D'Math University | Applied Mathematics
BSc Applied Mathematics
Bridge the gap between abstract theory and real-world problem-solving. This programme develops your ability to model physical, biological and economic phenomena mathematically — equipping you with tools used in aerospace, climate science, operations research and computational science.
Undergraduate
3 Years
Online & Blended
Applied Focus
30
Total Modules
£40k
Average Graduate Salary
45+
Partner Universities
8
Specialist Tracks
Programme Overview
Programme Overview
- Combines rigorous mathematical theory with computational and physical applications
- Eight specialist tracks: Fluid Dynamics, Control, Biology, Finance and more
- Year 1: mathematical foundations, mechanics and introductory computing
- Year 2: numerical methods, dynamical systems and continuum mechanics
- Year 3: specialist track modules and an applied research project
- Laboratory and simulation-based assessments alongside written exams
- Cross-disciplinary collaboration with engineering and science departments
What You'll Learn
- Formulate and solve differential equations modelling real physical systems
- Apply numerical methods and implement algorithms computationally
- Analyse stability, bifurcations and long-term behaviour of dynamical systems
- Model biological populations, epidemics and ecological interactions
- Optimise complex systems using linear and nonlinear programming
- Simulate fluid flow using both analytical and computational approaches
- Communicate mathematical findings to non-specialist audiences
Core Curriculum
Mathematical Modelling
Principles of building, solving and validating mathematical models for physical and social phenomena.
Fluid Dynamics
Navier-Stokes equations, viscous flow, boundary layers, turbulence and potential flow theory.
Numerical Methods
Finite differences, numerical integration, root-finding and iterative solvers for ODEs and PDEs.
Optimisation Theory
Linear programming, convex optimisation, Lagrange multipliers and dynamic programming.
Classical Mechanics
Newtonian, Lagrangian and Hamiltonian mechanics, conservation laws and rigid body dynamics.
Dynamical Systems
Phase portraits, bifurcation theory, chaos, attractors and stability analysis of nonlinear systems.
Control Theory
Feedback control, stability criteria, PID controllers and optimal control via Pontryagin's principle.
Mathematical Biology
Population dynamics, epidemic modelling (SIR), reaction-diffusion and pattern formation.
Course Catalogue
Click any course to view its objective and learning outcomes.
APM 101 Calculus & Linear Algebra +
Objective
To consolidate single-variable calculus and matrix algebra as the foundation for applied mathematics.
Learning Outcomes
- Compute derivatives, integrals and Taylor expansions.
- Solve linear systems by elimination and matrix factorisation.
- Apply eigenvalue decomposition to simple problems.
- Use vector and matrix notation for engineering problems.
- Verify numerical answers against analytical results.
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
APM 102 Mathematical Modelling I +
Objective
To translate scientific problems into mathematical structures and solve them.
Learning Outcomes
- Formulate dimensional and conservation arguments.
- Construct simple ODE and difference-equation models.
- Solve and interpret model output for the original problem.
- Identify limits and validity range of a model.
- Communicate modelling choices in a written report.
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 103 ODEs & Dynamical Systems +
Objective
To analyse ordinary differential equations and the qualitative behaviour of nonlinear dynamics.
Learning Outcomes
- Solve linear and separable ODEs analytically.
- Apply existence-uniqueness theorems.
- Analyse equilibria, phase portraits and bifurcations.
- Use Lyapunov methods to determine stability.
- Identify chaotic behaviour in low-dimensional systems.
APM 104 Numerical Methods I +
Objective
To compute approximate solutions to mathematical problems using stable algorithms.
Learning Outcomes
- Implement root-finding methods including Newton-Raphson.
- Apply numerical integration and differentiation.
- Solve linear systems with direct and iterative methods.
- Estimate error and conditioning of computations.
- Implement algorithms in a high-level language.
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 201 Vector Calculus & PDEs +
Objective
To extend calculus to several variables and introduce partial differential equations.
Learning Outcomes
- Compute gradient, divergence, curl and line/surface integrals.
- Apply Green's, Stokes' and Divergence theorems.
- Classify second-order PDEs and apply standard solution methods.
- Solve heat, wave and Laplace equations on simple domains.
- Interpret PDE solutions in physical contexts.
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 202 Optimisation Theory +
Objective
To find optima of constrained and unconstrained problems and analyse their properties.
