Application to Graduation

1. Application to Graduation • This is a rough guide to the options available to students on the 16 different courses available in the Department of Mathematical Sciences. • It is not intended to be definitive, and so you should always contact your programme director for advice before selecting your modules.

2. First Year Modules Compulsory Modules • MATH101 (Calculus 1) • Differentiate and integrate a wide range of functions; • sketch graphs and solve problems involving • optimisation and mensuration; • understand the notions of sequence and series; • and apply a range of tests to determine if a series is convergent. • MATH102 (Calculus 2) • Use Taylor series to obtain local approximations to functions; • obtain partial derivatives and use them in several applications such as, • error analysis, stationary points change of variables; • evaluate double integrals using Cartesian and polar co-ordinates • MATH103 (Introduction to Linear Algebra) • Manipulate complex numbers and solve simple equations involving them; • solve arbitrary systems of linear equations; • understand and use matrix arithmetic, including the computation of matrix inverses; • compute and use determinants; • understand and use vector methods in the geometry of 2 and 3 dimensions; • calculate eigenvalues and eigenvectors; • and apply these calculations to the geometry of conics and quadrics. Other Mathematical Sciences Modules • MATH105 (Numbers and Sets) • Use mathematical language and symbols accurately; • Understand the nature of a definition, & show that simple definitions are or are not satisfied by given examples; • Use theorems to draw logical conclusions from given information; • Understand the logic of direct proofs & proofs by contradiction, & construct very simple proofs, including proofs by induction; • Interpret statements involving quantifiers, and negate statements with one or two quantifiers; • Use the language of naive set theory; • Understand the integer, rational, real and complex number systems and the relationship between them. • MATH111 (Mathematical IT Skills) • Tackle project work, including writing up of reports detailing their solutions to problems; • use computers to create documents containing • formulae, tables, plots and references; • use Maple to manipulate mathematical expressions • and to solve simple problems; • better understand the mathematical topics covered, through direct experimentation with the computer. • MATH122 (Dynamic Modelling) • Solve simple differential equations; • understand some methods of mathematical modelling and, in particular, the need to attach meaning to mathematical results; • develop some differential equations for population growth, and interpret the results; • understand Newton's laws of Mechanics; • do simple problems in projectiles and orbits, some involving polar co-ordinates • MATH142 (Numbers, Groups & Codes) • Use the division algorithm to construct the greatest common divisor of a pair of positive integers; • Solve linear congruences & find the inverse of an integer modulo a given integer; • Code & decode messages using the public-key method; • Manipulate permutations with confidence; • Decide when a given set is a group under a specified operation & give formal axiomatic proofs; • Understand the concepts of a subgroup, a group action, an orbit & a stabiliser subgroup;use Lagrange’s theorem; • Understand the concept of a group homomorphism & be able to show that 2 groups are isomorphic; • Understand the principles of binary coding & how to construct error-detecting & error-correcting binary codes. • MATH162 (Introduction to Statistics) • to describe statistical data; • to use the Binomial, Poisson, Exponential and Normal distributions; • to perform simple goodness-of-fit tests; • to use the package Minitab to present data, and to make statistical analysis. Other Subjects’ Modules • Computer Science Modules Available: • COMP101 (Introduction to Programming in JAVA) • COMP102 (Introduction to Databases) • (GG14 ONLY) • COMP103 (Computer Systems) • COMP 108 (Algorithmic Foundations) • COMP 109 (Foundations of Computing) • Economics & Finance Modules Available: • (G1N3, GN11 & GL11 ONLY) • ECON121 (Principles of Microeconomics) • ECON123 (Principles of Macroeconomics) • ECON127 (Economic Principles for Business and Markets) • ECON130 (Cont Issues in Economic Policy) • ECON159 (European Economic Environment) • ACFI 101 (Introduction to Financial Accounting) • ACFI102 (Introduction to Management Accounting) • ACFI103 (Introduction to Finance) • Physics & Environmental Sciences Modules Available: • (F344, FGH1, FG31 ONLY) • PHYS102 (The Material Universe) • PHYS103 (Wave Phenomena) • PHYS104 (Foundations of Modern Physics) • PHYS156 (Practical Skills for Mathematical Physics) • (G1F7 ONLY) • ENVS100 (Study Skills and GIS) • ENVS111 (Climate, Atmosphere and Oceans) • ENVS158 (Ocean Chemistry and Life) • Psychology & Philosophy Modules Available: • (G1X3 ONLY) • PSYC101 (Introduction to Psychology 1) • PSYC102 (Introduction to Psychology 2: Development, Personality & Intelligence) • (GV15 ONLY) • PHIL107 (Analysing Philosophical Texts 1) • PHIL108 (Analysing Philosophical Texts 2) • PHIL127 (Symbolic Logic 1) • Modern Foreign Languages Modules Available: • (GR11 ONLY) • FREN101 (Modern French Language 1) • FREN102 (Modern French Language 2) • FREN122 (Introduction to the Short French Narrative) • MODL105 (Language Awareness) • (G1R9 ONLY) • 30 Credits’ worth of Spanish, French or German

