D'Math University | Computing & Interdisciplinary Mathematics
MSc Numerical Analysis
A rigorous postgraduate programme covering the mathematical theory and algorithms of numerical computation — approximation theory, differential equation solvers, spectral methods, and error analysis — with industrial collaboration at its core.
Programme Overview
What You Will Study
Numerical Analysis is the mathematical study of how to solve problems that have no closed-form solution — analysing error, convergence, and stability with full mathematical rigour while producing algorithms that run efficiently at scale.
- Theory: approximation theory, error analysis, convergence and stability proofs
- ODE & PDE Solvers: Runge-Kutta, finite difference, finite element, spectral
- Linear Systems: direct solvers, iterative methods, multigrid, preconditioning
- Research Project: industry-partnered or academic numerical analysis investigation
Programme Highlights
Graduates of this programme enter highly specialised roles in scientific software, aerospace, automotive engineering, and academic research — with some of the strongest mathematical credentials in the computing field.
- Industrial Partners: collaborations with aerospace, automotive, and engineering firms
- Software Focus: MATLAB, Python (NumPy/SciPy), C++, and FORTRAN for legacy codebases
- Theory & Practice: rigorous proofs alongside implementation in every module
- PhD Pathway: strong track record of graduates joining leading PhD programmes
Click any course to view its objective and learning outcomes.
NUM 501 Numerical Linear Algebra +
Objective
To solve large-scale linear systems and eigenvalue problems efficiently.
Learning Outcomes
- Apply LU, QR, Cholesky and SVD factorisations.
- Use Krylov-subspace methods.
- Apply preconditioning techniques.
- Analyse stability and conditioning.
- Implement BLAS-level routines.
NUM 502 Numerical PDEs +
Objective
To solve PDEs numerically with stable, convergent schemes.
Learning Outcomes
- Apply finite-difference methods.
- Analyse stability via von Neumann.
- Apply finite-volume methods.
- Use multigrid solvers.
- Verify against analytical solutions.
NUM 503 Finite Element Methods +
Objective
To apply FEM to elliptic and time-dependent problems.
Learning Outcomes
- Derive weak formulations.
- Choose finite-element spaces.
- Apply Galerkin methods.
- Use a posteriori error estimates.
- Implement FEM in software.
NUM 504 Iterative Methods +
Objective
To solve large sparse linear systems iteratively.
Learning Outcomes
- Apply CG, GMRES and BiCGSTAB.
- Use preconditioning effectively.
- Analyse convergence rates.
- Apply multigrid methods.
- Use domain decomposition.
NUM 505 Numerical Optimisation +
Objective
To implement and analyse modern optimisation algorithms.
Learning Outcomes
- Apply gradient and Newton methods.
- Use trust-region methods.
- Apply interior-point algorithms.
- Use SQP for constrained problems.
- Implement large-scale solvers.
NUM 506 Spectral Methods +
Objective
To use orthogonal polynomial expansions for high-accuracy computation.
Learning Outcomes
- Apply Fourier and Chebyshev expansions.
- Compute spectral derivatives.
- Apply spectral methods to PDEs.
- Use spectral element methods.
- Analyse exponential convergence.
NUM 507 Numerical ODEs +
Objective
To solve initial-value and boundary-value ODE problems numerically.
Learning Outcomes
- Apply Runge-Kutta methods.
- Use multistep methods.
- Apply implicit methods for stiff problems.
- Analyse convergence and stability.
- Use adaptive step-size control.
NUM 508 Computational Fluid Dynamics +
Objective
To discretise and solve fluid-flow equations.
Learning Outcomes
- Apply finite-volume methods.
- Use SIMPLE and PISO algorithms.
- Apply turbulence closures.
- Discretise compressible flows.
- Validate against benchmarks.
NUM 509 Inverse Problems +
Objective
To recover model parameters from indirect observations.
Learning Outcomes
- Apply Tikhonov regularisation.
- Use Bayesian inverse methods.
- Apply SVD analysis.
- Use iterative regularisation.
- Solve inverse problems in imaging.
NUM 510 High-Performance Computing +
Objective
To exploit parallel hardware for scientific computation.
Learning Outcomes
- Use MPI for distributed computing.
- Apply OpenMP for shared memory.
- Program GPUs with CUDA.
- Profile and optimise scientific code.
- Apply hybrid parallel models.
NUM 511 Approximation Theory +
Objective
To approximate functions using polynomials, splines and other bases.
Learning Outcomes
- Apply polynomial interpolation.
- Use spline approximation.
- Apply Chebyshev approximation.
- Use rational approximation.
- Apply best-approximation theory.
NUM 512 Numerical Analysis Project +
Objective
To complete an original numerical analysis research project.
Learning Outcomes
- Identify a research-quality problem.
- Apply rigorous numerical methods.
- Implement and validate code.
- Write a research-quality dissertation.
- Present to numerical analysts.
Core Modules
Approximation Theory
Polynomial interpolation, best approximation, Chebyshev polynomials, splines, and rational approximation theory.
Numerical ODEs
Runge-Kutta methods, multistep methods, stiffness, stability analysis, and adaptive step-size control.
Numerical PDEs
Finite difference, finite element, and finite volume methods for elliptic, parabolic, and hyperbolic equations.
Iterative Solvers for Linear Systems
Krylov subspace methods, GMRES, conjugate gradient, preconditioning strategies, and convergence theory.
Numerical Integration & Quadrature
Gaussian quadrature, adaptive integration, multi-dimensional cubature, and Monte Carlo integration methods.
Spectral Methods
Fourier and Chebyshev spectral discretisations, pseudospectral methods, and exponential convergence theory.
Error Analysis & Stability
Forward and backward error, condition numbers, floating-point arithmetic, and rounding error propagation.
Finite Difference & Volume Methods
Conservative discretisation, upwinding, flux limiters, and applications in fluid mechanics and heat transfer.
Multigrid Methods
Geometric and algebraic multigrid, smoothers, coarse-grid correction, and optimal convergence for elliptic problems.
Numerical Analysis Project
An extended research or industrial project applying numerical methods to a significant computational problem.
Career Outcomes
Numerical Analyst
Develop, analyse, and validate numerical algorithms for scientific and engineering computing in research or industry.
Computational Engineer
Apply numerical methods to structural analysis, fluid dynamics, and thermal modelling in engineering firms.
Scientific Software Developer
Build and maintain numerical software libraries and simulation platforms for research institutions and industry.
Finite Element Specialist
Expert implementation and analysis of FEM for structural, thermal, and electromagnetic engineering problems.
Research Mathematician
Advance the mathematical theory of numerical computation in university or national laboratory environments.
Aerospace / Automotive Engineer
Apply computational methods to aerodynamic optimisation, crash simulation, and propulsion system modelling.
Where Our Graduates Go & Top Global Universities
Why D'Math University — Our 4-Step Approach
Proof-Based Analysis
Every algorithm is studied with full convergence, stability, and error proofs — building mathematical confidence alongside coding ability.
Implementation Workshops
Weekly computing labs implement each method from scratch in Python, MATLAB, and C++ to build deep understanding.
Industrial Collaboration
Projects and guest lectures from aerospace, energy, and engineering partners bring real-world context to theoretical study.
Research Excellence
The programme project is conducted to journal standards, with many students co-authoring publications with supervisors.
Applications open year-round — become a specialist in the mathematics of computation.