D'Math University | Pure Mathematics
BSc Mathematics (Honours)
A four-year undergraduate honours programme that takes you beyond standard BSc content into advanced topics and original research. The hallmark Honours Dissertation gives you the experience of a research mathematician, producing a piece of original mathematical work supervised by a faculty expert.
Undergraduate Honours
4 Years
Research Dissertation
Global
40
Total Modules
£41k
Average Graduate Salary
38+
Partner Universities
1
Original Dissertation
Programme Overview
Programme Overview
- Years 1–2: comprehensive pure mathematics foundations
- Year 3: advanced analysis, algebra, geometry and combinatorics
- Year 4: specialist electives and the Honours Dissertation
- Dissertation: 8,000–12,000 words on an original mathematical problem
- Supervised one-to-one by a faculty research mathematician
- Honours classification (First, 2:1, 2:2) based on full four-year record
- Recognised by employers, professional bodies and top MSc/PhD programmes
Entry Requirements
- A-Levels: AAA including Mathematics (Further Mathematics highly preferred)
- Scottish Highers: AAAAB including Mathematics
- IB: 36 points with 7 in Higher Level Mathematics
- CBSE/ISC: 95%+ in Mathematics and strong overall performance
- English: IELTS 6.5+ or equivalent for non-native speakers
- Portfolio of independent mathematical work welcomed at interview
- Admissions interview may be offered to borderline applicants
Core Curriculum
Advanced Calculus
Multivariable calculus, differential forms, Stokes' theorem and calculus of variations.
Group Theory
Sylow theorems, group actions, normal series, solvable groups and introduction to representation theory.
Real & Complex Analysis
Measure theory, Lebesgue integration, analytic functions and complex integration techniques.
Combinatorics
Enumerative combinatorics, generating functions, Ramsey theory and probabilistic methods.
Differential Geometry (Intro)
Curves and surfaces, curvature, the Gauss-Bonnet theorem and smooth manifolds introduction.
Mathematical Physics
Lagrangian mechanics, electromagnetism, quantum mechanics and special relativity with rigorous analysis.
Statistics & Probability
Advanced probability, stochastic processes, statistical inference and Bayesian methods.
Honours Dissertation
An original supervised research project resulting in a substantial written dissertation and oral presentation.
Course Catalogue
Click any course to view its objective and learning outcomes.
MTH 101 Foundations of Mathematics +
Objective
To establish the formal language of proof and structure underlying all advanced mathematics.
Learning Outcomes
- Construct rigorous proofs by direct, contrapositive, contradiction and induction.
- Manipulate sets, functions, relations and equivalence classes.
- Apply logical structure to translate between English and symbols.
- Evaluate the validity of mathematical arguments.
- Communicate proofs in clear, well-structured prose.
MTH 102 Calculus I +
Objective
To master the differential and integral calculus of one variable.
Learning Outcomes
- Compute limits, derivatives and integrals of standard functions.
- Apply the Mean Value and Taylor theorems.
- Solve optimisation, related-rate and area problems.
- Determine convergence of sequences and series.
- Build calculus models for scientific contexts.
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
MTH 103 Linear Algebra +
Objective
To establish vector-space theory and matrix decompositions.
Learning Outcomes
- Solve large linear systems by factorisation.
- Compute eigendecomposition and diagonalisation.
- Apply inner-product geometry and Gram-Schmidt.
- Use linear algebra to solve least-squares problems.
- Identify invariant subspaces and apply spectral theorem.
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
MTH 201 Real Analysis I +
Objective
To rigorously develop the theory of real numbers and continuity.
Learning Outcomes
- Prove theorems about the completeness of ℝ.
- Apply epsilon-delta arguments fluently.
- Establish theorems on differentiability and integration.
- Analyse sequences and series of functions.
- Construct counter-examples for analytic concepts.
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 202 Multivariable Calculus +
Objective
To extend differential and integral calculus to several variables.
Learning Outcomes
- Compute multivariable derivatives, gradients and Hessians.
- Apply Lagrange multipliers in optimisation.
- Compute multiple integrals using transformations.
- Apply Green's, Stokes' and Divergence theorems.
- Use vector calculus in physical applications.
