Managing money means dealing with numbers and varying quantities. Mathematical models can be applied to complex behaviour in the financial markets. Well-qualified mathematicians and statisticians are therefore in great demand, with a wide choice of careers opportunities. This degree provides students with a particular set of mathematical skills that are ideal for work in the financial services technology sector. The course is a partnership with industry and includes project work related to capital markets and capital market instruments.
In 2020, more than 90% of 1st and 2nd year Maths students expressed overall satisfaction with their course
Mathematics with Finance highlights
Global Opportunities
We participate in the competitive IAESTE and Turing student exchange programmes, which enable students to obtain work experience in companies and universities throughout the world.
Industry Links
We have key links with local companies who hire mathematics graduates. Several local financial services companies (including Clarus FT, Effex Capital and AquaQ Analytics) were founded by our former maths graduates. Indeed these companies are partners in the development of this degree programme.
All students in the school have the option to include a year in industry as part of their studies. This is a fantastic opportunity to see mathematics at work in the real world, and to enhance your career prospects at the same time.
World Class Facilities
The school has its own dedicated teaching centre which opened in September 2016. This building houses lecture and group-study rooms, a hugely popular student social area and state-of-the-art computer facilities. The centre is an exciting hub for our students, and is situated directly adjacent to the Lanyon Building on the main university campus. This makes us the only school with a dedicated teaching space right at the heart of the university.
Internationally Renowned Experts
The School of Mathematics and Physics is a large school with staff from 13 countries, including UK, US, Ireland, Italy, Spain, Bulgaria, Russia, Argentina, Cuba, Germany, China, Greece, Kenya, Niger, The Netherlands and Romania. Many of our staff are leading international experts in their fields of mathematical research. In the 2021 REF peer-review exercise, Mathematics Research had the 11th highest impact in the UK.
Thus the ethos of the School is one of excellence in research informing excellence in teaching.
Student Experience
Many students find the transition from school to university somewhat daunting. In order to help with this transition, Mathematics students have introduced a Peer Mentoring scheme that is generally regarded as one of the most effective in the University. As well as providing a forum for first year students to obtain support, it also provides mentors with transferable skills which will increase graduate employment opportunities.
Further Study Opportunities
Placement Year
Students can take an optional placement year between years 2/3 of their course. Completion of an approved placement will be acknowledged in your final degree certificate with the addition of the words "with placement year".
Student Experience
School has the 3rd highest postgraduate research student satisfaction in the university.
Career Development
87% of Maths students are in graduate employment or further study 15 months after graduation (11th in the UK)
Student Testimonials
After graduating I joined Allstate (in Chicago and Belfast) to work as a Predictive Modeller. Two years ago I moved to my current position. Unlike some careers, I am given the opportunity to put into practice what I have learned at university daily, whether that is computer programming, critical thinking, problem solving or presenting. Many of the courses I studied at Queen’s are fundamental for my day to day work: my notes from these courses still sit on my desk!
Padraic Sheerin - Vice President, Data Science at Pramerica (Prudential Financial), Ireland
School of Maths & Physics Dr Huettemann is a Senior Lecturer in Mathematics with research interests in homological algebra, graded algebra and K-theory.
Contact Teaching Hours
Medium Group Teaching
4 (hours maximum) 4 hours of practical classes, workshops or seminars each week.
Large Group Teaching
10 (hours maximum) 10 hours of lectures.
Personal Study
21 (hours maximum) 21 hours studying and revising in your own time each week, including some guided study using handouts, online activities, etc.
Small Group Teaching/Personal Tutorial
1 (hours maximum) 1 hour of tutorials (or later, project supervision) each week.
Learning and Teaching
The BSc in Mathematics with Finance has been developed in partnership with industry, and combines the development of mathematical and statistical skills with finance modules in the Queen’s Management School to further insight into capital markets.
At Queen’s, we aim to deliver a high quality learning environment that embeds intellectual curiosity, innovation and best practice in learning, teaching and student support to enable students to achieve their full academic potential.
On the BSc in Mathematics with Finance we do this by providing a range of learning experiences which enable our students to engage with subject experts, develop attributes and perspectives that will equip them for life and work in a global society and make use of innovative technologies and a world class library that enhances their development as independent, lifelong learners. Examples of the opportunities provided for learning on this course are:
Computer based modules
These provide students with the opportunity to develop technical skills and apply theoretical principles to real-life or practical contexts.
E-learning technologies
Information associated with lectures and assignments is often communicated via a Virtual Learning Environment (VLE) called Canvas. A range of e-learning experiences are also embedded in the degree programme through the use of, for example, interactive support materials and web-based learning activities.
Lectures
These introduce basic information about new topics as a starting point for further self-directed private study/reading. Lectures also provide opportunities to ask questions, gain some feedback and advice on assessments (normally delivered in large groups to all year group peers). Some of the modules are taught by the Management School at Queen’s which means students will learn about capital financial markets, financial instruments and investment institutions, and thus develop their industry awareness to complement the technical training.
Personal Tutor
Undergraduates are allocated a Personal Tutor during Level 1 and 2 who meets with them on several occasions during the year to support their academic development.
Self-directed study
This is an essential part of life as a Queen’s student when important private reading, engagement with e-learning resources, reflection on feedback to date and assignment research and preparation work is carried out.
