D'Math University | Computing & Interdisciplinary
PhD Applied Mathematics
A research-intensive doctoral programme exploring the power of mathematics to model, analyse, and solve real-world problems in physics, biology, engineering, and data science. From fluid dynamics and PDEs to mathematical biology and computational modelling, graduates push the boundaries of what mathematics can achieve in applied settings.
Doctoral
3–5 Years
Research-Intensive
Interdisciplinary
6
Research Groups
£72k+
Average Graduate Salary
50+
Partner Universities
3–5
Year Programme
Programme Overview
Programme Overview
- Advanced doctoral research in applied and computational mathematics
- Year 1: Advanced coursework in PDEs, numerical methods, and mathematical modelling
- Year 2 onward: Supervised original research with leading applied mathematicians
- Research groups in fluid dynamics, mathematical biology, industrial mathematics, and scientific computing
- Close collaboration with physics, engineering, and computer science departments
- Publications in leading applied mathematics journals expected
- Conference presentations at SIAM, ICIAM, and other international venues
Entry Requirements
- MSc in Applied Mathematics, Mathematical Physics, or closely related field
- First-class or high merit at postgraduate level strongly preferred
- Strong background in PDEs, numerical analysis, and mathematical modelling
- Programming experience in MATLAB, Python, or C++ required
- Research proposal identifying a specific applied mathematics problem
- Two academic references with knowledge of your analytical and research ability
- English proficiency: IELTS 7.0+ or equivalent
Research Areas & Coursework
Partial Differential Equations
Elliptic, parabolic, and hyperbolic PDEs: existence, uniqueness, regularity theory, and advanced solution methods.
Numerical Methods for PDEs
Finite difference, finite element, and spectral methods; error analysis, stability, and high-performance implementation.
Fluid Dynamics
Navier-Stokes equations, turbulence modelling, boundary layers, and computational fluid dynamics techniques.
Mathematical Biology
Population dynamics, pattern formation, reaction-diffusion systems, and mathematical epidemiology.
Mathematical Physics
Classical mechanics, quantum mechanics, electromagnetism, and general relativity from a rigorous mathematical viewpoint.
Asymptotic Methods
Perturbation theory, matched asymptotic expansions, WKB theory, and averaging methods for singularly perturbed problems.
Scientific Machine Learning
Physics-informed neural networks, operator learning, and the integration of machine learning with mathematical models.
Doctoral Thesis
Original research making a substantial contribution to applied mathematics, supervised by expert faculty and assessed by international examiners.
Course Catalogue
Click any course to view its objective and learning outcomes.
APM 701 Research Methods +
Objective
To prepare doctoral candidates for original applied mathematics research.
Learning Outcomes
- Apply rigorous research design.
- Conduct interdisciplinary collaboration.
- Apply advanced computational methods.
- Critique published research.
- Write proposals for funding.
APM 702 Advanced PDEs +
Objective
To master advanced PDE theory for research.
Learning Outcomes
- Apply functional analytic methods.
- Use semigroup theory.
- Apply variational methods.
- Use viscosity solutions.
- Discuss nonlinear PDE methods.
APM 703 Advanced Numerical Methods +
Objective
To research cutting-edge numerical methods.
Learning Outcomes
- Apply adaptive mesh refinement.
- Use multilevel methods.
- Apply isogeometric analysis.
- Use reduced-order models.
- Discuss exascale computing.
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 704 Mathematical Modelling Research +
Objective
To pursue advanced research in mathematical modelling.
Learning Outcomes
- Build models for emerging scientific problems.
- Apply multiscale methods.
- Use uncertainty quantification.
- Apply data-driven modelling.
- Validate against experiments.
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 705 Computational Mathematics Research +
Objective
To research advanced computational methods.
Learning Outcomes
- Apply HPC to scientific problems.
- Use ML in scientific computing.
- Apply quantum-inspired algorithms.
- Develop scalable algorithms.
- Profile petascale codes.
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 706 Doctoral Seminar +
Objective
To engage with cutting-edge research.
Learning Outcomes
- Present and critique research papers.
- Engage with international research.
- Participate in peer review.
- Build a research network.
- Develop presentation skills.
APM 707 Teaching Practicum +
Objective
To develop university-level teaching skills.
Learning Outcomes
- Plan and deliver lectures.
- Design assessments.
- Apply pedagogical theory.
- Mentor undergraduates.
- Engage in curriculum development.
Interactive Activity — Truth Table Builder
Type a logical expression using p, q, r and operators (AND, OR, NOT). The truth table generates instantly.
Operators:
AND OR NOT XOR -> <->
APM 708 PhD Thesis I +
Objective
To produce original research towards a doctoral thesis.
Learning Outcomes
- Identify an original research question.
- Conduct extensive literature review.
- Develop a research methodology.
- Produce preliminary results.
- Present at international conferences.
APM 709 PhD Thesis II +
Objective
To advance the doctoral research project.
Learning Outcomes
- Develop original methodology.
- Generate substantial findings.
- Publish in peer-reviewed journals.
- Develop thesis structure.
- Defend research methodology.
APM 710 PhD Thesis III +
Objective
To consolidate doctoral research into a defendable thesis.
Learning Outcomes
- Write a thesis of 80,000-100,000 words.
- Synthesise multiple contributions.
- Defend viva voce.
- Publish multiple articles.
- Contribute to the field.
Career Pathways
Academic Applied Mathematician
Pursue a research and teaching career at a leading university, publishing in applied mathematics and mentoring future researchers.
Aerospace & Defence Researcher
Apply fluid dynamics, structural mechanics, and optimisation mathematics to aerospace, propulsion, and defence problems.
National Lab Scientist
Work at Turing Institute, Argonne, CERN, or similar institutions on large-scale computational and mathematical problems.
AI/ML Research Scientist
Leverage applied mathematics expertise to develop physically-grounded AI models at technology research laboratories.
Climate Modeller
Develop and validate mathematical models of atmospheric, oceanic, and climate systems at research institutions and agencies.
Computational Biologist
Apply mathematical modelling to drug discovery, disease dynamics, genomics, and biological systems simulation.
Top Global Universities
MIT
University of Cambridge
Caltech
ETH Zürich
University of Oxford
Imperial College London
Princeton University
University of Warwick
Courant Institute (NYU)
University of Minnesota
Why D'Math University
STEP 01
Interdisciplinary Research
Applied mathematics at its best lives at the intersection of disciplines. Our research groups collaborate actively with physics, engineering, and biology.
STEP 02
Computational Infrastructure
Access to HPC clusters, GPU computing resources, and scientific software for large-scale numerical simulation and data-intensive research.
STEP 03
Expert Supervisors
Work with world-leading applied mathematicians who are active contributors to SIAM, CMS, and international applied mathematics communities.
STEP 04
Global Impact
Applied mathematics PhD graduates shape decisions in climate policy, AI development, pharmaceutical research, and national security.
Doctoral applications reviewed year-round — contact us to discuss your research interests.