The Department of Mathematics developed a taught PhD programme by coursework and dissertation in 2016. The first in-take was in 2016/2017 academic year. The programme will run on a full-time basis for a period of 4 years. Coursework will be for one year and the dissertation (research part) for three years. The programme is composed of three streams, namely, Pure Mathematics, Applied Mathematics and Mathematical Statistics. It is envisaged that the programme will have an advantage over the current PhD by thesis in that it will broaden the mathematical and computational base of the students, which will be beneficial to the students when it comes to do the research part. It is anticipated the rich knowledge base will lead to a better on-time completion rate.
The main aim of this programme is to increase the number of graduates with PhD in Mathematics. These graduates are highly needed in our institutions of higher learning in our country and in the region. The Departments of Mathematics at UDSM, Makerere University (Uganda) and Rwanda University came together, through the support of the Sida Bilateral programme, to develop a common curriculum for the taught PhD programme. The aim of developing a common curriculum was mainly to form a strong base from which expertise in the institutions can be utilized easily for teaching and supervision of the PhD candidates within the region.
The Department of Mathematics of UDSM at the moment has 23 academic staff members with PhD degrees. These staff members will be involved in the running of this programme. The Department of Mathematics also has enough space, good library facilities, and computing facilitates to support this programme effectively.
Mapping of the four-year programme
Year of Study | Semester I | Semester II |
I | Coursework | Coursework |
II | Comprehensive Exam / Proposal writing | Research |
III | Research | Research |
IV | Research | Research |
Course Mappings of the Programme
Below is a list of core and electives courses for the three streams of the PhD in Mathematics degree programme.
Course Mapping for the Pure Mathematics Stream
CODE | TITLE | STATUS | CREDITS | |
Semester I | MT 701 | Measure Theory and Integration | Core | 18 |
MT 702 | Advanced Functional Analysis | Core | 18 | |
MT 703 | Partial Differential Equations | Core | 18 | |
Elective | Elective | 18 | ||
Elective | Elective | 18 | ||
Total | 90 | |||
Semester II | MT 707 | Algebra I | Core | 18 |
MT 716 | Differential Geometry | Core | 18 | |
MT 739 | Advanced Topics in Topology | Core | 18 | |
Elective | Elective | 18 | ||
Elective | Elective | 18 | ||
Total | 90 |
Course mapping for Applied Mathematics stream
CODE | TITLE | STATUS | CREDITS | |
Semester I | MT 701 | Measure Theory and Integration | Core | 18 |
MT 702 | Advanced Functional Analysis | Core | 18 | |
MT 703 | Partial Differential Equations | Core | 18 | |
Elective | Elective | 18 | ||
Elective | Elective | 18 | ||
Total | 90 | |||
Semester II | MT 705 | Techniques of Optimization | Core | 18 |
MT 712 | Numerical Linear Algebra | Core | 18 | |
MT 741 | Stochastic Processes | Core | 18 | |
Elective | Elective | 18 | ||
Elective | Elective | 18 | ||
Total | 90 |
Course mapping for the Mathematical Statistics Stream
CODE | TITLE | STATUS | CREDITS | |
Semester I | MT 701 | Measure Theory and Integration | Core | 18 |
MT 702 | Advanced Functional Analysis | Core | 18 | |
MT 703 | Partial Differential Equations | Core | 18 | |
Elective | Elective | 18 | ||
Elective | Elective | 18 | ||
Total | 90 | |||
Semester II | MT 704 | Probability and Statistics | Core | 18 |
MT 743 | Advanced Statistical Inference | Core | 18 | |
MT 748 | Bayesian Methods for Data Analysis | Core | 18 | |
Elective | Elective | 18 | ||
Elective | Elective | 18 | ||
Total | 90 |
Electives for Pure Mathematics stream
S/NCODE | TITLE | CREDITS | |
1 | MT 706 | Computational and Research Methods | 18 |
2 | MT 711 | Harmonic Analysis | 18 |
3 | MT 712 | Numerical Linear Algebra | 18 |
4 | MT 713 | Theory of Distributions | 18 |
5 | MT 714 | Nonlinear Analysis | 18 |
6 | MT 715 | Operator Theory | 18 |
7 | MT 716 | Differential Geometry | 18 |
8 | MT 717 | Algebra II | 18 |
9 | MT 718 | Algebraic Number Theory | 18 |
10 | MT 719 | Computational Algebraic Geometry | 18 |
11 | MT 720 | Representation and Lie Theory | 18 |
12 | MT 721 | Weyl and Commutative Algebra | 18 |
13 | MT 722 | Advanced Homological Algebra | 18 |
14 | MT 723 | Field and Category Theory | 18 |
15 | MT 724 | Cryptography and Coding Theory | 18 |
16 | MT 732 | Probabilistic Graphical models | 18 |
17 | MT 734 | Analytic Number Theory | 18 |
18 | MT 735 | Elliptic Curves | 18 |
19 | MT 736 | Diophantine Geometry | 18 |
20 | MT 737 | Algebraic Geometry | 18 |
21 | MT 738 | Enumerative Combinatorics | 18 |
22 | MT 740 | Complex Analysis | 18 |
23 | MT 747 | Wavelet Theory | 18 |
24 | MT 758 | Advanced Graph Theory | 18 |
25 | MT 759 | Probability Methods in Combinatorics | 18 |
Electives for Applied Mathematics stream
S/N | CODE | TITLE | CREDITS |
1 | MT 706 | Computational and Research Methods | 18 |
2 | MT 708 | Control Theory | 18 |
3 | MT 709 | Convex Optimization | 18 |
4 | MT 710 | Large Scale Optimization | 18 |
5 | MT 740 | Complex Analysis | 18 |
6 | MT 745 | Hydrodynamic Stability Theory | 18 |
7 | MT 746 | Numerical Solutions to Differential Equations | 18 |
8 | MT 747 | Wavelet Theory | 18 |
9 | MT 749 | Dynamical Systems | 18 |
10 | MT 750 | Mathematical Epidemiology | 18 |
11 | MT 751 | Mathematical Ecology | 18 |
12 | MT 752 | Mathematical Immunology | 18 |
13 | MT 753 | Mathematical Physiology | 18 |
14 | MT 754 | Applied Bioinformatics | 18 |
15 | MT 755 | Fuzzy Sets and Fuzzy Logic | 18 |
16 | MT 756 | Fuzzy Engineering | 18 |
17 | MT 757 | Fuzzy Data Analysis | 18 |
18 | MT 760 | Advance Fluid Dynamics | 18 |
19 | MT 761 | Applied Optimization | 18 |