D'Math University | Pure Mathematics

MSc Mathematics

An advanced postgraduate programme for graduates seeking deeper mathematical expertise and research capability. Covering functional analysis, algebraic topology, measure theory and advanced probability, this programme opens doors to research careers and elite quantitative roles.

Postgraduate 1–2 Years Online Research-Track
12
Taught Modules
£55k
Average Graduate Salary
40+
Partner Universities
5,000+
Global Alumni

Programme Overview

Programme Overview

  • Intensive taught modules paired with independent research
  • Specialisation tracks: pure mathematics or mathematical sciences
  • Culminates in a 15,000-word MSc dissertation
  • Weekly research seminars and guest lectures from leading mathematicians
  • Access to preprint archives and collaborative reading groups
  • Optional industrial placement or conference attendance
  • Direct progression route to PhD programmes worldwide

Entry Requirements

  • Bachelor's degree in Mathematics or closely related subject (2:1 or above)
  • GPA equivalent: 3.3+ on a 4.0 scale for US graduates
  • Strong background in real analysis and linear algebra essential
  • Personal statement outlining research interests
  • Two academic references from mathematics faculty
  • English: IELTS 6.5+ or TOEFL 90+ for non-native speakers
  • GRE Mathematics subject test recommended (not mandatory)

Core Curriculum

📐
Advanced Real Analysis
Metric spaces, compactness, uniform convergence, Lebesgue integration and function spaces.
🔭
Functional Analysis
Banach and Hilbert spaces, bounded operators, spectral theory and applications to PDEs.
🌐
Algebraic Topology
Fundamental groups, covering spaces, homology and cohomology theories with applications.
🌀
Differential Geometry
Smooth manifolds, tangent bundles, Riemannian metrics, geodesics and curvature.
〰️
Partial Differential Equations
Elliptic, parabolic and hyperbolic PDEs; Sobolev spaces and variational methods.
📏
Measure Theory
Sigma-algebras, Lebesgue and abstract measures, integration theory and Radon-Nikodym theorem.
🔑
Advanced Number Theory
Algebraic number fields, class groups, L-functions and modular forms introduction.
🔷
Representation Theory
Representations of finite groups, characters, Schur's lemma and applications to Lie algebras.

Course Catalogue

Click any course to view its objective and learning outcomes.

MTH 501 Real Analysis +

Objective

To rigorously develop modern real analysis on metric spaces.

Learning Outcomes

  • Apply metric and topological space concepts.
  • Use Lebesgue measure and integration.
  • Apply convergence theorems.
  • Use Lp spaces.
  • Apply functional analysis basics.
Interactive Activity — Sequence Convergence
Pick a sequence and an ε. The graph shows when a_n enters the ε-band around limit L. The smallest such N is the "epsilon-N" for convergence.
a_n = ε = 0.10
Interactive Activity — Epsilon-Delta for Continuity
For f(x) = x², set the point a and tolerance ε. The activity finds the largest δ such that |x − a| < δ ⟹ |f(x) − f(a)| < ε.
a = 1.0 ε = 0.50
MTH 502 Complex Analysis +

Objective

To study analytic functions and their applications.

Learning Outcomes

  • Apply Cauchy's theorem and integral formula.
  • Use residues to evaluate integrals.
  • Apply Riemann mapping theorem.
  • Use analytic continuation.
  • Apply elliptic functions.
Interactive Activity — Complex Function Visualizer
A grid in the z-plane (left) gets transformed by w = f(z) into the w-plane (right). Conformal maps preserve angles.
f(z) =
The orange grid is f(z) applied to the cyan z-plane grid.
MTH 503 Functional Analysis +

Objective

To extend linear algebra to infinite-dimensional spaces.

Learning Outcomes

  • Apply Banach and Hilbert space theory.
  • Use Hahn-Banach theorem.
  • Apply spectral theory of operators.
  • Use weak topologies.
  • Apply functional analysis to PDEs.
MTH 504 Algebra +

Objective

To study advanced topics in algebra including modules and homological methods.

Learning Outcomes

  • Apply module theory.
  • Use Galois theory.
  • Apply homological algebra.
  • Use category theory.
  • Discuss representation theory.
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 -> <->
MTH 505 Topology & Differential Geometry +

Objective

To study smooth manifolds and topology.

Learning Outcomes

  • Apply algebraic topology.
  • Use de Rham cohomology.
  • Apply Riemannian geometry.
  • Use connections and curvature.
  • Apply geodesic equations.
Interactive Activity — Surface Classification
Each surface has an Euler characteristic χ = V − E + F. Toggle between sphere, torus, double torus, Möbius and Klein bottle.
Interactive Activity — Open Sets in ℝ²
Pick a region — the activity tells you whether it is open, closed, both (clopen), or neither.
Pick a shape to see its topological classification.
MTH 506 Number Theory +

Objective

To study advanced number theory and arithmetic geometry.