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
MTH 203 Abstract Algebra I — Group Theory +
Objective
To study groups, their morphisms and standard examples.
Learning Outcomes
- Verify group axioms and identify subgroups.
- Apply Lagrange's theorem and the orbit-stabiliser theorem.
- Construct quotient groups and apply isomorphism theorems.
- Classify finite abelian groups.
- Analyse symmetry groups of geometric objects.
Interactive Activity — Cayley Table Generator
Pick a group; the operation table generates instantly.
Group:
Interactive Activity — Symmetries of a Polygon
Apply rotations and reflections from the dihedral group D_n.
n =
5
Group element: e (identity)
MTH 204 Ordinary Differential Equations +
Objective
To solve and analyse ordinary differential equations.
Learning Outcomes
- Solve linear ODEs by analytical methods.
- Apply existence-uniqueness theorems.
- Use Laplace transforms.
- Analyse stability and phase portraits.
- Use power-series solutions.
MTH 205 Probability & Inference +
Objective
To establish probability theory and the foundations of statistical inference.
Learning Outcomes
- Apply probability axioms and conditional probability.
- Identify and use standard distributions.
- Estimate parameters by maximum likelihood.
- Construct confidence intervals.
- Conduct hypothesis tests with proper interpretation.
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 301 Complex Analysis +
Objective
To develop the theory of analytic functions of a complex variable.
Learning Outcomes
- Verify analyticity using Cauchy-Riemann equations.
- Apply Cauchy's theorem and integral formula.
- Compute residues and evaluate real integrals.
- Apply Laurent expansions to classify singularities.
- Use conformal mappings to solve boundary problems.
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 302 Abstract Algebra II — Rings & Fields +
Objective
To extend algebra to rings, fields and Galois theory.
Learning Outcomes
- Identify rings, ideals and quotient rings.
- Apply unique-factorisation domains and PIDs.
- Construct field extensions and minimal polynomials.
- Apply Galois theory to polynomial solvability.
- Identify finite fields and their applications.
Interactive Activity — Cayley Table Generator
Pick a group; the operation table generates instantly.
Group:
Interactive Activity — Symmetries of a Polygon
Apply rotations and reflections from the dihedral group D_n.
n =
5
Group element: e (identity)
MTH 303 Topology +
Objective
To introduce point-set and elementary algebraic topology.
Learning Outcomes
- Verify topology axioms on standard spaces.
- Identify continuous maps between topological spaces.
- Apply compactness and connectedness in proofs.
- Compute fundamental groups of simple spaces.
- Classify surfaces using Euler characteristic.
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 304 Honours Dissertation +
Objective
To produce an extended written dissertation under expert supervision.
Learning Outcomes
- Identify and refine an honours-level research topic.
- Survey relevant primary literature.
- Construct original or expository proofs.
- Write a long-form mathematical dissertation.
- Defend the dissertation orally.
Career Pathways
Academic Researcher
Progress to a funded MSc or PhD programme at a world-leading university with strong preparation from the dissertation.
Actuary
Model insurance, pension and financial risk with the robust probability and statistical foundations built in Year 3–4.
Finance Professional
Work in investment banking, asset management or corporate finance applying advanced quantitative analysis.
Data Analyst
Translate complex data into business insight using rigorous statistical and mathematical modelling skills.
Educator
Teach mathematics at secondary or tertiary level with an honours degree that opens doors to PGCE and academic roles.
Government Analyst
Apply quantitative methods to policy analysis, defence, intelligence and national statistical services.
Top Global Universities
University of Edinburgh
University of St Andrews
University of Glasgow
University of Auckland
University of Melbourne
University of Toronto
University of Waterloo
University of Cape Town
University College Dublin
NUS Singapore
Why D'Math University
STEP 01
Expert Faculty
Honours students receive one-to-one dissertation supervision from active research mathematicians.
STEP 02
Research-Integrated Learning
The Year 4 dissertation gives genuine research experience and a head start for postgraduate applications.
STEP 03
Industry Connections
Honours graduates are highly regarded by employers in finance, data science, government and academia.
STEP 04
Flexible Online Delivery
Study the full four-year honours programme online with dissertation supervision conducted via video and written feedback.
Take the honours pathway — distinguish yourself with an original research degree.