Program Overview

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Mathematics and Computer Science (MSci)

Overview

Mathematics is the universal language of science while computer science is the study of the hardware and algorithms that are used in modern computer systems. Since many of the early pioneers of computer science, for instance Alan Turing, were mathematicians it is not surprising that these two subjects are closely related. This is a four-year joint degree programme, in conjunction with the School of Electronics, Electrical Engineering and Computer Science, that combines the study of the two subjects at each level.

Course Structure

• Stage 1: Students must take six compulsory modules.
• Stage 2: Students must take modules totalling 120 units to be approved by an advisor of studies, with at least two modules from each Mathematics and Computer Sciences.
• Stage 3: Students must take modules totalling 120 units to be approved by an advisor of studies, with at least two modules from Computer Sciences.
• Stage 4: Modules open to MSci. students offer students the opportunity to study a selection of topics in greater depth than is possible in the BSc programme. The centrepiece of the fourth-year is the double-weighted investigations module, in which a student has the opportunity to study an aspect of mathematics close to the frontier of knowledge.

People Teaching You

• Dr Thomas Huettemann: Associate Director of Education for Mathematics

Contact Teaching Hours

• Small Group Teaching/Personal Tutorial: 1 (hours maximum)
• Large Group Teaching: 10 (hours maximum)
• Medium Group Teaching: 4 (hours maximum)
• Personal Study: 21 (hours maximum)

Learning and Teaching

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.

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.

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, module co-ordinators, placement supervisors, personal tutors, advisers of study and your peers.

Career Prospects

• Introduction: Studying for a Mathematics and Computer Science 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.
• Employment after the Course: The School has links with over 500 IT companies both here and abroad. We benefit from the fact that there are more software companies located in N Ireland than any other part of the UK, outside of London.
• What Employers Say:
  • "At Citi, we value diverse thinking and we encourage Maths students to join our Graduate Programmes each year."
  • "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."

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.

Tuition Fees

• Northern Ireland (NI): £4,855
• Republic of Ireland (ROI): £4,855
• England, Scotland or Wales (GB): £9,535
• EU Other: £22,400
• International: £22,400

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.

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.

Scholarships

Each year, we offer a range of scholarships and prizes for new students.

International Scholarships

Information on scholarships for international students, is available at International Scholarships

How to Apply

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).

Terms and Conditions

The terms and conditions that apply when you accept an offer of a place at the University on a taught programme of study.

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.
• 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.
• Applying through agents and partners: The University’s in-country representatives can assist you to submit a UCAS application or a direct application.

Modules

Core Modules

• Mathematical Methods 1: Review of A-level calculus, Maclaurin expansion, complex numbers and Euler’s formula, differential equations, vectors in 3D, linear transformations in 2D, Newtonian mechanics, curves in 3D, functions of several variables.
• Algorithmic Thinking: Basic programming skills, introduction of software to present mathematical contents, basic understanding of the complexity of algorithms.
• Mathematical Reasoning: The notion of mathematical statements and elementary logic, mathematical symbols and notation, the language of sets, the concept of mathematical proof.
• Introduction to Algebra and Analysis: Elementary logic and set theory, number systems, bounds, supremums and infimums, basic combinatorics, functions, sequences of real numbers, convergence of sequences, completeness, the Bolzano-Weierstrass theorem.
• Procedural Programming: Fundamentals of procedural programming, problem- solving approach, real-world examples, code literacy, good algorithm design.
• Object Oriented Programming: Fundamentals of object-oriented programming, real-world problems, exemplar code solutions, abstraction, encapsulation, inheritance and polymorphism.

Optional Modules

• Linear Algebra: Recap and extend to fields such as C, the notions of abstract vector spaces and subspaces, linear independence, basis, dimension.
• Data Structures and Algorithms: Data structures, algorithms, asymptotic analysis of algorithms, programming languages representation and implementation.
• Group Theory: Definition and examples of groups and their properties, countability of a group and index, Lagrange’s theorem, normal subgroups and quotient groups.
• Professional and Transferrable Skills: Introduction to placement for mathematics and physics students, CV building, international options, interview skills, assessment centres, placement approval, health and safety and wellbeing.
• Metric Spaces: Definition and examples of metric spaces, open sets, closed sets, closure points, sequential convergence, density, separability.
• Mathematical Methods 2: Functions of a complex variable, series solutions to differential equations, Fourier series and Fourier transform, introduction to partial differential equations.
• Analysis: Cauchy sequences, infinite series, uniform continuity, mean value theorems, Riemann integration.
• Theory of Computation: Automata and Formal Languages, Computability Theory, Complexity Theory.
• Introduction to Artificial Intelligence and Machine Learning: Concepts of artificial intelligence and machine learning, fundamentals of supervised and unsupervised learning, experimental settings and hypothesis evaluation.
• Employability for Mathematics: Introduction to placement for mathematics and physics students, CV building, international options, interview skills, assessment centres, placement approval, health and safety and wellbeing.
• Classical Mechanics: Introduction to calculus of variations, recap of Newtonian mechanics, generalised coordinates, Lagrangian, least action principle.

