Science

Doctor of Philosophy in Pure Mathematics

The Doctor of Philosophy in Pure Mathematics is a postgraduate research programme offered at the University of Nairobi and Kenyatta University through their respective departments of mathematics. The programme trains scholars to conduct advanced research on abstract mathematical structures, including algebra, analysis, geometry, number theory, and topology, contributing to fundamental knowledge and applications in Kenya and globally.

Students engage with advanced algebra, real and complex analysis, topology, number theory, differential geometry, and research methodology. The programme combines coursework with thesis research, requiring candidates to develop a research proposal, conduct independent theoretical research, and produce a doctoral dissertation that makes an original contribution to pure mathematics.

Kenya's development in finance, cryptography, data science, and technology requires strong mathematical foundations. The programme addresses national priorities under Vision 2030 by training researchers who can advance mathematical knowledge, support teaching excellence, and contribute to research-intensive sectors.

Teaching methods include lectures, problem-solving seminars, research colloquia, and supervised thesis work. Students have access to UoN's School of Mathematics and KU's School of Pure and Applied Sciences, and collaborate with the Kenya Mathematical Society, the African Institute for Mathematical Sciences, and international mathematics institutions.

Graduates pursue careers as university lecturers, mathematicians, researchers, data scientists, and quantitative analysts in universities, research institutions, banks, technology companies, and government agencies.

This programme is ideal for holders of a Master's degree in pure mathematics, mathematics, or related quantitative fields who are committed to advancing knowledge in pure mathematics.

Duration: 3 years
Public, up to: Ksh 428,000
Private, up to: Ksh 150,000
Job market: Moderate

The programme

What you study, how long it takes, and how it is delivered.

Practicalities

Study mode: Full-time
Attachment: 0 months
Average class: 5 students
Award: PhD

What you study

10 subjects

Abstract Algebra
Real and Complex Analysis
Topology
Number Theory
Differential Geometry
Research Methodology
Functional Analysis
Thesis Research
Mathematical Logic
Combinatorics

Modules

12 in the programme

Advanced Abstract Algebra
Year 1Semester 13 creditsCore
Advanced algebra including groups, rings, fields, modules, Galois theory, and representation theory
Advanced Abstract Algebra and Group Theory
Year 1Semester 13 creditsCore
Abstract algebra, exploring cutting-edge developments, theoretical frameworks, and research methodologies at the forefront of the discipline.
Real and Complex Analysis
Year 1Semester 23 creditsCore
Advanced analysis including measure theory, functional analysis, complex analysis, and analytic methods
Real Analysis and Measure Theory
Year 1Semester 23 creditsCore
Real analysis, covering theoretical foundations, practical methodologies, and current analytical techniques used in advanced research and professional practice.
Topology and Geometry
Year 1Semester 33 creditsCore
Advanced topology and geometry including point-set topology, algebraic topology, differential geometry, and manifolds
Complex Analysis and Analytic Functions
Year 1Semester 33 creditsCore
Complex analysis, covering theoretical foundations, practical methodologies, and current analytical techniques used in advanced research and professional practice.
Number Theory
Year 2Semester 13 creditsCore
Advanced number theory including algebraic number theory, analytic number theory, and Diophantine equations
Topology and Differential Geometry
Year 2Semester 13 creditsCore
Topology, covering theoretical foundations, practical methodologies, and contemporary research developments relevant to doctoral study in this area.
Mathematical Logic and Foundations
Year 2Semester 23 creditsCore
Mathematical logic including model theory, set theory, computability, and foundations of mathematics
Number Theory and Cryptography
Year 2Semester 23 creditsCore
Number theory, examining foundational principles, conceptual frameworks, and theoretical debates that shape contemporary understanding in this field.
Combinatorics and Graph Theory
Year 2Semester 33 creditsCore
Combinatorics and graph theory including enumerative combinatorics, graph theory, and applications to computer science
Research Methods in Mathematics
Year 2Semester 33 creditsCore
Research methods, covering quantitative and qualitative approaches, data collection techniques, and analytical frameworks relevant to doctoral-level research in the field.

Specialisations

Data Science
Specialization in Data Science, preparing graduates for careers such as data-scientist.
Genomics Data Science
Specialization in Genomics Data Science, preparing graduates for careers such as genomics-data-scientist.
Operations Research Analysis
Specialization in Operations Research Analysis, preparing graduates for careers such as operations-research-analyst.
Academic Research in Science
Specialization in Academic Research in Science, preparing graduates for careers such as university-lecturer.
Mathematics Research
Specialization in Mathematics Research, preparing graduates for careers such as university-lecturer.
Economic Data Science
Specialization in Economic Data Science, preparing graduates for careers such as economic-data-scientist.
Abstract Algebra
Research on abstract algebra
Number Theory
Research on number theory
Topology and Geometry
Research on topology and geometry
Analysis
Research on analysis

A day as a student

A typical day combines theoretical problem-solving with reading advanced mathematical texts, writing proofs, attending research seminars, and working on the thesis. Students participate in mathematics colloquia and collaborate with peers and supervisors on original research.

