Master of Science in Mathematical Modelling (MTM)

(Applied Mathematics)

**Objectives**

(a) To provide skills for high quality research and teaching in the field of mathematical modelling in Africa

(b) To raise a critical mass of mathematical modellers in the region to popularize and meet challenges of computational and mathematical applications to the industry and society.

(c) To support the application of the methods and results of mathematical modelling in the areas of industry

(d) To facilitate efforts of researchers in biomathematics and modelling and draw them towards interdisciplinary research

(e) To have a combined effort at solving common regional problems such as common emerging and re-emerging tropical diseases

**Tuition fees**

**Full-time students:** Ugandans UgShs 3,525,000 per year. International students UgShs 6,262,000 per year.Admission Requirements

The main requirement is that the person to be admitted should posses any of the following

- (a)Mathematics major in Bachelor of Science, Science Education, of at least a good second class division.
- (b)Engineering, Statistics, Economics (with mathematics minor) of at least a good second class division.
- (c)Biological, Biomedical and Ecological Sciences (with interest in Modelling, Bioinformatics and Biodata analysis) with good analytical skills and Mathematics background at high school

** Examination**

Each course in the programme will have a written examination of three hours duration. Examinations will be done at the end of every semester. There will also be continuous coursework (CW) assessment throughout the course in form of take home assignments, group model formulation and analysis, tests, seminar presentation, industrial report and/or practical sessions. At the end of the course, pass mark will be obtained by combining the Examination mark and continuous assessment (coursework) mark.

** Course Assessments:** Each Course is assessed on the basis of 100 total marks with proportions as follows with a minimum of two course assignments and/or tests, and with Course Work constituting 40% and finalconstituting 60%

** Pass Mark.** The Pass mark for all courses in the programme will be at 60%, (CW+Exam) with the Pass Grade Point per Course is 3.0.

** Project report:** Each student must work on a research project, with a topic approved by the departmental research and higher degrees committee, following presentation of the topic in the regular departmental seminar series programme. The student will be assigned a supervisor to assist the student during proposal writing and research. The final proposal will be graded by a committee upon project defense during a departmental seminar. Each project must be passed with a minimum mark of 60%.

** Award:** Master of Science in Mathematical Modelling Degree of Makerere University (MSc MM).

** Curriculum**

The normal duration of this programme will be 18 months spread over 3 semesters for full time students. Two Semesters for coursework of minimum 10 courses and one semester for two courses and a research project.

**Structure of the Programme**

The Master of Science in Mathematical Modelling degree will comprise of three semesters of study (18 Months). The programme will consist of a minimum of 47 credit units (CU) spread over the three semesters, including a research project. The nature of the programme is such that the student takes five courses in Semester I and five courses in Semester II. In semester III, the student undertakes a research project (of 5 CU), and two course related to the project area. In addition, the students are required to get involved in seminar series in Semester III. There will be a Recess Term during which students will be involved in computer and research writing skills. This will take 2 CU. The duration of each semester should be 17 weeks (i.e. one week of registration, 15 weeks for teaching and one week for examinations).

Research Project: During the third and final semester a student will undertake a project and two advanced courses from the above related to the area of his/her project. The aim of the project is to introduce a student to research and Mathematical writing. The project will test how well a student has understood and can apply a given mathematical result or theory from the courses done to model real life situation. The student may, in addition get attached to an industry to gain insight on the operation of the organization, data collection for model validation and get to learn the terminology related to the industrial modelling aspect.

**Important:** At the beginning of the course, all students will be introduced to computational skills, by an IT tutor, to enable them use computers in learning, as many of courses will require this skill. This training will continue throughout the programme in computer labs. Between Semester II and Semester III, there is a short period of 2 months. This period will be used as a recess term for the students to do the following

Develop a concept paper for the research project with seminars given by staff on proposal and project writing skills

Get training in Mathematical programming and model simulation. This will be special training in computer Laboratory with a staff and attendant

The minimum semester load shall be 16 CU for Semester I and II. Semester III will have a maximum semester load of 13 CU to allow student time to do their project.

One course unit shall be equivalent to one contact hour per week per semester. Two hours of tutorial, practical or fieldwork should be equivalent to one contact hour. Four hours of internship attachment, industrial training should be equivalent to one contact hour.

**PART I: COURSE WORK YEAR**

SEMESTER I

Core Courses

MTM 7101 Differential Equations and Dynamical Systems (3CU)

MTM 7102 Stochastic Processes (3CU)

MTM 7103 Measure and Probability (4CU)

**Electives (Choose at least one course)**

MTM 7104 Mathematical Ecology and Natural Resource modelling (3CU)

MTM 7105 Introduction to Mathematics of Finance (3CU)

MTM 7106 Operations Research and Optimization Theory (3CU)

MTM 7107 Statistical Modelling (3CU)

MTM 7108 Economic Modelling (3CU)

MTM 7109 Systems Dynamics Modelling (3CU)

MTM 7110 Time Series and Forecasting (3CU)

MTH 7111 Environmental Modelling (3CU)

MTM 7112 Hydrodynamic Stability Theory (3CU)

MTM 7113 Systems Dynamics Modelling and Decision making (3CU)

MTM 7114 Fundamentals of Bioinformatics (3CU)** SEMESTER II **

** Core Courses**

MTM 7201 Numerical Methods for Partial Differential Equations (4CU)

MTM 7202 Stochastic Calculus (3CU)

MTM 7203 Applied Functional Analysis (3CU)

** Electives (Choose at least one course)**

MTM 7204 Mathematical Epidemiology (3CU)

MTM 7205 Mathematics Immunology (3CU)

MTM 7206 Applied Bioinformatics (3CU)

MTM 7207 Mathematical Physiology (3CU)

MTM 7208 Biostatistics and Data Analysis Techniques (3CU)

MTM 7209 Control Theory (3CU)

MTM 7210 Life Insurance Mathematics (3CU)

MTM 7211 Non-Life Insurance Mathematics (3CU)

MTM 7212 Financial Mathematics (3CU)

MTM 7213 Computational Neuroscience (3CU)

PART II: RESEARCH/DISSERTATION YEAR

SEMESTER III

Core course

MTM 7301 Computational and Research Methods (2CU)

SEMESTER IV

Core Courses

MTM 7401 Seminar Series (2CU)

MTM 7402** **Dissertation (8CU)