D'Math University | Computing & Interdisciplinary Mathematics

BSc Mathematical Physics

Pursue the pure mathematical foundations of physical theories — from classical field theory and differential geometry to quantum groups and symplectic mechanics — in one of the most theory-intensive undergraduate programmes in existence.

Undergraduate 3–4 Years Theory-Intensive Physics & Pure Math
34
Modules
£46k
Avg Graduate Salary
38+
Research Partners
4
Specialisation Areas

Programme Overview

What You Will Study

Mathematical Physics treats the laws of nature as mathematical structures to be understood in their full depth. You will study the geometry of spacetime, the algebra of symmetries, and the functional analysis underpinning quantum mechanics — with uncompromising mathematical rigour.

  • Geometry & Topology: differential geometry, Lie groups, symplectic manifolds
  • Algebra of Physics: group theory, Lie algebras, quantum groups, representation theory
  • Quantum Theory: Hilbert spaces, spectral theory, quantum field theory
  • Classical Theory: classical fields, thermodynamics, statistical physics

Programme Highlights

Four specialisation areas — Quantum Gravity, Integrable Systems, Quantum Information, and Statistical Field Theory — allow deep focus in Years 3–4 under expert supervision. Graduates regularly progress to the world's top PhD programmes.

  • Four Specialisations: Quantum Gravity, Integrable Systems, Quantum Information, Statistical Field Theory
  • Perimeter Institute Link: exchange and summer programme opportunities
  • PhD Pathway: exceptional preparation for doctoral study in mathematical physics
  • Seminar Programme: weekly research talks by leading international physicists and mathematicians
Course Catalogue

Click any course to view its objective and learning outcomes.

MPH 101 Mathematical Methods I +

Objective

To equip physicists with the analytical tools used throughout theoretical physics.

Learning Outcomes

  • Solve ODEs encountered in classical mechanics.
  • Use Fourier series and transforms to decompose signals.
  • Apply variational methods to mechanics.
  • Manipulate complex variables in physics contexts.
  • Identify and apply symmetry arguments.
MPH 102 Classical Mechanics +

Objective

To formulate mechanics through Newtonian, Lagrangian and Hamiltonian frameworks.

Learning Outcomes

  • Apply Newton's laws to particle and rigid-body motion.
  • Derive Euler-Lagrange equations from variational principles.
  • Apply Hamilton's equations and canonical transformations.
  • Analyse central-force motion including Kepler's laws.
  • Use action-angle variables in periodic motion.
Interactive Activity — Vector Field & Gradient Visualizer
Pick a scalar field f(x,y). Gradient arrows point in the direction of steepest ascent. Click anywhere to drop a particle that follows the gradient.
f(x,y) =
Click on the plot to drop a particle.
Interactive Activity — 1D Wave Equation
Solve ∂²u/∂t² = c² ∂²u/∂x² on a string fixed at both ends. Pick an initial profile and watch waves propagate, reflect and superpose.
Initial: c = 5.0
MPH 103 Calculus & Linear Algebra +

Objective

To strengthen the algebraic and analytic foundations needed for physics.

Learning Outcomes

  • Compute multivariable derivatives and integrals.
  • Apply linear-algebra concepts to quantum mechanics.
  • Use eigenvalue analysis in vibrational problems.
  • Apply tensor notation to relativistic kinematics.
  • Implement numerical solutions to linear systems.
Interactive Activity — Derivative as Slope of Tangent
Drag the slider to move point P along the curve. The tangent line updates — its slope is the derivative.
f(x): x = 1.00
Interactive Activity — Riemann Sum Approximation
Drag the slider to add more rectangles. Watch the approximation converge to the true integral.
Rectangles n = 8
MPH 104 Vector Calculus & PDEs +

Objective

To build the mathematics of fields needed for electromagnetism and continuum physics.