Supervised projects
Our partner companies are committed to support industry-led projects that will enable students to engage with real-life problems and gain invaluable industry experience, while learning practical mathematical skills relevant to local companies. In final year, students will be expected to carry out a significant piece of research on projects offered by these companies. Students will receive support from a course supervisor in addition to a company representative who will guide them in terms of how to carry out research and who will provide feedback during the project. These companies will also deliver professional skills workshops for students on this programme.
Tutorials
Significant amounts of teaching are carried out in small groups (typically 10-20 students). These provide an opportunity for students to engage with academic staff who have specialist knowledge of the topic, to ask questions of them and to assess their own progress and understanding with the support of peers.
Assessment
The way in which students are assessed will vary according to the learning objectives of each module. Details of how each module is assessed are shown in the Student Handbook which is available online via the school website.
Most modules are assessed through a combination of coursework and end of year examinations.
Some modules (eg, final year Honours Project module) are assessed solely through project work or written assignments.
Computer Based Assessment
Some modules use online quizzes/tests as part of the module assessment. This tests basic knowledge, understanding and problem solving.
Feedback
As students’ progress through their course at Queen’s they will receive general and specific feedback about their work from a variety of sources including lecturers, personal tutors, advisers of study and peers. University students are expected to engage with reflective practice and to use this approach to improve the quality of their work. Feedback may be provided in a variety of forms including:
Feedback provided via formal written comments and marks relating to work that you, as an individual or as part of a group, have submitted.
Face to face comment. This may include occasions when you make use of the lecturers’ advertised “office hours” to help you to address a specific query.
Placement employer comments or references.
Online or emailed comment.
General comments or question and answer opportunities at the end of a lecture, seminar or tutorial.
Pre-submission advice regarding the standards you should aim for and common pitfalls to avoid. In some instances, this may be provided in the form of model answers or exemplars that you can review in your own time.
Feedback and outcomes from practical classes.
Comment and guidance provided by staff from specialist support services such as, Careers, Employability and Skills or the Learning Development Service.
Once you have reviewed your feedback, you will be encouraged to identify and implement further improvements to the quality of your work.
Facilities
A new Teaching Centre for Mathematics and Physics opened in September 2016. This provides a dedicated space for teaching within the School. Facilities for mathematics include new lecture and group-study rooms, a new student social area and state-of-the-art computer facilities. The Centre will be the exciting central hub for our students.
What our academics say
This degree choice is a great way to combine a deep interest in mathematics with the practical skills and experience needed for a career working in finance. Students really enjoy developing and applying high-level mathematical techniques in a wide range of areas such as predicting behaviours and correlations in stock markets or estimating lifetimes of oil fields. Being able to apply your mathematical skills to areas such as these is highly rewarding not only for the sheer fun of solving the problem, but also because it is a skill that is highly sought after by employers.
Dr Daniel Dundas - Course Convenor for Mathematics with Finance.
The information below is intended as an example only, featuring module details for the current year of study (2024/25). Modules are reviewed on an annual basis and may be subject to future changes – revised details will be published through Programme Specifications ahead of each academic year.
This is a fundamental module which provides an introduction to probability theory and the key concepts found in statistics. The topics covered include the laws of probability, discrete and continuous random variables, standard discrete and continuous distributions, bivariate distributions, statistical models, sampling, estimation, hypothesis testing and statistical quality control.
Learning Outcomes
- Demonstrate an understanding of the concepts of probability, conditional probability, multiplicative law, independence, Bayes theorem and their interpretations.
- Be able to apply set theory to the proof and use of the axioms of probability.
- Understand and use combinatorial methods: counting rules; sampling with and without replacement; ordered and non-ordered samples.
- Be able to define discrete and continuous random variables and the corresponding probability distributions, probability functions, cumulative distribution functions and probability density functions.
- Understand and use transformations in the discrete and continuous variable context.
- Be able to define expectation and calculate expected values for the mean and variance of specific discrete and continuous distributions.
- Be able to define, interpret and apply the properties of the expectation and variance operators for discrete and continuous cases.
- Demonstrate an understanding of key discrete and continuous distributions including the specific circumstances when distributions may be applied.
- Demonstrate an ability to use statistical tables and deal with linear combinations of independent normal random variables.
- Be familiar with the Central limit theorem for the approximate distribution of sample mean and be able to utilise this theorem in the approximation of binomial and Poisson distributions.
- Understand and be able to define bivariate distributions, their joint probability (density) functions, cumulative distribution functions, marginal distributions, conditional distributions of discrete and continuous random variables.
- Demonstrate an understanding of independence for bivariate data.
- Be able to define expectation and to calculate expected values: means, variances and covariances, correlation coefficients for bivariate distributions and for linear combinations of random variables.
- Be able to define statistical models, experimental, systematic and random errors; precision and accuracy.
- Be able to describe and utilise the following methods of sampling: accessibility, judgement, quota, sequential, random, systematic, stratified and cluster sampling methods.
- Understand the concept of estimation, the definition of a statistic, sampling distribution, sample estimator, sample estimate and the desirable properties for an estimator.
- Be able to define and calculate an estimate of the population mean and variance from a single sample and from several samples.
- Demonstrate an understanding of and be able to implement the method of moments, maximum likelihood estimation and the method of least squares, in particular, the likelihood function, asymptotic variance, normal equations, and linear regression.
- Understand and be able to define the null and alternative hypotheses; one and two-sided tests; test statistic; critical region, P-value, significance level; type I and type II errors; power function and confidence intervals.
- Know when to apply the correct method for significance testing based on given circumstances.
