PhD. in Mathematics

Programme Type : Post Graduate Programme Duration : 48 Months Academic Unit : College Of Natural And Applied Sciences

Programme Descriptions

The PhD programme will consist of three streams namely:

i. Pure Mathematics stream

ii. Applied Mathematics stream

iii. Mathematical Statistics Stream

 

The minimum number of credits for graduation will be 540, out of which  a minimum of 180 credits will be for coursework and 360 credits will be for the dissertation. The coursework component will consist of core and elective courses and each course will be worth 18 credits. The core courses will account for 108 credits and the electives a minimum of 72 credits.

Course work runs for two semesters in year one and dissertation in three years. Each semester has a minimum of 5 courses and each course is 18 credits. A student must do a minimum of 5 courses (90 credits) per semester.  Courses are divided in three streams as follows:

 

Courses for Pure Mathematics Stream

 Code

Course Title        

Core/ Elective

Credit

First Year: 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

 

18

 

Elective

 

18

 

 Total Credits  Year 1 Semester I

 

90

     

First Year: Semester II

Core/Elective

 Credit

MT 707

Algebra I

Core

18

MT 716

Differential Geometry

Core

18

MT 739

Advanced Topics in Topology

Core

18

 

Elective

 

18

 

Elective

 

18

 

 Total Credits  Year 1 Semester II

 

90

         

 

Courses for Applied Mathematics Stream

 Code

Course Title        

Core/ Elective

Credit

First Year: 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

 

18

 

Elective

 

18

 

 Total Credits  Year 1 Semester I

 

90

     

First Year: Semester II

 Core/Elective

Credit

MT 705

Techniques of Optimization

Core

18

MT 712

Numerical Linear Algebra

Core

18

MT 741

Stochastic Processes

Core

18

 

Elective

 

18

 

Elective

 

18

 

 Total Credits  Year 1 Semester II

 

90

           

 

Courses for Mathematical Statistics Stream

 Code

Course Title        

Core/ Elective

Credit

First Year: 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

 

18

 

Elective

 

18

 

 Total Credits  Year 1 Semester I

 

90

     

First Year: Semester II

 Core/Elective

Credit

MT 704

Probability and Statistics

Core

18

MT 743

Advanced Statistical Inference

Core

18

MT 748

Bayesian Methods for Data Analysis

Core

18

 

Elective

 

18

 

Elective

 

18

 

 Total Credits  Year 1 Semester II

 

90

 

 

Students to choose minimum of four optional courses from the following three streams

Electives for Pure Mathematics stream

S/N

Code

Course Title

Core/ Elective

Credit

1

MT 706

Computational and Research Methods

Elective

18

2

MT 711

Harmonic Analysis

Elective

18

3

MT 712

Numerical Linear Algebra

Elective

18

4

MT 713

Theory of Distributions

Elective

18

5

MT 714

Nonlinear Analysis

Elective

18

6

MT 715

Operator Theory

Elective

18

7

MT 716

Differential Geometry

Elective

18

8

MT 717

Algebra II

Elective

18

9

MT 718

Algebraic Number Theory

Elective

18

10

MT 719

Computational Algebraic Geometry

Elective

18

11

MT 720

Representation and Lie Theory

Elective

18

12

MT 721

Weyl and Commutative Algebra

Elective

18

13

MT 722

Advanced Homological Algebra

Elective

18

14

MT 723

Field and Category Theory

Elective

18

15

MT 724

Cryptography and Coding Theory

Elective

18

16

MT 732

Probabilistic Graphical models

Elective

18

17

MT 734

Analytic Number Theory

Elective

18

18

MT 735

Elliptic Curves

Elective

18

19

MT 736

Diophantine Geometry

Elective

18

20

MT 737

Algebraic Geometry

Elective

18

21

MT 738

Enumerative Combinatorics

Elective

18

22

MT 740

Complex Analysis

Elective

18

23

MT 747

Wavelet Theory

Elective

18

24

MT 758

Advanced Graph Theory

Elective

18

25

MT 759

Probability Methods in Combinatorics

Elective

18

 

Electives for Applied Mathematics stream

S/N

CODE

TITLE

Core/ Elective

Credit

1

MT 706

Computational and Research Methods

Elective

18

2

MT 708

Control Theory

Elective

18

3

MT 709

Convex Optimization

Elective

18

4

MT 710

Large Scale Optimization

Elective

18

5

MT 740

Complex Analysis

Elective

18

6

MT 745

Hydrodynamic Stability Theory

Elective

18

7

MT 746

Numerical Solutions to Differential Equations

Elective

18

8

MT 747

Wavelet Theory

Elective

18

9

MT 749

Dynamical Systems

Elective

18

10

MT 750

Mathematical Epidemiology

Elective

18

11

MT 751

Mathematical Ecology

Elective

18

12

MT 752

Mathematical Immunology

Elective

18

13

MT 753

Mathematical Physiology

Elective

18

14

MT 754

Applied Bioinformatics

Elective

18

15

MT 755

Fuzzy Sets and Fuzzy Logic

Elective

18

16

MT 756

Fuzzy Engineering

Elective

18

17

MT 757

Fuzzy Data Analysis

Elective

18

18

MT 760

Advance Fluid Dynamics

Elective

18

19

MT 761

Applied Optimization

Elective

18

 

Electives for Mathematical Statistics stream

S/N

CODE

TITLE

Core/ Elective

Credit

1

MT 706

Computational and Research Methods

Elective

18

2

MT 710

Large Scale Optimization

Elective

18

3

MT 725

Multivariate statistics

Elective

18

4

MT 726

Computational Statistics

Elective

18

5

MT 727

Mathematical Insurance

Elective

18

6

MT 728

Mathematical Finance

Elective

18

7

MT 729

Biostatistics

Elective

18

8

MT 730

Time series Analysis

Elective

18

9

MT 731

Stochastic Calculus

Elective

18

10

MT 732

Probabilistic Graphical Models

Elective

18

11

MT 733

Experimental Design

Elective

18

12

MT 742

Linear Statistical Models

Elective

18

13

MT 743

Advanced Statistical Inference

Elective

18

14

MT 744

Advanced Probability Theory

Elective

18

15

MT 748

Bayesian Methods for Data Analysis

Elective

18

16

MT 755

Fuzzy sets and Fuzzy Logic

Elective

18

17

MT 756

Fuzzy Engineering

Elective

18

18

MT 757

Fuzzy data Analysis

Elective

18