Learning Outcomes

  • Compute gradient, divergence, curl and Laplacian.
  • Apply Green's, Stokes' and Divergence theorems.
  • Solve Laplace and Poisson equations on simple domains.
  • Apply separation of variables to wave and heat equations.
  • Use eigenfunction expansions in PDE solutions.
Interactive Activity — Vector Field & Gradient Visualizer
Pick a scalar field f(x,y). Gradient arrows point in the direction of steepest ascent. Click anywhere to drop a particle that follows the gradient.
f(x,y) =
Click on the plot to drop a particle.
MPH 201 Quantum Mechanics I +

Objective

To introduce quantum theory through the Schrödinger picture.

Learning Outcomes

  • Solve the time-independent Schrödinger equation in 1D.
  • Apply the harmonic oscillator and hydrogen atom solutions.
  • Use commutators and the uncertainty principle.
  • Apply perturbation theory to bound states.
  • Interpret measurements via the Born rule.
Interactive Activity — Vector Field & Gradient Visualizer
Pick a scalar field f(x,y). Gradient arrows point in the direction of steepest ascent. Click anywhere to drop a particle that follows the gradient.
f(x,y) =
Click on the plot to drop a particle.
Interactive Activity — 1D Wave Equation
Solve ∂²u/∂t² = c² ∂²u/∂x² on a string fixed at both ends. Pick an initial profile and watch waves propagate, reflect and superpose.
Initial: c = 5.0
MPH 202 Mathematical Methods II +

Objective

To extend analytical methods to special functions, contour integrals and Green's functions.

Learning Outcomes

  • Use contour integration to evaluate real integrals.
  • Apply special functions including Bessel and Legendre.
  • Construct Green's functions for ODEs and PDEs.
  • Apply asymptotic methods to integrals.
  • Use group-theoretic ideas in physics applications.
MPH 203 Statistical Mechanics +

Objective

To derive thermodynamics from microscopic ensembles.

Learning Outcomes

  • Compute partition functions for canonical ensembles.
  • Apply Boltzmann, Bose and Fermi statistics.
  • Derive thermodynamic potentials from partition functions.
  • Analyse phase transitions and critical exponents.
  • Apply statistical mechanics to simple models.
MPH 204 Special & General Relativity +

Objective

To formulate relativity using tensor calculus on spacetime.

Learning Outcomes

  • Apply Lorentz transformations to events and four-vectors.
  • Use the metric tensor in curved spacetime.
  • Derive geodesic equations.
  • Analyse the Schwarzschild solution.
  • Discuss observational tests of general relativity.
Interactive Activity — Vector Field & Gradient Visualizer
Pick a scalar field f(x,y). Gradient arrows point in the direction of steepest ascent. Click anywhere to drop a particle that follows the gradient.
f(x,y) =
Click on the plot to drop a particle.
Interactive Activity — 1D Wave Equation
Solve ∂²u/∂t² = c² ∂²u/∂x² on a string fixed at both ends. Pick an initial profile and watch waves propagate, reflect and superpose.
Initial: c = 5.0
MPH 301 Electromagnetic Theory +

Objective

To formulate Maxwell's equations and analyse classical electromagnetic phenomena.

Learning Outcomes

  • Solve electrostatics and magnetostatics problems.
  • Apply Maxwell's equations in differential and integral form.
  • Analyse plane and guided electromagnetic waves.
  • Compute radiation from accelerated charges.
  • Use gauge invariance in field theory.
MPH 302 Group Theory in Physics +

Objective

To apply group representation theory to symmetries in physics.

Learning Outcomes

  • Identify symmetry groups in molecules and crystals.
  • Apply representation theory of finite and Lie groups.
  • Use Wigner-Eckart theorem to evaluate matrix elements.
  • Apply Noether's theorem to conservation laws.
  • Discuss SU(2), SU(3) in particle physics.
Interactive Activity — Cayley Table Generator
Pick a group; the operation table generates instantly.
Group:
Interactive Activity — Symmetries of a Polygon
Apply rotations and reflections from the dihedral group D_n.
n = 5
Group element: e (identity)
MPH 303 Computational Physics +

Objective

To apply numerical methods to problems beyond analytical reach.

