D'Math University | Pure Mathematics
BSc Mathematics
A rigorous, globally recognised undergraduate programme that builds deep mathematical intuition and technical mastery. From real analysis and abstract algebra to probability and topology, this degree equips you for careers in academia, finance, data science and beyond.
Undergraduate
3 Years
Online & Blended
Global Curriculum
36
Total Modules
£38k
Average Graduate Salary
50+
Partner Universities
3
Year Programme
Programme Overview
Programme Overview
- Covers the full spectrum of undergraduate pure mathematics
- Year 1 builds calculus, linear algebra and mathematical reasoning foundations
- Year 2 introduces real analysis, abstract algebra and complex analysis
- Year 3 specialises in topology, number theory and advanced probability
- Optional dissertation or research project in Year 3
- Assessments via problem sets, written exams and oral vivas
- Transferable skills in logical reasoning, proof-writing and modelling
Entry Requirements
- A-Levels: AAB including Mathematics (Further Mathematics preferred)
- IB: 34 points with 6 in Higher Level Mathematics
- SAT/ACT: strong quantitative scores for US applicants
- CBSE/ISC: 90%+ in Mathematics at Class XII
- English proficiency: IELTS 6.5+ or equivalent
- No programming prerequisite; computing modules included
- Mature/non-standard entries assessed individually
Core Curriculum
Real Analysis
Sequences, limits, continuity, differentiation and Riemann integration with rigorous epsilon-delta proofs.
Linear Algebra
Vector spaces, linear maps, eigenvalues, diagonalisation and inner product spaces.
Calculus & Multivariable Calculus
Single and multivariable differentiation, integration, Green's, Stokes' and Divergence theorems.
Abstract Algebra
Groups, rings, fields, homomorphisms, quotient structures and Galois theory introduction.
Complex Analysis
Analytic functions, Cauchy's theorem, residues, Laurent series and conformal mappings.
Number Theory
Divisibility, primes, congruences, quadratic reciprocity and introduction to analytic methods.
Differential Equations
ODEs and introductory PDEs: existence, uniqueness, Laplace transforms and Fourier series.
Probability & Statistics
Probability spaces, random variables, distributions, hypothesis testing and Bayesian inference.
Course Catalogue
Click any course to view its objective and learning outcomes. The catalogue below covers the flagship core modules taught across the three years of study.
MTH 101 Foundations of Mathematics & Logic +
Objective
To equip students with the formal language of mathematics — sets, logic, relations and proof techniques — that underpins every later module in the degree.
Learning Outcomes
- Construct rigorous proofs using direct reasoning, contraposition, contradiction and mathematical induction.
- Manipulate sets, functions, relations and equivalence classes with formal precision.
- Apply propositional and predicate logic to translate mathematical statements between English and symbolic form.
- Evaluate the correctness and completeness of a written mathematical argument.
- Communicate mathematical ideas in clear, well-structured written prose.
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 -> (implies) <-> (iff)
Interactive Activity — Set Venn Diagram
Toggle regions to build set expressions. The diagram updates instantly.
Click any region to add it to your set expression.
MTH 102 Calculus I — Single-Variable +
Objective
To develop fluency in the differential and integral calculus of one real variable and the analytical techniques that support modelling in science and engineering.
Learning Outcomes
- Compute limits, derivatives and integrals of elementary, transcendental and parametric functions.
- Apply the Mean Value Theorem and Taylor's theorem to approximate functions and bound errors.
- Solve optimisation, related-rate and area / volume problems using calculus.
- Determine convergence of sequences and series using standard tests.
- Translate real-world quantitative scenarios into calculus-based mathematical models.
Interactive Activity — Derivative as Slope of Tangent
Drag the slider to move point P along the curve. Watch the tangent line update — its slope is the derivative at that point.
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 as n increases.
Rectangles n =
8
MTH 103 Linear Algebra +
Objective
To develop the algebraic and geometric theory of vector spaces and linear maps and to apply matrix methods to systems arising across mathematics and its applications.
Learning Outcomes
- Solve linear systems using Gaussian elimination and interpret solutions geometrically.
- Reason about vector spaces, subspaces, bases, dimension and linear independence.
- Compute determinants, eigenvalues and eigenvectors and diagonalise suitable matrices.
- Apply inner-product, orthogonality and Gram–Schmidt methods to projection and least-squares problems.
- Use linear-algebraic methods to model problems in geometry, computing and the sciences.
Interactive Activity — 2×2 Matrix Transformation
Set the entries of a 2×2 matrix. Watch how it transforms the unit square (cyan → orange) and how the basis vectors î, ĵ rotate. The determinant is the signed area of the transformed square.
a =
1.0
b =
0.5
c =
-0.3
d =
1.0
MTH 201 Real Analysis I +
Objective
To establish the rigorous foundations of the real number system and the analytical theory of sequences, series, continuity and differentiation.