- Be able to interpret results of a significance test and confidence intervals.
- Demonstrate an understanding and be able to describe non-parametric methods and their advantages and disadvantages.
- Understand, be able to carry out and interpret significance tests, in particular key parametric tests based on the Normal distribution, t-distribution, F-distribution and Chi squared distribution, and key non-parametric tests.
- Know when to apply and how to calculate nonparametric statistics and how to choose the appropriate technique to use for a practical example.
Skills
- Understanding when and how to apply probability theory and reasoning with uncertainty.
- Knowing how to apply estimation approaches and the appropriate technique to use.
- Being able to apply probability theory to a practical example.
- Understanding the principles of hypothesis testing.
- Knowing when to apply the correct method for significance testing.
- Calculating test statistics and being able to use these to draw a conclusion about a null hypothesis.
- Knowing when to apply and how to calculate nonparametric statistics and choosing the appropriate technique to use for a practical example.
Introduction to Statistical and Operational Research Methods
Overview
Introduction to statistical software for applying the following topics in Operational Research and Statistical Methods:
Linear Programming: Characteristics of linear programming models, general form. Graphical solution. Simplex method: standard form of linear programming problem, conversion procedures, basic feasible solutions. Simplex algorithm: use of artificial variables.
Decision Theory: Characteristics of a decision problem. Decision making under uncertainty: maximax, maximin, generalised maximin (Hurwicz), minimax regret criteria. Decision making under risk: Bayes criterion, value of perfect information. Decision tree; Bayesian decision analysis.
Random Sampling and Simulation: Random sample from a finite population, from a probability distribution. Use of random number tables. General method for drawing a random sample from a discrete distribution. Drawing a random sample from a continuous distribution: inverse transformation method, exponential distribution. Dynamic simulation techniques: application to queueing problems. Computer aspects: random number generators, sampling from normal distributions.
Initial Data Analysis: Scales of measurement. Discrete and continuous variables. Sample mean, variance, standard deviation, percentile for ungrouped data; boxplot. Frequency table for grouped discrete data: relative frequency, cumulative frequency, bar diagram; sample mean, variance, percentile. Frequency table for grouped continuous data: stem-and-leaf plot, histogram, cumulative percentage frequency plot; sample mean, variance, percentile. Linear transformation. Bivariate data; scatter diagram, sample correlation coefficient.
Learning Outcomes
Perform linear programming using computer software.
Utilise decision analysis methods, such as decision trees.
Simulate date and produce random samples.
Calculate descriptive statistics for a given data set identifying the key characteristics and any unusual features.
Summarise data using appropriate graphical and tabular techniques.
Skills
Apply a range of statistical and OR techniques to data using an appropriate method. Computational skills in statistical software to manage and analyse data. Ability to interpret results and add meaning to the analysis. Understanding sampling processes and the appropriate process to undertake.
Elementary logic and set theory, number systems (including integers, rationals, reals and complex numbers), bounds, supremums and infimums, basic combinatorics, functions.
Sequences of real numbers, the notion of convergence of a sequence, completeness, the Bolzano-Weierstrass theorem, limits of series of non-negative reals and convergence tests.
Analytical definition of continuity, limits of functions and derivatives in terms of a limit of a function. Properties of continuous and differentiable functions. L'Hopital's rule, Rolle's theorem, mean-value theorem.
Matrices and systems of simultaneous linear equations, vector spaces, linear dependence, basis, dimension.
Learning Outcomes
It is intended that students shall, on successful completion of the module, be able:
• to understand and to apply the basic of mathematical language;
• use the language of sets and maps and understand the basic properties of sets (finiteness) and maps (injectivity, surjectivity, bijectivity);
• demonstrate knowledge of fundamental arithmetical and algebraic properties of the integers (divisibility, prime numbers, gcd, lcm) and of the rationals;
• Solve combinatorial counting problems in a systematic manner.
• Understand the fundamental properties of the real numbers (existence of irrational numbers, density of Q, decimal expansion, completeness of R).
• Understand the notions of a sequence of real numbers, including limits, convergence and divergence.
• Define convergence of infinite series.
• Investigate the convergence of infinite series using convergence tests.
• Define limits of functions and define continuous functions.
• Prove that a function is continuous or discontinuous.
• Prove and apply basic properties of continuous functions including the intermediate value theorem and the existence of a maximum and a minimum on a compact interval.
• Define a differentiable function and a derivative.
• Prove whether a function is differentiable.
• Calculate (using analysis techniques) derivatives of many types of functions.
• Understand, apply and prove Rolle's theorem and the Mean Value Theorem.
• Prove the rules of differentiation such as the product.
• Understand and apply the theory of systems of linear equations.
• Produce and understand the definitions of vector space, subspace, linear independence of vectors, bases of vector spaces, the dimension of a vector space.
• Apply facts about these notions in particular examples and problems.
• Understand the relation between systems of linear equations and matrices.
Skills
• Understanding of part of the main body of knowledge for mathematics: analysis and linear algebra.
• Logical reasoning.
• Understanding logical arguments: identifying the assumptions made and the conclusions drawn.
• Applying fundamental rules and abstract mathematical results, equation solving and calculations; problem solving.
Review of A-level calculus: elementary functions and their graphs, domains and ranges, trigonometric functions, derivatives and differentials, integration. Maclaurin expansion. Complex numbers and Euler’s formula.
Differential equations (DE); first-order DE: variable separable, linear; second-order linear DE with constant coefficients: homogeneous and inhomogeneous.