3. Second Year Modules Mathematical Sciences Modules • MATH201 (Ordinary Differential Equations) • Elementary techniques for the solution of ODE's, • Basic properties of ODE, including main features of initial value problems and boundary value problems, such as existence & uniqueness of solutions; • The solution of linear systems • (homogeneous & non-homogeneous) • with constant coefficients matrix of size 2 & 3; • A range of applications of ODE. • MATH206 (Group Project Module) • Work effectively in groups, and delegate common tasks. • Write substantial mathematical documents in an accessible form. • Give coherent verbal presentations of more advanced mathematical topics. • Appreciate how mathematical techniques can be applied in a variety of different contexts. • MATH224 (Introduction To The Methods Of Applied Mathematics) • The solution of basic ordinary differential equations, including systems of first order equations; • The concept of Fourier series & their potential application to the solution of both ordinary & partial differential equations; • Solve simple first order partial differential equations; • Solve the basic boundary value problems for 2nd order linear partial differential equations using the method of separation of variables. • MATH225 (Vector Calculus With Applications In Fluid Mechanics) • Work confidently with different coordinate systems. • Evaluate line, surface and volume integrals. • Appreciate the need for the operators div, grad & curl together with the associated theorems of Gauss & Stokes. • Recognise the many physical situations that involve the use of vector calculus. • Apply mathematical modelling methodology to formulate and solve simple problems in electromagnetism and inviscid fluid flow. • MATH227 (Mathematical Models: Microeconomics & Population Dynamics) • Use techniques from several variable calculus in tackling problems in microeconomics. • Use techniques from elementary differential equations in tackling problems in population dynamics. • Apply mathematical modelling methodology in these subject areas • MATH228 (Classical Mechanics) • the motion of bodies under simple force systems, including calculations of the orbits of satellites, comets and planetary motions • rigid body motions including geophysical applications such as the precession of the axis of rotation of the earth. • MATH241 (Metric Spaces & Calculus ) • Be familiar with a range of examples of metric spaces. • Have developed their understanding of the notions of convergence and continuity. • Understand the contraction mapping theorem and appreciate some of its applications. • Be familiar with the concept of the derivative of a vector valued function of several variables as a linear map. • Understand the inverse function and implicit function theorems and appreciate their importance. • Have developed their appreciation of the role of proof and rigour in mathematics. • MATH243 (Complex Functions) • The central role of complex numbers in mathematics; • All the classical holomorphic functions; • Compute Taylor & Laurent series of such functions; • The content & relevance of the various • Cauchy formulae and theorems; • The reduction of real definite integrals to contour integrals; • Computing contour integrals. • MATH244 (Linear Algebra And Geometry) • The geometric meaning of linear algebraic ideas, • The concept of an abstract vector space & how it is used in different mathematical situations, • apply a change of coordinates to simplify a linear map, • manipulate matrix groups (in particular Gln, On & Son), • Bilinear forms from a geometric point of view. • MATH247 (Commutative Algebra) • Work confidently with the basic tools of algebra (sets, maps, binary