PhD in Mathematics

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/N
CODE 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