Vectors in 3D, definitions and notation, operations on vectors, scalar and vector products, triple products, 2x2 and 3x3 determinants, applications to geometry, equations of a plane and straight line. Rotations and linear transformations in 2D, 2x2 and 3x3 matrices, eigenvectors and eigenvalues.
Curves in 3D (length, curvature, torsion). Functions of several variables, derivatives in 2D and 3D, Taylor expansion, total differential, gradient (nabla operator), stationary points for a function of two variables. Vector functions; div, grad and curl operators and vector operator identities. Line integrals, double integrals, Green's theorem. Surfaces (parametric form, 2nd-degree surfaces). Curvilinear coordinates, spherical and cylindrical coordinates, orthogonal curvilinear coordinates, Lame coefficients. Volume and surface integrals, Gauss's theorem, Stokes's theorem. Operators div, grad, curl and Laplacian in orthogonal curvilinear coordinates.
Learning Outcomes
On completion of the module, the students are expected to be able to:
• Sketch graphs of standard and other simple functions;
• Use of the unit circle to define trigonometric functions and derive their properties;
• Integrate and differentiate standard and other simple functions;
• Expand simple functions in Maclaurin series and use them;
• Perform basic operations with complex numbers, derive and use Euler's formula;
• Solve first-order linear and variable separable differential equations;
• Solve second-order linear differential equations with constant coefficients (both homogeneous and inhomogeneous), identify complementary functions and particular integrals, and find solutions satisfying given initial conditions;
• Perform operations on vectors in 3D, including vector products, and apply vectors to solve a range of geometrical problems; derive and use equations of straight lines and planes in 3D;
• Calculate 2x2 and 3x3 determinants;
• Use matrices to describe linear transformations in 2D, including rotations, and find eigenvalues and eigenvectors for 2x2 matrices.
• Define basis quantities in mechanics, such as velocity, acceleration and momentum, and state Newton’s laws;
• Use calculus for solving a range of problems in kinematics and dynamics, including projectile motion, oscillations and planetary motion;
• Define and recognise the equations of conics, in Cartesian and polar coordinates;
• Investigate curves in 3D, find their length, curvature and tension;
• Find partial derivatives for a function of several variables;
• Expand functions of one and two variables in the Taylor series and investigate their stationary points;
• Find the partial differential operators div, grad and curl for scalar and vector fields;
• Calculate line integrals along curves;
• Calculate double and triple integrals, including surface and volume integrals;
• Transform between Cartesian, spherical and cylindrical coordinate systems;
• Investigate simple surfaces in 3D and evaluate surface for the shapes such as the cube, sphere, hemisphere or cylinder;
• State and apply Green's theorem, Gauss's divergence theorem, and Stokes's theorem
Skills
• Proficiency in calculus and its application to a range of problems.
• Constructing and clearly presenting mathematical and logical arguments.
• Mathematical modelling and problem solving.
• Ability to manipulate precise and intricate ideas.
• Analytical thinking and logical reasoning.
Theory of money. Monetary Union. The theory of financial intermediation. Operational structure and operations of the Central Bank. Banking regulation. Other non-bank financial intermediaries. An introduction to the stock market. An introduction to the bond market. An introduction to money markets.
Learning Outcomes
Understand the economic functions and workings of financial institutions and markets. Understand the financial intermediation process.
Skills
Have a general understanding of financial institutions and markets. Have an understanding of elementary financial ratios and terms as applied in the stock, bond and money markets. Be able to access relevant financial information from publications such as the Financial Times.
- Recap and extend to fields such as C, the notions of abstract vector spaces and subspaces, linear independence, basis, dimension.
- Linear transformations, image, kernel and dimension formula.
- Matrix representation of linear maps, eigenvalues and eigenvectors of matrices.
- Matrix inversion, definition and computation of determinants, relation to area/volume.
- Change of basis, diagonalization, similarity transformations.
- Inner product spaces, orthogonality, Cauchy-Schwarz inequality.
- Special matrices (symmetric, hermitian, orthogonal, unitary, normal) and their properties.
- Basic computer application of linear algebra techniques.
Additional topics and applications, such as: Schur decomposition, orthogonal direct sums and geometry of orthogonal complements, Gram-Schmidt orthogonalization, adjoint maps, Jordan normal form.
Learning Outcomes
It is intended that students shall, on successful completion of the module: have a good understanding and ability to use the basics of linear algebra; be able to perform computations pertaining to problems in these areas; have reached a good level of skill in manipulating basic and complex questions within this framework, and be able to reproduce, evaluate and extend logical arguments; be able to select suitable tools to solve a problem, and to communicate the mathematical reasoning accurately and confidently.
Skills
Analytic argument skills, computation, manipulation, problem solving, understanding of logical arguments.
Functions of a complex variable: limit in the complex plane, continuity, complex differentiability, analytic functions, Cauchy-Riemann equations, Cauchy’s theorem, Cauchy’s integral formula, Taylor and Laurent series, residues, Cauchy residue theorem, evaluation of integrals using the residue theorem.
Series solutions to differential equations: Frobenius method.
Fourier series and Fourier transform. Basis set expansion.
Introduction to partial differential equations. Separation of variables. Wave equation, diffusion equation and Laplace’s equation.