Learning Outcomes

  • Implement numerical integration of ODEs.
  • Use finite-difference methods for PDEs.
  • Run Monte Carlo simulations of statistical systems.
  • Apply Fourier methods to signals.
  • Profile and parallelise scientific code.
Interactive Activity — Vector Field & Gradient Visualizer
Pick a scalar field f(x,y). Gradient arrows point in the direction of steepest ascent. Click anywhere to drop a particle that follows the gradient.
f(x,y) =
Click on the plot to drop a particle.
MPH 304 Mathematical Physics Project +

Objective

To pursue an extended investigation in mathematical physics under supervision.

Learning Outcomes

  • Frame a research question at the maths-physics interface.
  • Apply both analytical and numerical techniques.
  • Write a research-style report with rigorous notation.
  • Present findings to a panel of physicists.
  • Reflect on the methodology of theoretical physics.
Interactive Activity — 1D Wave Equation
Solve ∂²u/∂t² = c² ∂²u/∂x² on a string fixed at both ends. Pick an initial profile and watch waves propagate, reflect and superpose.
Initial: c = 5.0

Core Modules

⚛️

Classical Field Theory

Lagrangian field theory, Noether's theorem, symmetry and conservation laws, gauge invariance, and the Standard Model structure.

🔢

Group Theory for Physics

Finite groups, continuous Lie groups, representations, and their central role in particle physics and crystallography.

🌌

Differential Geometry for Relativity

Manifolds, tensors, connections, curvature, Riemannian geometry, and the geometric formulation of general relativity.

📐

Hilbert Space Methods

Functional analysis, self-adjoint operators, spectral theorem, and the mathematical framework of quantum mechanics.

🧮

Lie Algebras

Structure theory, root systems, Dynkin diagrams, highest weight representations, and classification of simple Lie algebras.

💫

Thermodynamics & Statistical Physics

Equilibrium thermodynamics, ensemble theory, phase transitions, critical phenomena, and the renormalisation group.

🔬

Quantum Groups

Hopf algebras, deformation of Lie algebras, braided categories, and applications in quantum integrable systems.

🌊

Spectral Theory

Spectrum of operators, self-adjointness, Schrödinger operators, and connections to quantum mechanics and PDE theory.

📊

Mathematical Cosmology (Intro)

FLRW models, Friedmann equations, dark energy, inflation, and the large-scale structure of the mathematical universe.

⚡

Symplectic Geometry

Symplectic manifolds, Hamiltonian mechanics, Poisson brackets, moment maps, and geometric quantisation.

Career Outcomes

⚛️

Theoretical Physicist

Pursue fundamental research into quantum field theory, string theory, or quantum gravity at leading research universities and institutes.

🔢

Mathematical Physics Researcher

Investigate the mathematical structures underlying physical laws in dedicated mathematical physics groups worldwide.

💻

Quantum Technology Specialist

Apply deep quantum theory knowledge to quantum computing hardware, algorithms, and sensing technologies.

🔬

National Lab Scientist

Conduct theoretical and experimental physics research at Fermilab, CERN, RAL, or national laboratory environments.

📚

Academic Lecturer

Join a university mathematics or physics department, teaching and researching in mathematical physics at degree level.

🌌

CERN Researcher

Contribute to particle physics experiments and theoretical physics work at the European Organisation for Nuclear Research.

Where Our Graduates Go & Top Global Universities

Cambridge Oxford Imperial College London Perimeter Institute University of Chicago Princeton Utrecht University University of Edinburgh University of Amsterdam University of Bonn

Why D'Math University — Our 4-Step Approach

01

Pure Mathematical Rigour

Physics is formulated entirely in the language of modern mathematics — no hand-waving, no approximations without proof.

02

Geometry & Algebra Focus

Differential geometry and Lie theory are introduced early and used continuously as the backbone of physical theory.

03

Specialisation Depth

Four specialisation areas in Years 3–4 allow genuine expertise development under direct supervision of active researchers.

04

Global Research Network

Links with Perimeter Institute, CERN, and leading European mathematical physics centres open international opportunities.

Enrol in BSc Mathematical Physics →

Applications open year-round — master the mathematics that describes physical reality.