Stage 3 Modules

• Mathematical Investigations: Investigation processes of mathematics, construction of conjectures, testing of conjectures, case studies.
• Investigations: Short practice investigation, two short investigations, long investigation, literature study of a Mathematical or Theoretical Physics topic.
• Financial Mathematics: Introduction to financial derivatives, future markets and prices, option markets, binomial methods and risk-free portfolio.
• Modelling and Simulation: Real-life situations, mathematical model, solution of the model, analysis and interpretation of the results.
• Topological Data Analysis: Simplicial complexes, PL functions, simplicial homology, filtrations and barcodes.
• Geometry of Optimisation: Functionals on R^n, linear equations and inequalities, convex polytopes, faces.
• Fourier Analysis and Applications to PDEs: Introduction, examples of important classical PDEs, method of separation of variables, Fourier series.
• Functional Analysis: Characterisation of finite-dimensional normed spaces, the Hahn-Banach theorem, the bidual and reflexive spaces.
• Dynamical Systems: Continuous dynamical systems, fundamental theory, linear systems, topological dynamics.
• Numerical Analysis: Introduction and basic properties of errors, solution of equations in one variable, solution of linear equations.
• Formal Methods: A rigorous approach to software development, logical foundations, specification of data types.
• Concurrent Programming: Concurrent Programming Abstraction and Java Threads, the Mutual Exclusion Problem, Semaphores.
• Deep Learning: Overview of generic machine learning pipelines, deep learning, feedforward neural networks.
• Video Analytics and Machine Learning: Overview of imaging and video systems, generic machine learning pipelines, pattern recognition problems.
• Algebra: Rings, subrings, prime and maximal ideals, quotient rings, homomorphisms.
• Measure and Integration: Sigma-algebras, measure spaces, measurable functions, Lebesgue integral.
• Quantum Theory: Overview of classical physics, basic principles, states and the superposition principle.
• Project: A substantial investigation of a research problem, literature survey, development of appropriate theoretical models.

Stage 4 Modules

• Algorithms: Analysis and Application: Analysis and design of algorithms, complexity, n-p completeness, algorithms for searching, sorting.
• Digital Transformation: Software Design, Management and Practical Implementation: Opportunity Analysis, Entrepreneurship and Innovation, Business Planning, Modelling and documenting software design.
• Project: An extended project based on the research interests of members of staff, attendance at a sequence of presentations on projects offered in Level 4.
• Applied Algebra and Cryptography: Finite fields and rings of polynomials, the division algorithm, ideals and quotient rings.
• Fourier Analysis and Applications to PDEs: Introduction, examples of important classical PDEs, method of separation of variables, Fourier series.
• Functional Analysis: Characterisation of finite-dimensional normed spaces, the Hahn-Banach theorem, the bidual and reflexive spaces.
• Geometry of Optimisation: Functionals on R^n, linear equations and inequalities, convex polytopes, faces.
• Mathematical Methods for Quantum Information Processing: Operatorial quantum mechanics, review of linear algebra in Dirac notation.
• Practical Methods for Partial Differential Equations: Basics, solving first order ordinary differential equations, partial derivatives.
• Integration Theory: Sigma-algebras, measure spaces, measurable functions, Lebesgue integral.
• Topology: Definition and examples, continuity and homeomorphisms, compact, connected, Hausdorff.
• Information Theory and Biodiversity: Introduction to information theory, basic modular arithmetic and factoring.
• Advanced Quantum Theory: Review of fundamental quantum theory, coupled angular momenta.
• Topological Data Analysis: Simplicial complexes, PL functions, simplicial homology, filtrations and barcodes.