Learning Outcomes
- Use the completeness axiom of the real numbers to prove existence theorems.
- Construct epsilon–delta proofs of limit, continuity and uniform-continuity statements.
- Determine convergence and divergence of sequences and series with formal justification.
- Prove and apply foundational results such as the Bolzano–Weierstrass and Intermediate Value theorems.
- Analyse the differentiability of real-valued functions and prove key theorems of differential calculus.
Interactive Activity — Sequence Convergence Visualizer
Pick a sequence formula and an ε (epsilon). The graph shows when a_n enters the ε-band around the 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, the tolerance ε around f(a). The activity finds the largest δ such that |x − a| < δ ⟹ |f(x) − f(a)| < ε.
a =
1.0
ε =
0.50
MTH 202 Multivariable Calculus & Vector Analysis +
Objective
To extend the calculus to functions of several variables and to develop the integral theorems of vector analysis used widely in physics and engineering.
Learning Outcomes
- Compute partial derivatives, gradients, divergences and curls of multivariate fields.
- Evaluate double, triple, line and surface integrals in suitable coordinate systems.
- Apply Green's, Stokes' and the Divergence theorems to physical and geometric problems.
- Solve constrained optimisation problems using Lagrange multipliers.
- Interpret vector fields geometrically and recognise conservative and solenoidal fields.
Interactive Activity — Vector Field & Gradient Visualizer
Pick a scalar field f(x,y). Watch its gradient vectors point in the direction of steepest ascent. Click anywhere on the plot to drop a particle that follows the gradient.
f(x,y) =
Click on the plot to drop a particle and watch it climb the gradient.
MTH 203 Abstract Algebra I — Group Theory +
Objective
To introduce the theory of groups as a unifying framework for symmetry and structure in mathematics, supported by formal proof and worked examples.
Learning Outcomes
- State and apply the axioms of a group and identify standard examples.
- Reason about subgroups, cosets, normal subgroups and quotient groups.
- Prove and use Lagrange's theorem and the isomorphism theorems.
- Analyse cyclic, symmetric, dihedral and permutation groups in detail.
- Recognise group actions and apply the orbit–stabiliser theorem to counting problems.
Interactive Activity — Cayley Table Generator
Pick a group and the operation table generates instantly. Click any cell to highlight that element's row and column — see how the group "closes" under its operation.
Group:
Interactive Activity — Symmetries of a Polygon
Apply rotations and reflections from the dihedral group D_n. Each click shows the group element applied to a regular polygon.
n =
5
Group element: e (identity)
MTH 204 Ordinary Differential Equations +
Objective
To develop analytical and qualitative techniques for solving ordinary differential equations and modelling dynamic systems.
Learning Outcomes
- Solve first-order ODEs by separation, integrating factors and exact-equation methods.
- Solve linear higher-order ODEs with constant coefficients using characteristic and variation-of-parameters methods.
- Apply Laplace transforms to initial-value problems and discontinuous forcing.
- Analyse linear systems of ODEs through eigenvalue and phase-plane methods.
- Formulate ODE models for problems in physics, biology and engineering and interpret their solutions.
Interactive Activity — Direction Field & Solution Curves
For dy/dx = f(x,y), each tiny arrow shows the slope at that point. Click anywhere to drop a starting point and trace the solution curve through that point.
dy/dx =
Click anywhere to drop a starting point and trace the solution curve.
MTH 205 Probability & Statistical Inference +
Objective
To develop the axiomatic theory of probability and the methods of classical and Bayesian statistical inference for data analysis.
Learning Outcomes
- Work with probability spaces, conditional probability and independence to model random experiments.
- Identify and apply standard discrete and continuous distributions and their moment-generating functions.
- Prove and apply the Law of Large Numbers and the Central Limit Theorem.
- Construct point estimators, confidence intervals and hypothesis tests with quantified error rates.
- Compare frequentist and Bayesian approaches to inference on real datasets.
Interactive Activity — Distribution Plotter
Pick a distribution and adjust its parameters. Watch the PDF/PMF and CDF reshape in real time. 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 from a chosen distribution and average them. Repeat. The histogram of averages converges to a normal distribution — the CLT in action.
Source:
Sample size n =
10
Total sample means: 0
Interactive Activity — Hypothesis Testing Visualizer
Set null hypothesis μ₀, sample mean x̄, sample size n and σ. The activity computes the z-statistic, p-value (shaded tail), and tells you whether to reject H₀ at significance α.
μ₀ =
x̄ =
σ =
n =
α =
0.050
Tail:
MTH 301 Complex Analysis +
Objective
To develop the theory of analytic functions of a complex variable and the contour-integration techniques central to modern analysis.
