This module will provide you with a range of applied statistical techniques that can be used in professional life.

You’ll be introduced to the theory of Newtonian fluids, its application to flow problems, and the dynamics of waves on water and in other contexts.

You'll be presented with the basic theory and practice of finite element methods and polynomial and piecewise polynomial approximation theory.

This module will provide you with experience of the skills required to undertake project work and to communicate the findings in written and oral form. You’ll use a variety of sources like books, journals and the internet.

You’ll be introduced to a range of modern statistical methods and practices used in industry, commerce and research. You’ll also develop skills in your application and presentation.

Here, you’ll learn the application of mathematical models to a variety of problems in biology, medicine and ecology. For example, the use of mathematical modelling in biochemical reactions, the application of partial differential equations. The marine population modelling element will introduce the use of difference models to represent population processes through applications to fisheries, and the use of coupled ODE system to represent ecosystems. Practical work will include example class case studies that will explore a real-world application of an ecosystem model.

This module will demonstrate the central role network theory plays in mathematical modelling. It'll also show the intimate connection between linear algebra and graph theory and how to use this connection to develop a sound theoretical understanding of network theory. Finally, it'll apply this theory as a tool for revealing structure in networks.

You’ll learn new statistical methodology and apply it to real data from medical research studies. There will be an emphasis on how to interpret the statistical results in the context of the medical problems being investigated. This skill is necessary for the application of statistics to medical data and differs from the traditional, standard interpretation of statistical textbook problems.