D'Math University | Applied Mathematics

MSc Applied Mathematics

An intensive one-year postgraduate programme for graduates who want to deploy advanced mathematical methods in science, engineering and finance. From asymptotic analysis and inverse problems to stochastic modelling and computational fluid dynamics, this programme produces highly sought-after applied mathematical scientists.

Postgraduate 1 Year Online Applied Research
10
Core Modules
£60k
Average Graduate Salary
35+
Partner Universities
6
Research Streams

Programme Overview

Programme Overview

  • Six research streams: fluids, biology, finance, engineering, climate, inverse problems
  • Three taught terms followed by a substantial research dissertation
  • Dissertation of 15,000–20,000 words on an applied mathematical problem
  • Collaborative projects with industrial and research partners
  • Guest lectures from practitioners in aerospace, finance and biomedical research
  • Computing labs using Python, MATLAB and FEniCS for simulation
  • Preparation for PhD programmes and senior applied roles

Entry Requirements

  • Bachelor's degree in Mathematics, Physics or Engineering (2:1 or above)
  • Solid background in ODEs, PDEs and linear algebra required
  • Experience with computational tools (Python/MATLAB) advantageous
  • Personal statement describing applied mathematics interests
  • Two academic references; industrial references also accepted
  • English: IELTS 6.5+ or TOEFL 88+ for non-native speakers
  • Interviews may be conducted for competitive places

Core Curriculum

🔢
Advanced Numerical Analysis
Finite element methods, spectral methods, stability and convergence analysis for PDEs.
🪨
Continuum Mechanics
Stress tensors, constitutive laws, elasticity, viscoelasticity and solid-fluid interaction.
📉
Asymptotic Methods
Perturbation theory, matched asymptotic expansions and WKB methods for singular problems.
💹
Mathematical Finance
Black-Scholes equation, option pricing, portfolio optimisation and interest rate modelling.
🔍
Inverse Problems
Ill-posedness, regularisation methods and applications in imaging, geophysics and medical science.
📈
Advanced Optimisation
Nonlinear programming, semi-definite programming, interior point methods and combinatorial optimisation.
🎲
Stochastic Modelling
Brownian motion, Ito calculus, stochastic differential equations and Monte Carlo simulation.
🌊
Computational Fluid Dynamics
Discretisation schemes, turbulence modelling, finite volume methods and high-performance computing.

Course Catalogue

Click any course to view its objective and learning outcomes.

APM 501 Advanced ODEs & Dynamical Systems +

Objective

To analyse nonlinear dynamics, bifurcations and chaos.

Learning Outcomes

  • Apply phase-plane analysis to nonlinear systems.
  • Identify Hopf and saddle-node bifurcations.
  • Apply Lyapunov methods for stability.
  • Identify chaotic dynamics.
  • Use centre manifold theory.
APM 502 PDEs & Boundary Value Problems +

Objective

To solve and analyse partial differential equations rigorously.

Learning Outcomes

  • Classify second-order PDEs.
  • Solve boundary-value problems.
  • Apply Sobolev space methods.
  • Use Green's functions and fundamental solutions.
  • Apply variational methods.
APM 503 Numerical Analysis +

Objective

To analyse and design stable, convergent numerical schemes.

Learning Outcomes

  • Analyse stability and convergence of finite-difference schemes.
  • Apply finite-element methods.
  • Use Krylov-subspace solvers.
  • Apply spectral methods.
  • Quantify computational error.
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.
APM 504 Mathematical Modelling +

Objective

To construct, analyse and validate models of complex systems.

Learning Outcomes

  • Translate scientific problems into mathematical models.
  • Apply asymptotic and perturbation methods.
  • Validate models against data.
  • Use sensitivity analysis.
  • Communicate models to non-mathematicians.
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.
APM 505 Continuum Mechanics +

Objective

To unify the mechanics of solids and fluids using tensor calculus.

Learning Outcomes

  • Apply tensor algebra to stress and strain.
  • Derive constitutive equations.
  • Solve elastostatic problems.
  • Apply Eulerian and Lagrangian descriptions.
  • Verify continuum models numerically.
APM 506 Optimisation Theory +

Objective

To find optima of constrained problems using modern algorithms.