Learning Outcomes

  • Apply quadratic reciprocity.
  • Use class field theory.
  • Apply elliptic curves.
  • Use modular forms.
  • Discuss zeta functions.
Interactive Activity — Sieve of Eratosthenes
Watch the algorithm find all primes up to N. Composites get crossed out as their prime factors are processed.
N = 100
Interactive Activity — Euclidean Algorithm
Compute gcd(a, b) using repeated division. Bezout coefficients are also computed.
a = b =
Interactive Activity — Modular Exponentiation (RSA core)
Compute b^e mod n using fast modular exponentiation.
b = e = mod n =
MTH 507 PDEs +

Objective

To study partial differential equations rigorously.

Learning Outcomes

  • Apply Sobolev spaces.
  • Use weak solutions.
  • Apply variational methods.
  • Use semigroup theory.
  • Apply nonlinear PDE methods.
MTH 508 Probability Theory +

Objective

To study probability theory at advanced level.

Learning Outcomes

  • Apply measure-theoretic probability.
  • Use martingale theory.
  • Apply Brownian motion.
  • Use Itô calculus.
  • Apply ergodic theory.
Interactive Activity — Distribution Plotter
Pick a distribution and adjust its parameters. Read off mean and variance directly from the plot.
Distribution: p1 = 0.0 p2 = 1.0
Interactive Activity — Central Limit Theorem Simulator
Sample n values, take their average, repeat. The histogram of averages converges to a normal distribution — CLT in action.
Source: Sample size n = 10
Total sample means: 0
MTH 509 Mathematical Logic +

Objective

To study mathematical logic and foundations.

Learning Outcomes

  • Apply first-order logic.
  • Use ZFC set theory.
  • Apply Gödel's theorems.
  • Use model theory.
  • Discuss proof theory.
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 -> <->
Interactive Activity — Set Venn Diagram
Click regions to build set expressions. The diagram updates instantly.
Click any region (A or B) or their intersection.
MTH 510 Operator Algebras +

Objective

To study C* and von Neumann algebras.

Learning Outcomes

  • Apply Gelfand-Naimark theorem.
  • Use spectral theorem for normal operators.
  • Apply von Neumann algebras.
  • Use K-theory of operator algebras.
  • Discuss noncommutative geometry.
MTH 511 Algebraic Geometry +

Objective

To study schemes and algebraic varieties.

Learning Outcomes

  • Apply scheme theory.
  • Use sheaf cohomology.
  • Apply Riemann-Roch.
  • Use intersection theory.
  • Discuss moduli spaces.
MTH 512 Master's Dissertation +

Objective

To complete an original mathematics research project.

Learning Outcomes

  • Identify a research-quality problem.
  • Apply rigorous mathematical methods.
  • Survey primary literature.
  • Write a 15,000-word dissertation.
  • Defend orally to a panel.

Career Pathways

🔬
Research Mathematician
Conduct original research at universities or institutes, publishing in top journals and presenting at international conferences.
📊
Quantitative Analyst
Build mathematical models for pricing derivatives, managing risk and optimising portfolios at investment banks and hedge funds.
🎓
Academic Lecturer
Teach undergraduate and postgraduate mathematics at universities worldwide following PhD completion.
🤖
Data Scientist
Apply advanced statistical and mathematical methods to large-scale data challenges in technology and industry.
⚙️
Algorithm Engineer
Design and analyse algorithms for search, optimisation and machine learning at leading technology companies.
⚠️
Risk Analyst
Model financial, operational and systemic risk using stochastic processes and probability theory in banking and insurance.

Top Global Universities

MIT University of Oxford Stanford University University of Cambridge Princeton University ETH Zürich Sorbonne Université University of Bonn NYU Courant Institute Tata Institute of Fundamental Research

Why D'Math University

STEP 01
Expert Faculty
Study under internationally recognised mathematicians with strong research publication records in leading journals.
STEP 02
Research-Integrated Learning
Engage with frontline mathematical research through seminars, reading groups and a substantial dissertation project.
STEP 03
Industry Connections
Exclusive access to finance, tech and government employers seeking postgraduate-level mathematical talent.
STEP 04
Flexible Online Delivery
Balance postgraduate study with professional commitments through our asynchronous and live-session hybrid model.
Enrol in MSc Mathematics →

Rolling admissions — contact our postgraduate team to discuss your application.