Theoretical Physics MPhys

Module details Programme Year One

For these programmes you may take (a-c), (e) and the Physics modules Electricity and Magnetism, Practical Techniques in Physics, Introduction to Relativity, Introduction to Quantum Physics, Thermal Physics and Computing Techniques in Physics. After passing the first year, you have the flexibility of transferring to Mathematics or Physics if you wish, subject to approval. For F344 or FGH1 you may take (d) instead of one of the Physics modules. For F344 there is another route, taking more Physics modules; if you take this route you will study the same mathematics modules as Physics students. Please see the Physics subject brochure for more information or call +44(0) 151 794 5927 to obtain a copy.

Compulsory modules

• Calculus I (MATH101) Level 1 Credit level 15 Semester First Semester Exam:Coursework weighting 80:20 Aims

  1.       To introduce the basic ideas of differential and integral calculus, to develop the basic  skills required to work with them and to  apply these skills to a range of problems.

  2.       To introduce some of the fundamental concepts and techniques of real analysis, including limits and continuity.

  3.       To introduce the notions of sequences and series and of their convergence.

  Learning Outcomes

  After completing the module students should be able to:

  ·      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.

• Calculus Ii (MATH102) Level 1 Credit level 15 Semester Second Semester Exam:Coursework weighting 80:20 Aims

  ·      To discuss local behaviour of functions using Taylor’s theorem.

  ·      To introduce multivariable calculus including partial differentiation, gradient, extremum values and double integrals.

  Learning Outcomes

  After completing the module, students should be able to:

  ·         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.

• Introduction To Linear Algebra (MATH103) Level 1 Credit level 15 Semester First Semester Exam:Coursework weighting 80:20 Aims
  •      To develop techniques of complex numbers and linear algebra, including equation solving, matrix arithmetic and the computation of eigenvalues and eigenvectors.
  •      To develop geometrical intuition in 2 and 3 dimensions.
  •      To introduce students to the concept of subspace in a concrete situation.
  •    To provide a foundation for the study of linear problems both within mathematics and in other subjects.
  Learning Outcomes

  After completing the module students should be ableto:

  •     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, if time permits, apply these calculations to the geometry of conics and quadrics.
• Dynamic Modelling (MATH122) Level 1 Credit level 15 Semester Second Semester Exam:Coursework weighting 80:20 Aims

  1. to provide the basic methods for modelling mathematically topics in subjects like biology, engineering, physical sciences and social sciences;

  2. to discuss the advantages of using mathematics in modelling;

  3. to demonstrate some simple models involving differential equations and difference equations;

  
  4. to provide a foundation for an understanding of mechanics. Learning Outcomes

  After completing the module students should be able to:
  

  . 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.

Programme Year Two

In the second and subsequent years of all programmes, there is a wide range of modules. For the programme that you choose there may be no compulsory modules (although you may have to choose a few from a subset such as Pure Mathematics). If you make a different choice, you will find that one or more modules have to be taken. Each year you will choose the equivalent of eight modules. Please note that we regularly review our teaching so the choice of modules may change.

Year Two modules

• Ordinary differential equations
• Group projects
• Iteration and Fourier series
• Complex functions
• Linear algebra and geometry
• Commutative algebra
• Geometry of curves
• Introduction to the methods of applied mathematics
• Vector calculus with applications in fluid mechanics
• Mathematical models of non-physical systems
• Classical mechanics
• Numerical analysis, solution of linear equations
• Introduction to methods of operational research
• Introduction to financial mathematics
• Statistical theory and methods I
• Statistical theory and methods II
• Operational research: probabilistic models

Programme Year Three

In the second and subsequent years of all programmes, there is a wide range of modules. For the programme that you choose there may be no compulsory modules (although you may have to choose a few from a subset such as Pure Mathematics). If you make a different choice, you will find that one or more modules have to be taken. Each year you will choose the equivalent of eight modules. Please note that we regularly review our teaching so the choice of modules may change.

Year Three modules

• History of mathematics
• Number theory
• Group theory
• Combinatorics
• Differential geometry
• Riemann surfaces
• Chaos and dynamical systems
• Further methods of applied mathematics
• Cartesian tensors and mathematical models of solids and viscous fluids
• Quantum mechanics
• Relativity
• Introduction to variational calculus and homogenization theory
• Non-physical applications I (mathematical economics)
• Non-physical applications II (population dynamics)
• Theory of statistical inference
• Linear statistical models
• Networks in theory and practice
• Applied probability
• Mathematical physics essay (F326)
• Risk management
• Introduction to modern particle physics
• Metric spaces and topology
• Medical statistics
• Projects in pure and applied mathematics, statistics and theoretical physics

Programme Year Four

There is a large set of modules available, some of which are taught in alternate years. MMath/MPhys students will take at least seven of these during Years Three and Four. There is also a compulsory project.

The modules listed above are illustrative and subject to change. Please refer to the department site for further information