Learning Outcomes
On completion of the module, the students are expected to be able to:
• determine whether or not a given complex function is analytic;
• recognise and apply key theorems in complex integration;
• use contour integration to evaluate real integrals;
• apply Fourier series and transforms to model examples;
• solve the wave equation, diffusion equation and Laplace’s equation with model boundary conditions, and interpret the solutions in physical terms.
Skills
• Proficiency in complex calculus and its application to a range of problems.
• Constructing and presenting mathematical and logical arguments.
• Mathematical modelling and problem solving.
• Ability to manipulate precise and intricate ideas.
• Analytical thinking and logical reasoning.
Financial Environment; Time Value of Money; The Investment Decision - Capital Budgeting; Risk and Return; Cost of Capital; The Financing Decision; Working Capital Investment; Introduction to Personal Finance.
Learning Outcomes
To promote an appreciation of how long term financial decisions are taken through an understanding of the concepts and principles involved.
Skills
To formulate procedures for problem solving within a financial environment. To understand the issues surrounding a company's investment and financing decisions.
Statistical investigations. Initial data analysis. Sample diagnostics. Point estimation: maximum likelihood, least squares. Multiple linear regression. Significance tests: Neyman-Pearson approach, likelihood ratio tests. Confidence intervals. Introduction to Experimental design. Bayesian methods. Oral presentation of aspects of statistics.
Learning Outcomes
On completion of the module, it is intended that students will be able to: understand how to build statistical models, know the issues involved with using real data and use sample diagnostic methods to test data for independence, normality and goodness of fit; understand the difference between estimates and estimators in terms of finding an unknown parameter and understand the assessment of an estimator's unbiasedness, relative efficiency, mean square error, sufficiency and whether a distribution belongs to the regular exponential class; understand and use the method of moments, of maximum likelihood and of least squares to provide unbiased estimates of distribution parameters; understand and use experimental design, the different forms of analysis of variance techniques and use and interpret methods of association; rates, relative risk and the odds ratio; through expanding their knowledge of significance and hypothesis tests, formulate confidence intervals and regions and use pivotal quantities; understand Bayesian inference; the prior and posterior distributions, and degree of belief; be able to carry out a statistical investigation of real data in group work using SAS and present the results in a written and oral presentation.
Skills
Statistical modelling and problem solving. Application of statistical methods in data analysis. Presentation skills.
Deterministic and stochastic inventory models; simple and adaptive forecasting; theory of replacement of equipment; quality control, acceptance sampling by attribute and variable; network planning including the use of PERT, LP, Gantt charts and resource smoothing; decision theory, including utility curves, decision trees and Bayesian statistics; simple heuristics.
Learning Outcomes
On completion of the module, it is intended that students will be able to: demonstrate understanding of the Economic Order Quantity model and its use in determining minimum inventory costs; use Lagrange multipliers to obtain optimal batch sizes; use dynamic programming techniques to determine optimal replacement policies; determine both single and double sampling plans and understand how to decide which is the more appropriate in different circumstances; determine critical activities of a project and apply linear programming methods to determine the optimal duration; use decision tress to determine an optimal course of action; use a range of techniques based on past experience to forecast future sales.
Skills
Formulating problems in accordance with simple mathematical models. Use of spreadsheets.
Upon successful completion of this module students will:
have an understanding of the constraints faced by fund-managers when constructing portfolios to meet investors financial objectives.
have a theoretical and practical understanding of CAPM and factor models.
have an appreciation of the risk and returns characteristics of the major asset classes and their importance when constructing portfolios to meet investors' investment objective(s).
be able to apply valuation methodologies to the analysis of securities: equities, bonds, and derivatives.
have an understanding of how derivatives securities are used in risk-management.
be able to critically evaluate portfolio evaluation methodologies.
Skills
Quantitative analysis, problem solving, logical reasoning, ability to evaluate/interpret financial data.
Introduction to placement for mathematics and physics students, CV building, international options, interview skills, assessment centres, placement approval, health and safety and wellbeing. Workshops on CV building and interview skills. The module is delivered in-house with the support of the QUB Careers Service and external experts.
Learning Outcomes
Identify gaps in personal employability skills. Plan a programme of work to result in a successful work placement application.
Skills
Plan self-learning and improve performance, as the foundation for lifelong learning/CPD. Decide on action plans and implement them effectively. Clearly identify criteria for success and evaluate their own performance against them .
• Business skills workshop: presentation skills, negotiation skills, customer relationships, project management/team building.
• Teams required to negotiate, plan, develop and deliver a completed task working as a group, commissioned by the 'client' company.
The project will require software development skills.
Learning Outcomes
On completion of the module, it is intended that students will be able to
• Apply their mathematical knowledge to real-world business problems.
• Work successfully, as part of a team, to deliver a commissioned piece of work.
• Understand the different roles required in a successful consultancy firm and assign these roles based on the skills of each team member.
• Understand the costs associated with carrying out consultancy work and be able to produce accurate costings for the commissioned work.
• Build successful relationships with client companies through negotiation and by successfully delivering work to deadlines.
• Report the findings of your work to both technical and non-technical audiences.
Introduction to Data Mining; Exploratory Data Analysis; Cluster analysis; Classification including Probabilistic Modelling, Bayesian Networks, Decision tree analysis; Prediction including Regression trees, Random Forests, Neural nets.