operations and equivalence relations). • Recognise abelian groups, different kinds of rings • (integral, Euclidean, principal ideal and unique factorisation domains) and fields. • Find greatest common divisors using the Euclidean algorithm in Euclidean domains. • Apply commutative algebra to solve simple number-theoretic problems. • MATH248 (Geometry Of Curves) • use a computer package to study curves and their evolution in both parametric and algebraic forms. • determine and work with tangents, inflexions, curvature, cusps, nodes, length and other features. • calculate envelopes and evolutes. • solve the position and shape of some algebraic curves including conics. • MATH261 (Introduction To Methods Of Operational Research) • Appreciate the operational research approach. • Be familiar with a range of standard problems. • Be able to formulate simple `real-world' problems using standard models. • Be able to apply standard techniques. • Appreciate the importance of sensitivity analysis. • MATH262 (Financial Mathematics II) • Modern portfolio theory • Introduction to markets and options • Discrete time Finance • Continuous time finance • MATH263 (Statistical Theory & Methods I) • Have a conceptual and practical understanding • of a range of commonly applied statistical procedures. • Have also developed some familiarity with the • statistical package MINITAB. • MATH264 (Statistical Theory & Methods II) • understand basic probability calculus. • be familiar with a range of techniques for solving • real life problems of a probabilistic nature. • MATH265 (Measure Theory And Probability ) • master the basic results about measures, measurable functions, Lebesgue integrals and their properties; • to understand deeply the rigorous foundations of the probability theory; • to know certain applications of the measure theory to probability and financial mathematics. . MATH266 (Numerical Analysis, Solution Of Linear Equations) apply numerical methods in a number of different contexts; solve systems of linear & nonlinear algebraic equations to specified precision; compute eigenvalues & eigenvectors by the power method; solve boundary value & initial problems to finite precision; develop quadrature methods for numerical integration. • MATH267 (Financial Mathematics I) • Time value of money • Annuities • Loans and the equation of value • Cash flow models & Investment projects • Bonds, Fixed interest security & index-linked security • Term structure of interest rates & • Stochastic interest rates models • MATH268 (Operational Research: Probabilistic Models) • be familiar with a range of techniques for solving probabilistic problems arising in OR and Mathematical Finance. • EDUC500 (Mathematics In Schools) • insight into children's mathematical thinking; • growing confidence in working with pupils; • an informed view of the role of secondary mathematics teachers and of the environment in which they work; • Experience in the use of computers for word-processing. Other Subjects’ Modules • Physics & Environmental Sciences Modules Available: • Economics & Finance Modules Available: • (G1N3, GN11 & GL11 ONLY) • Computer Science Modules Available: • (GG14 & G1R9 ONLY) • COMP201 • COMP202 • COMP207 • COMP213 • COMP218 • COMP219 • ECON211 • ECON212 • ECON221 • ECON222 • ECON223 • ECON224 • ECON241 • (F344, FGH1, FG31 ONLY) • PHYS201 • PHYS202 • PHYS203 • PHYS204 • (G1F7 ONLY) • ENVS202 • ENVS222 • ENVS266 • ENVS260 • Modern Foreign Languages Modules Available: • (GR11 ONLY) • FREN201 • FREN202 • (G1R9 ONLY) • 30 Credits’ worth of Spanish, French or German • Philosophy Modules Available: • (GV15 ONLY) • PHIL207 • PHIL212 • PHIL215 • PHIL219 • PHIL227 • PHIL228 • PHIL236 • PHIL237 • PHIL239