Learning Outcomes

  • Apply convex optimisation theory.
  • Use interior-point methods.
  • Apply duality and Lagrangian relaxation.
  • Use stochastic optimisation.
  • Solve large-scale optimisation problems.
Interactive Activity — 2×2 Matrix Transformation
Set the entries of a 2×2 matrix. Watch how it transforms the unit square. Determinant = signed area of the transformed square.
a = 1.0 b = 0.5 c = -0.3 d = 1.0
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.
APM 507 Inverse Problems +

Objective

To recover model parameters from indirect observations.

Learning Outcomes

  • Apply Tikhonov regularisation.
  • Use Bayesian inverse methods.
  • Apply singular value decomposition.
  • Use iterative regularisation.
  • Solve inverse problems in imaging.
APM 508 Mathematical Biology +

Objective

To model biological systems using continuous and discrete dynamics.

Learning Outcomes

  • Build epidemic and ecology models.
  • Analyse pattern formation via reaction-diffusion.
  • Apply stochastic models for small populations.
  • Build evolutionary game-theory models.
  • Validate biological models against data.
APM 509 Computational Fluid Dynamics +

Objective

To simulate fluid flow numerically.

Learning Outcomes

  • Discretise Navier-Stokes equations.
  • Apply finite-volume methods.
  • Use turbulence models.
  • Apply spectral methods.
  • Validate simulations against benchmarks.
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.
APM 510 Industrial Mathematics +

Objective

To apply mathematics to real industrial problems.

Learning Outcomes

  • Frame industrial problems mathematically.
  • Apply rigorous models with practical constraints.
  • Communicate with industrial sponsors.
  • Use real datasets effectively.
  • Document modelling assumptions.
APM 511 Asymptotic & Perturbation Methods +

Objective

To analyse problems involving small or large parameters.

Learning Outcomes

  • Apply regular and singular perturbation.
  • Use matched asymptotic expansions.
  • Apply WKB approximation.
  • Use multiple-scales analysis.
  • Verify expansions numerically.
APM 512 Master's Project +

Objective

To complete an original applied mathematics research project.

Learning Outcomes

  • Identify an applied research problem.
  • Apply rigorous mathematical methods.
  • Use computational tools effectively.
  • Write a 15,000-word dissertation.
  • Defend orally to a panel.

Career Pathways

📊
Quantitative Researcher
Develop systematic trading strategies and risk models at quantitative hedge funds and proprietary trading firms.
✈️
Aerospace Modeller
Simulate aerodynamic behaviour and structural performance for next-generation aircraft and spacecraft programmes.
🧬
Biomedical Mathematician
Model drug diffusion, tumour growth and physiological systems to accelerate pharmaceutical and medical research.
⚠️
Risk Engineer
Quantify operational and financial risk for banks, insurance companies and infrastructure projects using stochastic models.
🖥️
Simulation Scientist
Build high-fidelity simulations for national laboratories, engineering consultancies and advanced manufacturing.
🌍
Climate Analyst
Develop and run climate and ocean circulation models for government agencies and international climate research bodies.

Top Global Universities

University of Oxford Imperial College London University of Cambridge University of Edinburgh ETH Zürich TU Delft University of Waterloo University of Melbourne NUS Singapore Carnegie Mellon University

Why D'Math University

STEP 01
Expert Faculty
Taught by leading applied mathematicians with publications in Nature, SIAM and the Journal of Fluid Mechanics.
STEP 02
Research-Integrated Learning
Solve real-world modelling challenges sourced from our research and industry partnerships throughout the programme.
STEP 03
Industry Connections
Direct pathways to careers in aerospace, energy, finance and biomedical sectors via our employer network.
STEP 04
Flexible Online Delivery
Complete coursework and simulation labs remotely, with structured supervision and dedicated online office hours.
Enrol in MSc Applied Mathematics →

Limited places available — secure your position in the next cohort.