Learning Outcomes
On completion of the module, it is intended that students will be able to: demonstrate understanding of the field of data mining, how it has developed and the need for data mining techniques in today’s society; demonstrate knowledge familiarity with data warehouses, webhouses and data marts, the various forms of storing, managing and maintaining large amounts of data; employ exploratory data analysis techniques for univariate analyses, when one outcome variable is considered compared to bivariate, or multivariate analyses for more than one variable in terms of multivariate exploratory analysis of both quantitative and qualitative data and to apply and interpret the results of principal component analysis for multiple variables; demonstrate knowledge of classification and of classification methods including simple linear, nearest neighbour, decision tree models, Bayes classifying, neural networks and random forests; demonstrate knowledge of the purpose of clustering and to use hierarchical clustering and the non-hierarchical clustering methods of k means and nearest neighbour when applied to real data sets; understand and use association rules and their application on real data sets.
• Introduction and basic properties of errors: Introduction; Review of basic calculus; Taylor's theorem and truncation error; Storage of non-integers; Round-off error; Machine accuracy; Absolute and relative errors; Richardson's extrapolation.
• Solution of equations in one variable: Bisection method; False-position method; Secant method; Newton-Raphson method; Fixed point and one-point iteration; Aitken's "delta-squared" process; Roots of polynomials.
• Solution of linear equations: LU decomposition; Pivoting strategies; Calculating the inverse; Norms; Condition number; Ill-conditioned linear equations; Iterative refinement; Iterative methods.
• Interpolation and polynomial approximation: Why use polynomials? Lagrangian interpolation; Neville's algorithm; Other methods.
• Approximation theory: Norms; Least-squares approximation; Linear least-squares; Orthogonal polynomials; Error term; Discrete least-squares; Generating orthogonal polynomials.
• Numerical quadrature: Newton-Cotes formulae; Composite quadrature; Romberg integration; Adaptive quadrature; Gaussian quadrature (Gauss-Legendre, Gauss-Laguerre, Gauss-Hermite, Gauss-Chebyshev).
• Numerical solution of ordinary differential equations: Boundary-value problems; Finite-difference formulae for first and second derivatives; Initial-value problems; Errors; Taylor-series methods; Runge-Kutta methods.
Learning Outcomes
On completion of the module, it is intended that students should: appreciate the importance of numerical methods in mathematical modelling; be familiar with, and understand the mathematical basis of, the numerical methods employed in the solution of a wide variety of problems;
through the computing practicals and project, have gained experience of scientific computing and of report-writing using a mathematically-enabled word-processor.
Skills
Problem solving skills; computational skills; presentation skills.
Linear regression. Non-singular case: analysis of variance, extra sum of squares principle, generalised least squares, residuals. Singular case: generalised inverse solution, estimable functions. Experimental designs: completely randomised, randomised block, factorial; contrasts, analysis of covariance; Generalised linear model (GLM): maximum likelihood and least squares; exponential family; Poisson and logistic models; model selection for GLM.
Learning Outcomes
On completion of the module, it is intended that students will be able to: understand and use linear models and multiple linear regression for modelling a measured response as a function of explanatory variables using the least squares approach, and so perform model selection and diagnostics expanding their knowledge to the weighted least squares model; understand ANOVA as a method of analysis for experimentally designed data using non-singular and singular cases; apply the extra sum of squares principle to analyse and interpret residuals, the generalized inverse solution, and assess whether a function is estimable and the hypotheses testable; recognise, apply and interpret the results of analysis of variance for the completely randomized, randomized block, and factorial designs; demonstrate familiarity with using contrasts and apply analysis of covariance; upon developing a full understanding of linear models, extend this to Generalized Linear Models and apply them and model selection to discrete recorded responses using maximum likelihood and least square estimation for distributions from the exponential family, Poisson and logistic; build on their ability to use SAS for the development and selection of linear models.
Skills
Use of appropriate statistical software in applying linear and generalised linear models.
Logic and Boolean algebra, counting and combinatorics, set algebra, inclustion-exclusion theorem, mutually exclusive events, De Morgan Laws.
Axioms of probability, events and probability spaces, sigma-field, random variables, conditional probability, and expectation, Bayes’ theorem, discrete and continuous random variables, moments and moment generating function. Laws of large numbers and central limit theorem.
Pairs of random variables, marginal probabilities, Cauchy Schwartz Inequality in statistics, correlation and covariance.
Discrete time Markov chains, Chapman Kolmogorov relation, limiting behaviour, transient, recurrent states and periodic states, limiting stationary distribution, hitting times and hitting probabilities.
Continuous time Markov chains, Kolmogorov forward equations, stationary distribution for continuous time Markov chains, Poisson process, MM1 Queue, inhomogeneous Poisson process and compound Poisson process.
Learning Outcomes
By the end of this module students will be able to:
- Calculate expectations and variances directly, using the moment generating function and by using the conditional expectation theorem. Students should also be able to explain what predictions can be made given the expectation and/or the variance.
- Recognize which type of random variable is appropriate for modeling a given phenomenon, to identify the assumptions that they have made in constructing this model and to critically assess its validity.
- Explain what it means when we state that a time dependent process has independent and stationary increments and how this differs from a Markov process. By using their understanding of this distinction students should be able to construct probabilistic models for time dependent phenomena, explain the assumptions that they have made in constructing these models and critically assess their validity.
Skills
Write computer programs that generate random variables as well as computer programs for evaluating sample means, histograms and confidence limits.
Discuss the results obtained by running the computer programs described in the previous point.
Introduction to financial derivatives: forwards, futures, swaps and options; Future markets and prices; Option markets; Binomial methods and risk-free portfolio; Stochastic calculus and random walks; Ito's lemma; the Black-Scholes equation; Pricing models for European Options; Greeks; Credit Risk.