4. Third Year Modules Mathematical Sciences Modules • MATH302 (History Of Mathematics) • Acquire a historical perspective on the development of mathematical ideas and their relationship with contemporary culture, and through the various methods of assessment become more articulate about their importance and relevance in the educational scene • MATH322 (Chaos And Dynamical Systems) • Understand the possible behaviour of dynamical systems with particular attention to chaotic motion; • be familiar with techniques for extracting fixed points and exploring the behaviour near such fixed points; • understand how fractal sets arise and how to characterise them. • MATH323 (Further Methods Of Applied Mathematics ) • to use the method of "Variation of Arbitrary Parameters" to find the solutions of some inhomogeneous ODE’s, solve simple integral extremal problems including cases with constraints; • classify a system of simultaneous 1st-order linear partial differential equations, & to find the Riemann invariants & general or specific solutions in appropriate cases; classify 2nd-order linear partial differential equations &, in appropriate cases, find general or specific solutions. • MATH324 (Cartesian Tensors And Mathematical Models Of Solids And Viscous Fluids) • understand and actively use the basic concepts of continuum mechanics such as stress, deformation and constitutive relations, and apply mathematical methods for analysis of problems involving the flow of viscous fluid or behaviour of solid elastic materials. • MATH325 (Quantum Mechanics) • solve Schrodinger’s equation for simple systems, and have some intuitive understanding of the significance of quantum mechanics for both elementary systems and the behaviour of matter. • MATH326 (Relativity) • understand why space-time forms a non-Euclidean four-dimensional manifold; • be proficient at calculations involving Lorentz transformations, energy-momentum conservation, and the Christoffel symbols. • understand the arguments leading to Einstein's field equations and how Newton's law of gravity arises as a limiting case. • be able to calculate the trajectories of bodies in a Schwarzschild space-time. • MATH331 (Mathematical Economics) • Have further extended their appreciation of the role of mathematics in modelling in Economics and the Social Sciences. • Be able to formulate, in game-theoretic terms, situations of conflict and cooperation. • Be able to solve mathematically a variety of standard problems in the theory of games. • To understand the relevance of such solutions in real situations. • MATH332 (Population Dynamics) • Use analytical and graphical methods to investigate population growth and the stability of equilibrium states for continuous-time and discrete-time models of ecological systems. • Relate the predictions of the mathematical models to experimental results obtained in the field. • Recognise the limitations of mathematical modelling in understanding the mechanics of complex biological systems.. • MATH334 (Mathematical Physics Projects) • understood an area of advanced theoretical physics • had experience in consulting relevant literature • gained experience in using appropriate mathematics • made a critical appraisal of the current understanding of the area • learnt how to construct a written essay and given an oral presentation. • MATH342 (Number Theory) • understand and solve a wide range of problems about the integers and rationals, and have a better understanding of the properties of prime numbers. • MATH343 (Group Theory) • Understanding of abstract algebraic systems (groups) by concrete, explicit realisations (permutations, matrices) • The ability to understand and explain classification results to users of group theory. • To have a general understanding of the origins and history of the subject. • MATH344 (Combinatorics) • understand the type of problem to which the methods of Combinatorics apply, and model these problems; • solve counting and arrangement problems; • solve general recurrence relations using the generating function method; • appreciate the elementary theory of partitions and its application to the study of symmetric functions. • MATH349 (Differential Geometry) • Using differential calculus to discover geometrical properties of explicitly given curves & surfaces; • the role played by special curves on surfaces & making explicit calculations with these curves; • Acquiring an intuitive ‘feel’ for what is meant by surface shape; • Understanding the difference between extrinsically defined