Learning Outcomes
- Verify analyticity using the Cauchy–Riemann equations and identify standard analytic functions.
- Evaluate contour integrals using Cauchy's integral theorem and integral formula.
- Expand functions in Taylor and Laurent series and classify singularities.
- Apply the residue theorem to evaluate real integrals and sum series.
- Use conformal mappings to solve boundary-value problems in two dimensions.
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 — see it happen for real.
f(z) =
The orange grid is f(z) applied to the cyan z-plane grid.
MTH 302 Abstract Algebra II — Rings & Fields +
Objective
To extend algebraic reasoning from groups to rings, fields and modules, and to introduce the ideas of Galois theory.
Learning Outcomes
- Reason about rings, ideals, quotient rings and ring homomorphisms.
- Distinguish integral domains, principal-ideal domains and unique-factorisation domains.
- Construct field extensions and compute minimal polynomials and degrees.
- State and apply the fundamental theorem of Galois theory in worked examples.
- Use algebraic structures to solve classical problems such as ruler-and-compass constructibility.
Interactive Activity — Modular Arithmetic Clock
A "clock" with n positions visualises ℤ/nℤ. Click any position to add to the running total — the clock hand wraps around. Watch addition mod n.
n =
12
Running total: 0 (mod 12)
Interactive Activity — Polynomial Division in ℤ[x]
Type two polynomials. The activity performs polynomial long division and shows quotient and remainder step-by-step.
f(x) =
÷ g(x) =
MTH 303 Topology +
Objective
To introduce point-set topology and the topological viewpoint on continuity, compactness, connectedness and convergence.
Learning Outcomes
- Define and work with topological spaces, open sets, bases and subspace topologies.
- Prove statements about continuous maps, homeomorphisms and product topologies.
- Establish whether given spaces are compact, connected or Hausdorff.
- Apply convergence of nets and sequences to characterise topological properties.
- Recognise the role of topology as a foundation for analysis and geometry.
Interactive Activity — Surface Classification (Euler Characteristic)
Each surface has a topological invariant χ = V − E + F. Toggle between sphere, torus, double torus, Klein bottle. The Euler characteristic and orientability are computed automatically.
Interactive Activity — Open Sets in ℝ²
Click and drag to draw a region. The activity tells you whether your shape is open, closed, both (clopen), or neither — based on whether boundary points are included.
Pick a shape to see its topological classification.
MTH 304 Number Theory +
Objective
To explore the arithmetic of the integers — divisibility, primes, congruences and quadratic forms — and to introduce analytic and algebraic methods of modern number theory.
Learning Outcomes
- Apply the Euclidean algorithm and unique factorisation to integer problems.
- Solve linear and quadratic congruences and use the Chinese Remainder Theorem.
- Use Fermat's little theorem, Euler's theorem and primitive roots in computations.
- Apply quadratic reciprocity to determine solvability of quadratic congruences.
- Discuss applications of number theory to public-key cryptography.
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 Step-by-Step
Compute gcd(a, b) using repeated subtraction or division. Each step is shown with the current remainders. Bezout coefficients are also computed.
a =
b =
Interactive Activity — Modular Exponentiation (RSA)
Compute b^e mod n using fast modular exponentiation. This is the core of RSA cryptography.
b =
e =
mod n =
Career Pathways
Data Analyst
Transform raw datasets into actionable insights using statistical methods, SQL and visualisation tools across every industry sector.
Actuary
Model financial risk for insurance and pension companies using probability theory, statistics and regulatory frameworks.
Secondary Teacher
Inspire the next generation of mathematicians in secondary schools, with strong demand and career progression pathways.
Financial Analyst
Evaluate investments, build financial models and advise clients in banking, asset management and corporate finance.
Statistician
Design studies, analyse data and communicate findings in government, healthcare, social research and tech sectors.
Research Mathematician
Pursue postgraduate research and contribute original results to the global mathematical literature at leading institutions.
Top Global Universities
MIT
University of Oxford
University of Cambridge
Princeton University
ETH Zürich
Imperial College London
University of Chicago
Caltech
Harvard University
University of Edinburgh
Why D'Math University
STEP 01
Expert Faculty
Learn from PhD-qualified mathematicians with active research portfolios and international publication records.
STEP 02
Research-Integrated Learning
Engage with current mathematical research from Year 1 through seminars, reading groups and guided projects.
STEP 03
Industry Connections
Benefit from partnerships with leading employers in finance, technology and government for internships and graduate roles.
STEP 04
Flexible Online Delivery
Study on a schedule that suits you with asynchronous lectures, live tutorials and recorded problem sessions.
Applications open year-round — join the next cohort today.