Learning Outcomes
On completion of the module, it is intended that students will be able to: explain and use the basic terminology of the financial markets; calculate the time value of portfolios that include assets (bonds, stocks, commodities) and financial derivatives (futures, forwards, options and swaps); apply arbitrage-free arguments to derivative pricing; use the binomial model for option pricing; model the price of an asset as a stochastic process; define a Wiener process and derive its basic properties; obtain the basic properties of differentiation for stochastic calculus; derive and solve the Black-Scholes equation; modify the Black-Scholes equation for various types of underlying assets; price derivatives using risk-neutral expectation arguments; calculate Greeks and explain credit risk.
Skills
Application of Mathematics to financial modelling. Apply a range of mathematical methods to solve problems in finance. Assimilating abstract ideas.
A maximum of one BTEC/OCR Single Award or AQA Extended Certificate will be accepted as part of an applicant's portfolio of qualifications with a Distinction* being equated to a grade A at A-level and a Distinction being equated to a grade B at A-level.
Irish leaving certificate requirements
H2H2H3H3H3H3 including Higher Level grade H2 in Mathematics
Access Course
Successful completion of Access Course with a minimum of 80% in each Level 3 module. Must be relevant Access Course with substantial Mathematics modules (eg: Mathematics and Computing).
International Baccalaureate Diploma
36 points overall including 6,6,6 at Higher Level including 6 in Mathematics.
Graduate
A minimum of a 2:2 Honours Degree, provided any subject requirements are also met.
Note
All applicants must have GCSE English Language grade C/4 or an equivalent qualification acceptable to the University.
How we choose our students
Applications are dealt with centrally by the Admissions and Access Service rather than by the School of Mathematics and Physics. Once your on-line form has been processed by UCAS and forwarded to Queen's, an acknowledgement is normally sent within two weeks of its receipt at the University.
Selection is on the basis of the information provided on your UCAS form. Decisions are made on an ongoing basis and will be notified to you via UCAS.
For entry last year, applicants for programmes in the School of Mathematics and Physics offering A-level/BTEC Level 3 qualifications must have had, or been able to achieve, a minimum of five GCSE passes at grade C/4 or better (to include English Language and Mathematics), though this profile may change from year to year depending on the demand for places. The Selector also checks that any specific entry requirements in terms of GCSE and/or A-level subjects can be fulfilled.
Offers are normally made on the basis of three A-levels. The offer for repeat candidates may be one grade higher than for first time applicants. Grades may be held from the previous year.
Applicants offering two A-levels and one BTEC Subsidiary Diploma/National Extended Certificate (or equivalent qualification), or one A-level and a BTEC Diploma/National Diploma (or equivalent qualification) will also be considered. Offers will be made in terms of the overall BTEC grade(s) awarded. Please note that a maximum of one BTEC Subsidiary Diploma/National Extended Certificate (or equivalent) will be counted as part of an applicant’s portfolio of qualifications. The normal GCSE profile will be expected.
For applicants offering the Irish Leaving Certificate, please note that performance at Irish Junior Certificate (IJC) is taken into account. For last year’s entry, applicants for this degree must have had a minimum of five IJC grades at C/Merit. The Selector also checks that any specific entry requirements in terms of Leaving Certificate subjects can be satisfied.
Applicants offering other qualifications will also be considered. The same GCSE (or equivalent) profile is usually expected of those candidates offering other qualifications.
The information provided in the personal statement section and the academic reference together with predicted grades are noted but, in the case of degree courses in the School of Mathematics and Physics, these are not the final deciding factors in whether or not a conditional offer can be made. However, they may be reconsidered in a tie break situation in August.
A-level General Studies and A-level Critical Thinking would not normally be considered as part of a three A-level offer and, although they may be excluded where an applicant is taking four A-level subjects, the grade achieved could be taken into account if necessary in August/September.
Candidates are not normally asked to attend for interview.
If you are made an offer then you may be invited to a Faculty/School Visit Day, which is usually held in the second semester. This will allow you the opportunity to visit the University and to find out more about the degree programme of your choice and the facilities on offer. It also gives you a flavour of the academic and social life at Queen's.
If you cannot find the information you need here, please contact the University Admissions and Access Service (admissions@qub.ac.uk), giving full details of your qualifications and educational background.
International Students
Our country/region pages include information on entry requirements, tuition fees, scholarships, student profiles, upcoming events and contacts for your country/region. Use the dropdown list below for specific information for your country/region.
If you need to improve your English language skills before you enter this degree programme, INTO Queen's University Belfast offers a range of English language courses. These intensive and flexible courses are designed to improve your English ability for admission to this degree.
Academic English: an intensive English language and study skills course for successful university study at degree level
Pre-sessional English: a short intensive academic English course for students starting a degree programme at Queen's University Belfast and who need to improve their English.
International Students - Foundation and International Year One Programmes
INTO Queen's offers a range of academic and English language programmes to help prepare international students for undergraduate study at Queen's University. You will learn from experienced teachers in a dedicated international study centre on campus, and will have full access to the University's world-class facilities.
These programmes are designed for international students who do not meet the required academic and English language requirements for direct entry.