properties and those which depend only on the surface metric; • Understanding the passage from local to global properties exemplified by the Gauss-Bonnet Theorem. • MATH350 (Analytic Methods In Higher Geometry) • understand the concept of duality in Linear Algebra, • be able to work with tensors, • understand the basic concepts of geometry of smooth manifolds, • be able to perform computations with differential forms in local coordinates, • know certain applications of differential forms to topology and Hamiltonian mechanics. • MATH351 (Analysis & Number Theory) • Completions & irrationality, diophantineapprox’n & its relation to uniform distribution, appreciate that analysis has a complex unity & have a feel for basic computations in analysis. Calculate rational approx’ns to real & padic numbers & use this in number theoretic situations. Find approx’ns to functions from families of simpler functions. Work with basic tools from analysis, like Fourier series & continuous functions to prove distributional properties of sequences of numbers. • . • MATH360 (Applied Stochastic Models ) • a grounding in the theory of continuous-time Markov chains and diffusion processes. They should be able to solve corresponding problems arising in epidemiology, mathematical biology, financial mathematics, etc. • MATH361 (Theory Of Statistical Inference) • a good understanding of the classical approach to and especially the likelihood methods for statistical inference. The students should also gain an appreciation of the blossoming area of Bayesian approach to inference. • MATH362 (Applied Probability ) • To give examples of empirical phenomena for which stochastic processes provide suitable mathematical models. To provide an introduction to the methods of probabilistic model building for ``dynamic" events occurring over time. To familiarise students with an important area of probability modelling. • MATH363 (Linear Statistical Models ) • General Linear Models: simple linear regression; one-way analysis of variance; estimation and inference; two and three-way analysis of variance; more complex designs. • Generalized Linear Models: foundations; exponential family of distributions; estimation and inference; binary response variables; normal response variables; contingency tables and log-linear models; other applications • MATH364 (Medical Statistics) • identify the types of problems found in medical statistics; demonstrate the advantages and disadvantages of different epidemiological study designs; apply appropriate statistical methods to problems arising in epidemiology and interpret results; explain and apply statistical techniques used in survival analysis; critically evaluate statistical issues in the design & analysis of clinical trials • discuss statistical issues related to systematic review & apply appropriate methods of meta-analysis • apply Bayesian methods to simple medical problems MATH366 (Mathematical Risk Theory ) Decision Theory  Applications of Probability Theory to actuarial risk models  (The collective risk model (aggregate loss models)   The individual risk model (group insurance models)   Ruin Theory  Claim reserving methods • MATH367 (Networks In Theory And Practice) • be able to model problems in terms of networks. • be able to apply effectively a range of exact and heuristic optimisation techniques • MATH399 (Mathematical Project Module) • A range of projects are available within each division, as well as a Maths in Society project. Other Subjects’ Modules • Economics & Finance Modules Available: • (G1N3 & GL11 ONLY) • ENVS332 • ENVS335 • ENVS349 • ENVS366 • ENVS372 • ENVS376 • ENVS377 • ENVS389 • ENVS461 • PHIL306 • PHIL309 • PHIL310 • PHIL316 • PHIL317 • PHIL326 • PHIL329 • PHIL332 • PHIL340 • PHIL346 • PHIL361 • PHIL362 • COMP304 • COMP305 • COMP309 • COMP310 • COMP313 • COMP315 • COMP317 • COMP319 • COMP323 • ECON306 • ECON308 • ECON311 • ECON322 • ECON325 • ECON326 • ECON327 • ECON333 • ECON335 • ECON340 • ECON343 • ACFI301 • ACFI302 • ACFI303 • ACFI304 • ACFI305 • ACFI341 • PHYS363 • PHYS370 • PHYS374 • PHYS375 • PHYS377 • PHYS378 • PHYS381 • PHYS382 • PHYS387 • PHYS388 • PHYS389 • PHYS393 • Modern Foreign Languages Modules Available: • (G1R9 ONLY) • 15 Credits’ worth of Spanish, French or German • Philosophy Modules Available: • (GG13 ONLY) • PHIL346 • Environmental Sciences Modules Available: • (G1F7 ONLY) • Philosophy Modules Available: • (GG13 & GV15 ONLY) • Computer Science Modules Available: • (GG14 ONLY) • Physics Modules Available: • (F344, FGH1, FG31 ONLY)