The trade offs

In its favour

Develops strong analytical and problem-solving skills valued across sectors
Skills applicable to cryptography, data science and finance
Two public universities offer the programme providing choice and fee range
Strong international linkages through AIMS, IMU, and CIMPA

Against it

UoN PhD is expensive (KSh 1,324,000 total)
Pure mathematics is abstract and demanding
UoN fees are high at KES 432,000 per year
Competition for academic positions is high

What it costs

Tuition at both ends of the market, and how to pay for it.

What it costs, and where

Against 243 science courses

Public337k to 428k

337k at Kenyatta University428k at University of Nairobi

Private150k to 150k

150k at Mount Kenya University150k at Mount Kenya University

Annual tuition in Kenyan shillings, rounded. The upright tick is the median for this field, so a bar sitting entirely to its right is an expensive programme by the standards of its own subject.

The fine print

UoN 428K/yr (uonbi.ac.ke), KU 336.6K/yr (ku.ac.ke). MKU 150K/yr (mku.ac.ke).

Students may access HELB postgraduate loans, DAAD scholarships, NRF research grants, and IMU research grants for pure mathematics research.

Funding options

HELB Postgraduate Loan
LoanKsh 80,000
DAAD Scholarship
Scholarship
NRF Research Grant
Grant
IMU Research Grant
Grant

Scholarships

5 recorded

NACOSTI Research Grant
GrantKenyan
Science and technology researchers in Kenya
HELB Postgraduate Scholarship
LoanKsh 200,000Kenyan
Kenyan postgraduate students
DAAD Kenya Scholarship
ScholarshipKenyan
Postgraduate students in Kenya
HELB Postgraduate Loan
LoanKsh 80,000Kenyan
Kenyan postgraduate students enrolled in recognised universities
DAAD Scholarship
ScholarshipKenyan
African graduates meeting academic criteria for doctoral study

Getting in

The grades, the alternatives, and who accredits the award.

What you need

KCSE mean grade: C+
Alternative entry: Relevant diploma or equivalent qualification

Master's Degree
MSc in Pure Mathematics, Mathematics, or related quantitative field from a recognised university
Undergraduate qualification
Bachelor's degree in Mathematics or related quantitative field
Research capability
Evidence of research ability through publications, reports, or academic work

How you are assessed

5 components

Thesis
Thesis50% of the mark
Doctoral thesis research, submission and oral defence
Coursework
Continuous assessment30% of the mark
Assignments, problem sets and seminar presentations
Thesis Proposal Defence
Oral defence20% of the mark
Defence of research proposal before faculty panel
Thesis Examination
Coursework100% of the mark
Continuous Assessment Tests (CATs)
Coursework30% of the mark

Accreditation

Accredited by the Commission for University Education (CUE).

Accredited by

Commission for University Education (CUE)
Academic accreditationRequired
Mandatory accreditation for all university programmes in Kenya
Commission for University Education
AcademicRequired
Statutory body responsible for accreditation of university programmes in Kenya

Where it leads

The roles it opens, and what you leave with.

Where graduates go

7 roles

Cryptographer
High demandKsh 300,000 to Ksh 700,000
Cryptography at tech companies
University Professor
High demandKsh 200,000 to Ksh 500,000
Teaching and research in mathematics departments
Mathematics Researcher
Moderate demandKsh 200,000 to Ksh 500,000
Research at research institutes
Quantitative Analyst
Moderate demandKsh 100,000 to Ksh 250,000
Applies mathematical modelling in finance, insurance, or risk analysis
Data Scientist
High demandKsh 100,000 to Ksh 250,000
Applies mathematical and computational methods to data analysis in industry
Mathematician
Moderate demandKsh 90,000 to Ksh 200,000
Conducts advanced mathematical research at institutions or universities
University Lecturer (Mathematics)
High demandKsh 90,000 to Ksh 200,000
Teaches mathematics and conducts research in university mathematics departments

Graduate outcomes

Graduates work as university lecturers, mathematicians, researchers, and data scientists in universities, research institutions, banks, technology companies, and government agencies.

Where these fields lead

8 careers

Tools you will learn

Microsoft Excel
SpreadsheetPrimary
SPSS
AnalyticsPrimary
Google Scholar
Research
NVivo
Analytics
Zotero
Research
ChatGPT / Claude
Ai

Certifications

Industry links

Common misconceptions

Pure mathematics is too abstract to be useful
Pure mathematics provides foundations for cryptography, computer science, finance, data science, and physics, with many real-world applications.
A PhD in pure mathematics only leads to academic careers
Graduates work in finance, data science, cybersecurity, technology, and research, not only in universities.
Pure mathematics research is not relevant to Kenya
Kenya's growing tech and finance sectors require strong mathematical foundations, and pure mathematics supports teaching and research capacity.
Pure mathematics is the same as applied mathematics
Pure mathematics studies abstract structures for their own sake, while applied mathematics focuses on solving practical problems, though they often overlap.