1. Introduction
This course is designed to provide students with a broad training in mathematics useful in analysis and solution of problems in applied sciences. The programme is also ideally suited for students who want to pursue research towards a doctoral degree in applied mathematics and related areas.
More specifically, the aims of this course are to enable the students to:
• Acquire advanced training in mathematical theory and methods.
• Acquire competence in analysis and solution of applied problems in Science and Engineering.
2. Entry Requirements
2.1 Holders of a degree of the University of Embu of at least Upper Second Class in Mathematics, Physics, or Engineering or an equivalent qualification from a university recognised by Senate.
2.2 Holders of a Lower Second Class degree plus at least two years relevant research experience or academic work may be considered for admission.
2.3 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 School of Pure and Applied Sciences 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 eight level-500 course units, which must include all the five prescribed core course units. In addition the candidates shall be required to take four level-600 course units and 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 School of Pure and Applied Sciences.
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
6.1.1 Candidates shall be required to submit a written project report to the School for examination.
6.1.2 The project shall be graded independently out of 100 marks, distributed as follows: 70% for the project report and 30% for oral presentation.
6.1.3 The pass mark shall be 50.
6.1.4 A candidate who fails to obtain the pass mark in the project may be allowed to resubmit the project a maximum of two times.
6.1.5 A pass obtained by re-submission of the project will be recorded as 50.
6.1.6 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. Courses Outline
Core Units
SMA 531 Applied Complex Analysis
5MA 532 Methods of Applied Mathematics
5MA 533 Ordinary Differential Equations I
SMA 535 Partial Differential Equations I
SMA 536 Applied Functional Analysis
Elective Units
SMA 534 Ordinary Differential Equations II
SMA 537 Applied Differential Topology
5MA 538 Applied Dynamical Systems I
SMA 539Numerical Analysis
SMA 540 Numerical Solution of Ordinary Differential Equations
SMA 541 Fluid Dynamics I
SMA 542 Fluid Dynamics II
SMA 543 Gas Dynamics
SMA 544 Riemannian Geometry I
SMA 545 General Theory of Relativity I
Elective Units
SMA 631 Applied Dynamical Systems II
SMA 632 Numerical Dynamical Systems
SMA 633 Delay Differential Equations I
SMA 634 Delay Differential Equations II
SMA 635 Ordinary Differential Equations III
SMA 636 Riemannian Geometry II
SMA 637 General Theory of Relativity II
SMA 638 Applied Field Theory
SMA 639 Quantum Mechanics
SMA 640 Statistical Mechanics
SMA 641 Numerical Solution of Partial Differential Equations
SMA 642 Topics in Numerical Analysis
SMA 643 Partial Differential Equations II
SMA 644 Partial Differential Equations III
SMA 645 Fluid Dynamics III
SMA 646 Topics in Fluid Dynamics
SMA 647 Topics in Computational Fluid Dynamics
SMA 648 Compressible Flows
SMA 649 Project in Applied Mathematics
8. Degree Award
The final degree award shall be Master of Science in Applied Mathematics.