5. Fourth Year Modules Mathematical Sciences Modules • MATH410 (Manifolds, Homology & Morse Theory) • give examples of manifolds, particularly in low dimensions; • compute homology groups, Euler characteristics and degrees of maps in simple cases; • determine whether an explicitly given function is Morse & to identify its critical points & their indices; • use the Morse complex to compute Euler characteristics and, in simple cases, homology. • MATH420 (Advanced Mathematical Physics Project) • understood an area of current research in theoretical physics • had experience in locating and consulting relevant research material, particularly through use of journals and the Internet • learnt & deployed appropriate mathematical techniques • learnt how to produce a dissertation • acquired and practised skills of oral presentation • MATH421 (Linear Differential Operators in Mathematical Physics) • understand and actively use the basic concepts of mathematical physics, such as the concept of generalised functions, Sobolev spaces, weak solutions, and apply powerful mathematical methods to problems of electro-magnetism, elasticity, heat conduction and propagation of waves • MATH423 (Introduction To String Theory) • The properties of the classical string. • The basic structure of modern particle physics and how it may arise from string theory. • The basic properties of first quantized string and the implications for space-time dimensions. • String toroidal compactifications and T-duality. • MATH424 (Analytical & Computational Methods For Applied Mathematics) • obtain solutions to certain important PDEs using a variety of analytical techniques and should be familiar with important properties of the solution. • apply a range of standard numerical methods for solution of PDEs and should have an understanding of relevant practical issues • MATH425 (Quantum Field Theory) • be able to compute simple Feynman diagrams, • understand the basic principles of regularisation and renormalisation • be able to calculate elementary scattering cross-sections. • MATH426 (Mathematical Biology) • Use techniques from difference equations and ordinary and partial differential equations in tackling problems in biology. • Apply mathematical modelling methodology in this area. • MATH427 (Waves. Mathematical Modelling) • Students will learn essential modelling techniques in problems of wave propagation. They will also understand that mathematical models of the same type can be successfully used to describe different physical phenomena. Students will also study background mathematical theory in models of acoustics, gas dynamics, and water waves • MATH431 (Introduction To Modern Particle Theory) • The Feynman diagram pictorial representation of particle interactions. • The role of symmetries & conservation laws in distinguishing the strong, weak & electromagnetic interactions. • Spectrum & interactions of elementary particles & their embedding into Grand Unified Theories (GUTs). • The flavour structure of the standard particle model & generation of mass through symmetry breaking. • Phenomenological aspects of GUTs. • MATH432 (Mathematical Physics Project) • understood an area of advanced theoretical physics • had experience in consulting relevant literature • gained expertise in using appropriate mathematics • made a critical appraisal of the current state of knowledge of the area • learnt how to construct an essay • gained familiarity with a scientific word-processing package such as TeX • acquired skills of oral presentation. • MATH441 (Higher Arithmetic) • apply analytic techniques to arithmetic functions • understand basic analytic properties of the Riemann zeta function • understand Dirichlet characters and L-series • understand the connection between Ingham's theorem and the Prime Number Theorem • MATH442 (Representation Theory of Finite Groups ) • use representation theory as a tool to understand finite groups; • calculate character tables of a variety groups. • MATH443 (Curves & Singularities) • A confident use of the singularity theory of functions of one variable, including unfolding theory, in concrete applications. A knowledge of fundamental constructions such as that of an envelope of curves or surfaces, and the dual of a curve or surface. A grounding in the theory of differentiable manifolds and transversality as geometrical tools. A preparation for further study of singularity theory, including functions of several variables and mappings, and elements of symplectic geometry • MATH444 (Elliptic Curves) • The ability to describe and to work with the group structure on a given elliptic curve. Understanding and application of the Abel-Jacobi theorem. To estimate the number of points on an elliptic curve over a finite field. To use the reduction map to investigate torsion points on a curve over Q. To apply descent to obtain so-called Weak Mordell-Weil Theorem. Use heights of points on elliptic curves to investigate the group of rational points on an elliptic curve. Understanding and application of Mordell-Weil theorem. Encode and decode using public keys. • MATH446 (Lie Groups & Lie Algebras) • basic results about Lie groups and Lie algebras and their relation, classical Lie groups and Lie algebras, basic structure and classification results about Lie groups and Lie algebras. • MATH449 (Galois Theory) • Know why and how a polynomial equation of degree up to 4 can be solved in radicals. • Understand why a solution in radicals is impossible in general for the degree greater than or equal to 5. • Understand when a polynomial can be solved in radicals. • Know when a geometric construction can be done by a ruler and compass. • Know what is the Galois group of a polynomial which permits the above results. • MATH455 (Differentiable Functions) • technique of reducing functions to local normal forms; • understand the concept of stability of mappings; • construct versal deformations of isolated function singularities. • MATH456 (Intro to Knot Theory & Low Dimensional Topology) • tell whether two simple knots in 3-space can be transformed into one another without cutting or tearing; compute the Jones, Alexander, HOMFLY & Kauffman polynomials in simple cases; represent a link as the closure of a braid; give e.g.’s of orientable surfaces that bound a given knot in 3-space; determine whether two braids (say given by their diagrams) represent the same element in the braid group; compute the genus & the Euler characteristic of 2-manifold; compute the genus of a ramified covering of a 2-manifold • MATH490 (Project For M.Math) • (30 Credits) • Gained a greater understanding of the chosen mathematical topic. Gained an appreciation of the historical context. learned how to abstract mathematical concepts and explain them. • had experience in consulting related relevant literature. Learned how to construct a written project report. Had experience in making an oral presentation. Gained familiarity with the standard scientific word-processing packages LaTeX or TeX • MATH499 (Project For M.Math) • (15 Credits) • Gained a greater understanding of the chosen mathematical topic. Gained an appreciation of the historical context. learned how to abstract mathematical concepts and explain them. • had experience in consulting related relevant literature. Learned how to construct a written project report. Had experience in making an oral presentation. Gained familiarity with the standard scientific word-processing packages LaTeX or TeX • Physics Modules Available: • (F344, FGH1, ONLY) • PHYS480 • PHYS489 • PHYS490 • PHYS491 • PHYS493 • PHYS497 • PHYS499 • Modern Foreign Languages Modules Available: • (GR11 ONLY) • FREN301 • FREN302 • PLUS OTHER FRENCH MODULES Other Subjects’ Modules

