User Rating: 5 / 5

Course Code    : PMAT 42833

Title                   : Measure Theory

Pre-requisites   : PMAT 42793

 Learning Outcomes:

At the end of the course the student should be able to demonstrate knowledge of the concepts and theorems of abstract Measure Theory and to apply them in Lebesgue integrals.

 Course Contents:

Measure Theory: Algebra, -algebra, additivity properties of a set function, Measure, Borel sets, Lebesgue measure, outer Measure, measurable subsets, measurable functions, Integral, Properties that hold almost everywhere, integrable functions, Additivity Theorem, Monotone convergence theorem, Dominated convergence theorem, Fatou's lemma, Relation of Riemann and  Lebesgue integrals, Modes of convergence.

 Method of Teaching and Learning: A combination of lectures, tutorial discussions and presentations.

Assessment: Based on tutorials, tests, presentations and end of course examination.

 Recommended Reading:

1. Cohn, D.L., (2^nd edition, 2015) Measure Theory, Springer New York.
2. Barra, G., (2^nd edition, 2003) Measure Theory and Integration, Elsevier.

User Rating: 5 / 5

Course Code    : PMAT 41962

Title                   : Research Methodology

 Learning Outcomes:

At the end of this course, the student should be able to understand the methods in research and independent-study in areas in Mathematics/Statistics.

Course Contents:

This course unit is meant to provide honors students with some of the background skills needed to successfully engage in mathematical research, familiarizes students with some of the famous problems which mathematicians are involved in. This will also guides students through the processes of selecting an area of mathematical inquiry, developing research questions, choosing and implementing appropriate methodologies, building outlines, developing bibliographies, writing literature reviews, and preparing drafts.

 Method of Teaching and Learning: A series of seminars by senior academic members in the department.                                            

 Assessment: Submission of a research/study proposal.

 Recommended Reading:

Required reading material will be distributed during each seminar.

User Rating: 5 / 5

Course Code    : PMAT 43976

Title                   : Research/Study Project

 Learning Outcomes:

At the end of this course, the student should be able to demonstrate competence in research/independent-study in an area in Mathematics/Statistics.

 Course Contents:

Undergraduate research project is an inquiry, investigation, or creation produced by a final year honours degree undergraduate that makes a contribution to the discipline and reaches beyond the traditional curriculum. Undergraduate research project is designed to provide students with the opportunity to develop and practice advanced discipline-specific projects in collaboration with senior academics in the department.

 Method of Teaching and Learning: A research/study project under the supervision of a senior staff member of the Department.

 Assessment: Submission of a research/study project report and an oral presentation.

 Recommended Reading:

Required reading material will be recommended by the supervisor depending on the relevant project

User Rating: 4 / 5

Course Code    : PMAT 41823

Title                   : Topology

Pre-requisites   : PMAT 21553

 Learning Outcomes:

By the end of this course, the student should be able to,

• demonstrate knowledge of definitions of topological and metric spaces and should be able to demonstrate knowledge of the difference between standard topological and non-topological properties
• explain the roles of open sets and their interconnections in topological spaces
• describe the topological notion of connectedness and its relation to path-connectedness
• describe the topological notion of compactness, and its significance in basic analysis.

 Course Contents:

Topological spaces, Basis for a topology, the subspace topology, Closed sets, Limit points, Continuous functions, the product topology, the metric topology, Connected spaces, Compact spaces.

 Method of Teaching and Learning: A combination of lectures, tutorial discussions and presentations.

 Assessment: Based on tutorials, tests, presentations and end of course examination.

 Recommended Reading:

1. Munkres, J.R., (2015). Topology, a first course, Prentice-Hall, India.