1.  Introduction
The overall objective of the course is to enable students to acquire an understanding of the fundamental structures of mathematics, and lay a firm foundation for the study of mathematics and its applications.

More specifically, the aims of the course are to:

• Provide the student with advanced training in pure mathematics
• Expose the student to current research trends in pure mathematics.
  
  

2.  Entry requirements

2.1 Common regulations for the Master of Science degree in the University of Nairobi and the Faculty of Science shall be applicable
2.2 Holders of a degree of the University of Embu  of at least Upper Second Class in Mathematics or an equivalent qualification from a university recognised by Senate.
2.3 Holders of a Lower Second Class degree plus at least two years relevant research experience or academic work may be considered for admission.
2.4 Non-holders of a first degree who can show evidence of relevant research experience or academic work may be considered for admission provided that they pass relevant qualifying examinations.

3.  Exemption(s) and Credit Transfer(s)

A candidate may be exempted from some course units and credit transferred from institutions, recognised by senate, subject to the following conditions.

3.1 Must have passed in similar course units at Masters level
3.2 Request for exemption should be made in writing, on admission, addressed to the Dean of the  Faculty of Science and must be accompanied by officially endorsed supporting documents including the institutions syllabuses for the relevant courses.
3.3 Payment of appropriate exemption fees.
3.4 No candidate shall be exempted from more than one third of the total number of course units required in the course.

4. Course Structure and Duration
4.1  The minimum duration of the course shall be four semesters and the maximum duration shall be 12 semesters, each of 15 weeks.
4.2  A course unit will be defined as consisting of 45 contact hours of lectures, tutorials and practicals.
4.3  Candidates shall be required to take all the eight level-500 course units and four level-600 course units by course work. In addition the candidates shall be required to take a project.
4.4 The project will be regarded as equivalent to four course units.
4.5 Candidates will be required to participate in weekly School postgraduate seminars. The seminars will be of one hour duration, and will cover special topics by means of lectures and informational conferences.
4.6 In each semester candidates shall be required to take a minimum of three course units and a maximum of five course units.

5. Examination Regulations and Evaluation
Written Examination
5.1.1    Masters examinations shall be governed by the general regulations for the degree of Master of Science in the Faculty of Science.
5.1.2    course units taken in a given semester shall normally be examined at the end of that semester.
5.1.3    A candidate for the Master of Science shall be required to complete satisfactorily all such course work and assignments that may be required for the scheme of study.
5.1.4    Each taught course unit shall be examined by a two-hour written examination.
5.1.5    Each course unit shall be graded independently out of 100 marks.
5.1.6    The pass mark shall be 50.
5.1.7    The complete assessment of a taught course unit shall consist of continuous assessment tests, coursework or practical assignments and a written examination. The contribution towards the unit aggregate score shall be 30% for course work and 70% for written examination.
5.1.8    A candidate who fails to obtain a pass mark in any course unit may be allowed to re-sit or re-take the failed units, a maximum of two times.
5.1.9     A pass obtained by re-sitting a course unit shall be recorded as 50.
5.1.10 A candidate who fails in the second re-sit or re-take or fails to complete the course in the prescribed time shall be discontinued.

    6. The Project

a.     Candidates shall be required to submit a written project report to the School for examination.
b.     The project shall be graded independently out of 100 marks, distributed as follows: 70% for the project report and 30% for oral presentation.
c.     The pass mark shall be 50.
d.     A candidate who fails to obtain the pass mark in the project may be allowed to resubmit the project a maximum of two times.
e.     A pass obtained by re-submission of the project will be recorded as 50.
f.     A candidate who fails to obtain the pass mark in the project at the second re-submission of the project or fails to complete the course within the prescribed period will be discontinued.

7. Course Outline
First Semester
Core Courses

5MA 501 - Measure Theory
SMA 502 - Functional Analysis I
SMA 503 - Algebra I
SMA 504 - General Topology 1


Second Semester
Core Courses
SMA 505 - General Topology II
SMA 506-Functional Analysis II
SMA 507- Complex Analysis
SMA 508 - Algebra II

Elective Courses
SMA 601 - Algebraic Topology
SMA 602 - Homological Algebra
SMA 603 - Dimension Theory I
SMA 604 - Functional Analysis III
SMA 605 - Distribution Theory
SMA 606- Differential Topology
SMA 607- Non-commutative Ring Theory
SMA 608 - Commutative Algebra
SMA 609- Lie Algebras
SMA 610- Functional Analysis IV
SMA 611 - Representation Theory
SMA 612 - Topics in Pure Mathematics
SMA 613 - Differential Geometry
SMA 614 - Project in Pure Mathematics

8.  Degree Award
The final degree award shall be Master of Science in Pure Mathematics.