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.

User Rating: 5 / 5

Course Code    : PMAT 44962

Title                   : Research Methodology

 Learning Outcomes:

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

1. recognize the importance of research and discuss the methods of research designs and process

2. demonstrate knowledge and skills acquired in research methods necessary for undertaking and completion of a research related to the field of study

3. assess the key characteristics of both quantitative and qualitative research methods in the field of study

4. demonstrate the awareness of the development of the area of study

5. critically analyze, synthesize, and utilize information and data related to the field of study

6. apply research methodology and /or scholarly inquiry techniques specific to the field of study

7. critically analyze, verify, and interpret the results and provide valid conclusions

8. exercise research ethics and respect for other cultural perspectives in scientific research

9. proficiently communicate and disseminate information in a manner relevant to the field and intended audience.

Course Contents:

1. Fundamentals of research: Meaning and objective of research, understanding about Research, Applications of Research, Criteria and Characteristics of Research, Research strategies, Types of Research, Research design, Research process and steps involved in research, Research proposal.

2. Literature survey and documentation: Methods of literature survey, Use library and web resources (books, journals, e-journals, thesis), importance of documentation, documentation techniques

3. Data collection, Sampling techniques, Descriptive and Inferential methods: Classification of data, methods of data collection, Questionnaire, Sampling procedure and methods, Data processing and graphical representation of data, Estimation and Hypothesis testing, Using statistical software/packages in data analysis.

4. Research ethics, plagiarism, and impact of research: Research ethics, responsibility and accountability of researchers, Plagiarism and use of plagiarism detection software.

5. Technical writing and reporting of research: Types of research report, Structure, and organization of research reports, use of reference managing software, Impact factor, rating, indexing and citation of journals.

6. Publishing research and Research grants: Conferences, Journals, applying for research grants.

7. Developing presentation skills: structuring the presentation, how to improve presentation skills, available software.

 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:

1. Zina, O. (2 nd Ed., 2021). The essential guide to doing your research project, Sage.

2. Cohen, L., Manion, L. & Morrison, K. (2017). Research methods in education, Routledge. Curriculum Revision- Department of Mathematics- 2022 57

3. Mishra, S.B. & Alok, S. (2017). Handbook of research methodology.

4. Singh, Y.K. (2006). Fundamental of research methodology and statistics. New Age International.

5. Flick, U. (2 nd Ed., 2015). Introducing research methodology: A beginner's guide to doing a research project, Sage. 6. Kumar, R. (2018). Research methodology: A step-by-step guide for beginners. Sage.

User Rating: 5 / 5

Course Code    : PMAT 41813

Title                   : Functional Analysis

Pre-requisites   : PMAT 21553

 Learning Outcomes:

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

1. demonstrate knowledge of the functionals and its analysis under a topological background comprehending
2. understand how algebra and analysis combine to form a separate part of Pure Mathematics.

 Course Contents:

Metric spaces, Completion of metric spaces, Normed spaces, Banach spaces, Linear operators and functionals, Inner product spaces, Hilbert spaces, Fundamental theorems for normed and Banach 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. Madox, I.J., (1992) Elements of Functional Analysis, Cambridge University Press.
2. Jain, P.K., Ahuja, O.P. & Ahmad, K., (2^nd edition, 2010) Functional Analysis, New Age Science Limited
3. Kreyszig, E., (2007) Introductory Functional Analysis with Applications, John Wiley, New York.
4. Pannasamy, S., (2^nd edition, 2005) Foundations of Complex Analysis, Alpha Science International.