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Mathematical Physics



Explore the mathematical structures that underpin our understanding of the physical universe through a substantial programme of advanced study spanning calculus, classical mechanics, electromagnetism, quantum mechanics, relativity, statistical physics and advanced mathematical methods. From the mathematics of motion, waves and fields to general relativity, quantum theory and the foundations of modern theoretical physics, the programme provides a rigorous progression from fundamental mathematical techniques to some of the most fascinating ideas in contemporary physics.


Designed for serious enthusiasts and independent learners, the 360-credit Advanced Diploma progresses through three levels of study, with opportunities at Level 6 to explore specialist areas including quantum field theory, string theory, cosmology, nonlinear dynamics, fluid dynamics, advanced electromagnetism, and geometry and topology. Study the complete programme over three years or longer, or begin with an individual Level 4 module and build from there.

KEY INFORMATION

What is Mathematical Physics

Mathematical Physics uses advanced mathematical ideas and techniques to describe, model and understand the physical universe. It provides the mathematical foundations of areas such as mechanics, electromagnetism, quantum theory, relativity, cosmology and modern theoretical physics.

Mode of Delivery

Asynchronous lectures, reading materials and extensive resources are shared on our Moodle platform to which you will be granted access. The course is delivered entirely online, under the guidance of our expert lecturers and academic staff. The academic year begins in September but you can also enter the programme in January.

What do you study

Broadly similar to a three year undergraduate degree, there are three levels (levels 4 to 6). In level 4 (year 1) you will study four core modules to give you the foundations of Mathematical Physics. In year 2 you study at level 5, with further core modules to advance your knowledge, and begin to make choices from our optional modules. In year 3 you will specialise by choosing from a variety of optional modules, and complete your dissertation on a topic chosen in collaboration with the academic staff and your supervisor. The modules are detailed below.

Cost

Each 15 credit module is £200, with a 30 credit module costing £400. This includes everything for the module, with no hidden cost. The entire programme therefore costs £4800, but you can study a module at a time and exit the programme when you wish. You will receive a certificate for each module, and a certificate of completion should you exit early which summarises the extent of your study.

Founding Cohort Discount

As these programmes are new, we are offering a limited number of places with a scholarship discount of 80%. T&Cs apply. This is an excellent opportunity to learn something new, and be involved with the development of a new course, at a really low cost. Email us today to find out more (info@wessexacademia.co.uk). 

MODULES

Year One (Level 4 Equivalent)

Foundations (120 credits)

Calculus for Mathematical Physics

30 credits

Develops the core techniques of single and multivariable calculus, series and differential equations required for the mathematical study of physical systems.

Linear Algebra and Mathematical Structures

15 credits

Introduces vectors, matrices, vector spaces, linear transformations and eigenvalue methods, with emphasis on their applications throughout mathematical physics.

Classical Mechanics

30 credits

Develops the mathematical description of motion through Newtonian mechanics, oscillations, central forces and conservation principles, progressing towards analytical mechanics.

Vector Calculus and Fields

15 credits

Explores gradient, divergence, curl and the major integral theorems through their application to vector fields and physical phenomena.

Waves, Oscillations and Mathematical Modelling

15 credits

Examines harmonic and coupled oscillations, normal modes and wave phenomena while developing techniques for constructing and analysing mathematical models of physical systems.

Introduction to Electromagnetism

15 credits

Introduces the mathematical description of electric and magnetic fields, potentials and circuits and establishes the foundations for the later study of Maxwell’s theory.


Year 2 (Level 5 Equivalent)

Developing Expertise 120 Credits

Advanced Classical Mechanics

15 credits

Extends classical mechanics through variational principles, Lagrangian and Hamiltonian formulations, phase space and canonical methods.

Partial Differential Equations and Fourier Methods

15 credits

Develops methods for formulating and solving partial differential equations in physics, including separation of variables, Fourier series and Fourier transforms.

Complex Analysis and Special Functions

15 credits

Introduces complex-variable methods, contour integration, residues and important special functions used in the solution of mathematical-physics problems.

Electromagnetic Theory

15 credits

Develops a mathematical treatment of electromagnetism through Maxwell’s equations, electromagnetic waves, potentials, boundary-value problems and radiation.


Quantum Mechanics I

30 credits

Introduces the mathematical foundations of quantum mechanics through wave functions, operators, observables, eigenstates, uncertainty and solutions of fundamental quantum systems.

Special Relativity and Tensor Methods

15 credits

Examines Lorentz transformations, four-dimensional spacetime and relativistic mechanics while introducing tensor methods required for more advanced theories of physics.

Thermal and Statistical Physics

15 credits

Connects macroscopic thermodynamics with microscopic statistical descriptions of physical systems through probability, ensembles and statistical mechanics.

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Year 3 (Level 6 Equivalent)

Advanced

Quantum Mechanics II

30 credits

Develops advanced quantum theory through angular momentum, spin, identical particles, approximation techniques and the analysis of more complex quantum systems.

General Relativity

30 credits

Introduces the mathematical theory of gravitation through differential geometry, spacetime metrics, curvature and Einstein’s field equations, with applications to astrophysics and cosmology.

Advanced Methods of Mathematical Physics

15 credits

Develops sophisticated mathematical techniques used across theoretical physics, including Green’s functions, distributions, integral transforms, perturbation methods and asymptotic analysis.

Symmetry and Group Theory in Physics

15 credits

Year 3 (Level 6 Equivalent) - Options

Options - Choose 2

Introduction to Quantum Field Theory

15 credits

Introduces the principles of quantum field theory, exploring fields, quantisation, particles and interactions and the relationship between quantum mechanics and special relativity.

Introduction to String Theory

15 credits

Introduces the mathematical and physical foundations of string theory, including classical strings, quantisation, extra dimensions and the theory’s approach to gravity and unification.

Cosmology and the Early Universe

15 credits

Applies relativity and mathematical physics to the origin and evolution of the Universe, including cosmic expansion, the early Universe and the development of large-scale structure.

Nonlinear Dynamics and Chaos

15 credits

Explores nonlinear dynamical systems, stability, bifurcations, deterministic chaos and the emergence of complex behaviour from comparatively simple mathematical models.

Fluid Dynamics

15 credits

Develops the mathematical description of fluids through conservation laws, flow equations, vorticity and selected applications in physical systems.

Advanced Electromagnetic Theory

15 credits

Extends electromagnetic theory through advanced treatments of fields, radiation, wave propagation and mathematically challenging electromagnetic systems.

Geometry and Topology in Physics

15 credits

Introduces geometric and topological ideas used in modern theoretical physics and examines how global mathematical structure can determine the behaviour of physical systems.

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