Studying for a Maths and Finance degree at Queen’s will assist students in developing the core skills and employment-related experiences that are valued by employers, professional organisations and academic institutions. Graduates from this degree at Queen’s are well regarded by many employers in the financial services. The following is a list of some of the companies that have attracted our graduates in recent years:
• First Derivatives
• Citi Group
• Allstate NI
• AquaQ Analytics
• Effex Capital
• Ulster Bank
• Pramerica
According to the Institute for Fiscal Studies, 5 years after graduation, Maths graduates earn 20 per cent more on average than other graduates (IFS 2018) and are the 3rd highest earners compared to all other subjects.
Employment after the Course
Typical career destinations of graduates include:
• Finance
• Banking
• Data Science
Employment Links
• Clarus FT
• Liberty Mutual Insurance
• First Derivatives
• Citi Group
• Allstate NI
• AquaQ Analytics
• Effex Capital
• Ulster Bank
• Pramerica
What employers say
We have Mathematics graduates working across many parts of the business and they play a central role in creating cutting edge solutions for our customers, enabling them to push the boundaries of science.
Claire Greenwood, Director of Engineering, Andor Technology
At Citi, we value diverse thinking and we encourage Maths students to join our Graduate Programmes each year. The Maths graduates that we have hired have been extremely successful in their careers within Citi, in particular our Software Engineering opportunities. They excel in their profession with us as they are able to transfer their analytical, numerical and problem solving skills to their day to day responsibilities.
Aislinn Wilson, Applications Development Senior Manager, Citi group
Prizes and Awards
Top performing students are eligible for a number of prizes within the School.
Degree Plus/Future Ready Award for extra-curricular skills
In addition to your degree programme, at Queen's you can have the opportunity to gain wider life, academic and employability skills. For example, placements, voluntary work, clubs, societies, sports and lots more. So not only do you graduate with a degree recognised from a world leading university, you'll have practical national and international experience plus a wider exposure to life overall. We call this Degree Plus/Future Ready Award. It's what makes studying at Queen's University Belfast special.
1EU citizens in the EU Settlement Scheme, with settled status, will be charged the NI or GB tuition fee based on where they are ordinarily resident. Students who are ROI nationals resident in GB will be charged the GB fee.
2 EU students who are ROI nationals resident in ROI are eligible for NI tuition fees.
3 EU Other students (excludes Republic of Ireland nationals living in GB, NI or ROI) are charged tuition fees in line with international fees.
The tuition fees quoted above for NI and ROI are the 2024/25 fees and will be updated when the new fees are known. In addition, all tuition fees will be subject to an annual inflationary increase in each year of the course. Fees quoted relate to a single year of study unless explicitly stated otherwise.
Tuition fee rates are calculated based on a student’s tuition fee status and generally increase annually by inflation. How tuition fees are determined is set out in the Student Finance Framework.
Additional course costs
All essential software will be provided by the University, for use on University facilities, however for some software, students may choose to buy a version for home use.
All Students
Depending on the programme of study, there may be extra costs which are not covered by tuition fees, which students will need to consider when planning their studies.
Students can borrow books and access online learning resources from any Queen's library. If students wish to purchase recommended texts, rather than borrow them from the University Library, prices per text can range from £30 to £100. Students should also budget between £30 to £75 per year for photocopying, memory sticks and printing charges.
Students undertaking a period of work placement or study abroad, as either a compulsory or optional part of their programme, should be aware that they will have to fund additional travel and living costs.
If a programme includes a major project or dissertation, there may be costs associated with transport, accommodation and/or materials. The amount will depend on the project chosen. There may also be additional costs for printing and binding.
Students may wish to consider purchasing an electronic device; costs will vary depending on the specification of the model chosen.
There are also additional charges for graduation ceremonies, examination resits and library fines.
How do I fund my study?
There are different tuition fee and student financial support arrangements for students from Northern Ireland, those from England, Scotland and Wales (Great Britain), and those from the rest of the European Union.
Application for admission to full-time undergraduate and sandwich courses at the University should normally be made through the Universities and Colleges Admissions Service (UCAS). Full information can be obtained from the UCAS website at: www.ucas.com/students.
When to Apply
UCAS will start processing applications for entry in autumn 2025 from early September 2024.
The advisory closing date for the receipt of applications for entry in 2025 is still to be confirmed by UCAS but is normally in late January (18:00). This is the 'equal consideration' deadline for this course.
Applications from UK and EU (Republic of Ireland) students after this date are, in practice, considered by Queen’s for entry to this course throughout the remainder of the application cycle (30 June 2025) subject to the availability of places. If you apply for 2025 entry after this deadline, you will automatically be entered into Clearing.
Applications from International and EU (Other) students are normally considered by Queen's for entry to this course until 30 June 2025. If you apply for 2025 entry after this deadline, you will automatically be entered into Clearing.
Applicants are encouraged to apply as early as is consistent with having made a careful and considered choice of institutions and courses.
The Institution code name for Queen's is QBELF and the institution code is Q75.
Additional Information for International (non-EU) Students
Applying through UCAS
Most students make their applications through UCAS (Universities and Colleges Admissions Service) for full-time undergraduate degree programmes at Queen's. The UCAS application deadline for international students is 30 June 2025.
Applying direct
The Direct Entry Application form is to be used by international applicants who wish to apply directly, and only, to Queen's or who have been asked to provide information in advance of submitting a formal UCAS application. Find out more.
Applying through agents and partners
The University’s in-country representatives can assist you to submit a UCAS application or a direct application. Please consult the Agent List to find an agent in your country who will help you with your application to Queen’s University.