Learning Outcomes
- Apply Lagrange multipliers and KKT conditions.
- Solve linear and quadratic programmes.
- Use gradient and Newton-type algorithms numerically.
- Analyse convexity to guarantee global optima.
- Apply optimisation in engineering and operations contexts.
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.
Interactive Activity — Gradient Descent on a 2D Loss Surface
Click anywhere on the surface to drop a starting point. Animation traces the descent path on the chosen loss function. Adjust the learning rate to see how step size affects convergence.
Loss:
η =
0.10
Click on the loss surface to drop a starting point.
APM 203 Mathematical Biology +
Objective
To model biological systems using continuous and discrete dynamics.
Learning Outcomes
- Build population, predator-prey and epidemic models.
- Analyse equilibria and oscillations in biological systems.
- Apply reaction-diffusion equations to pattern formation.
- Use stochastic models for small populations.
- Validate models against laboratory data.
APM 204 Fluid Dynamics +
Objective
To derive and solve the equations of inviscid and viscous fluid motion.
Learning Outcomes
- Derive the continuity and Navier-Stokes equations.
- Apply potential-flow theory to aerodynamics.
- Analyse laminar boundary layers and flow stability.
- Solve simple flow problems analytically and numerically.
- Interpret dimensionless numbers including Reynolds.
APM 301 Continuum Mechanics +
Objective
To unify the mechanics of solids and fluids using tensor calculus and conservation laws.
Learning Outcomes
- Apply tensor algebra to stress and strain tensors.
- Derive constitutive equations for elastic and viscous materials.
- Solve simple elastostatic and elastodynamic problems.
- Distinguish Eulerian and Lagrangian descriptions.
- Verify continuum models against discrete simulations.
APM 302 Computational Methods +
Objective
To implement numerical schemes for differential equations and large-scale linear algebra.
Learning Outcomes
- Implement finite-difference methods for PDEs.
- Apply finite-element methods to elliptic problems.
- Use Krylov subspace solvers for sparse systems.
- Analyse stability, consistency and convergence.
- Compare runtime and accuracy across schemes.
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 303 Industrial Mathematics Project +
Objective
To apply mathematical modelling to a real-world industrial problem under supervision.
Learning Outcomes
- Scope and refine an industrial problem statement.
- Build, validate and iterate a quantitative model.
- Communicate findings to a non-mathematical sponsor.
- Manage time, deliverables and version control.
- Reflect on the process of consulting practice.
APM 304 Applied Statistics +
Objective
To equip applied mathematicians with statistical inference tools relevant to engineering and science.
Learning Outcomes
- Estimate parameters by maximum likelihood and Bayesian methods.
- Apply linear regression and ANOVA to experimental data.
- Design experiments to estimate effects efficiently.
- Quantify uncertainty using bootstrap and Monte Carlo.
- Communicate statistical conclusions with appropriate caveats.
Career Pathways
Aerospace Engineer
Apply fluid dynamics and control theory to design aircraft, spacecraft and propulsion systems at leading aerospace companies.
Climate Modeller
Develop numerical models of atmospheric and oceanic systems to improve climate prediction and environmental policy.
Operations Researcher
Optimise supply chains, logistics, scheduling and resource allocation for governments and large corporations.
Computational Scientist
Develop high-performance simulations and algorithms for scientific computing in research labs and tech companies.
Systems Engineer
Design and analyse complex engineering systems using mathematical modelling, control and optimisation techniques.
Finance Analyst
Model financial systems, assess risk and build quantitative strategies using applied mathematical frameworks.
Top Global Universities
MIT
ETH Zürich
Caltech
Imperial College London
University of Cambridge
TU Munich
University of Waterloo
University of Auckland
NTU Singapore
IIT Bombay
Why D'Math University
STEP 01
Expert Faculty
Learn from applied mathematicians with real industry experience in aerospace, climate, finance and engineering.
STEP 02
Research-Integrated Learning
Tackle authentic modelling challenges inspired by current research problems in science and engineering.
STEP 03
Industry Connections
Internship and graduate scheme connections with engineering firms, government agencies and financial institutions.
STEP 04
Flexible Online Delivery
Access lectures, simulation labs and problem sessions online from anywhere in the world on your schedule.
Join a cohort of future engineers, scientists and analysts — apply today.