6. G100: BSc MathematicsFrom Application to Graduation Graduation! Application Successful!

7. G1X3: BSc Mathematics With EducationFrom Application to Graduation Graduation! Application Successful!

8. G110: BSc Pure MathematicsFrom Application to Graduation Graduation! Application Successful!

9. G1F7: BSc Mathematics with Ocean and Climate StudiesFrom Application to Graduation Graduation! Application Successful!

10. GG13: BSc Mathematics and StatisticsFrom Application to Graduation Graduation! Application Successful!

11. GG14: BSc Mathematics & Computer ScienceFrom Application to Graduation Graduation! Application Successful!

12. GV15: BA Philosophy & MathematicsFrom Application to Graduation Graduation! Application Successful!

13. GL11: BA Economics and Mathematics From Application to Graduation Graduation! Application Successful!

14. GN11: BSc Mathematics & Business StudiesFrom Application to Graduation Graduation! Application Successful!

15. G1N3: BSc Mathematics with FinanceFrom Application to Graduation Graduation! Application Successful!

16. FG31: BSc Physics and MathematicsFrom Application to Graduation Graduation! Application Successful!

17. FGH1: MMath Mathematical PhysicsFrom Application to Graduation Graduation! Application Successful!

18. F344: MPhys Theoretical PhysicsFrom Application to Graduation Graduation! Application Successful!

19. G101: MMath MathematicsFrom Application to Graduation Graduation! Application Successful!

20. G1R9: BSc Mathematical Sciences with a European Language From Application to Graduation Graduation! Application Successful!

21. GR11: BA French and Mathematics From Application to Graduation Graduation! Application Successful!