Research

1.1.1. General introduction to research methodology

Meaning and objective of scientific research, Types and significance of research, Methods of scientific research, Research process and criteria for good research, Stages of research. Reference : Research Methodology, by C.R. Kothari et al.

1.1.2. Methodology of Research in Mathematics Identifying a broad area.

Collecting materials for deep understanding of fundamentals as well as recent findings. Identifying an area for in-depth study. Collecting and reading as many documents as possible. Studying recent research findings and trying solutions independently. Fixing exact problem/concept or research.

1.1.3. Information Resources and Publication

This section deals with the sources of information. Classical sources, Modern sources, availability of online resources (free and subscribed), Accessibility of Journals and other print documents. Needs, ways and means of publication of research findings.

This course comprises of topics of research methodology in general, methodology of research in Mathematics, methodology of teaching Higher Mathematics, modern tools for teaching and research and Ethics in research.

1.2.1. Modern and classical methods and techniques of teaching.

Teaching of Higher Mathematics. Challenges and opportunities. Difficulties in teaching and learning Mathematics. Traditional and Modern approaches. Teaching techniques, proof techniques-inductive reasoning, deductive reasoning, contrapositive, counter examples.

1.2.2. Innovative Methods of Teaching and Learning.

* Graphing and computation (KMPlot, Geogebra, Scilab, SageMath, GGAP and R) * Document preparation (LaTeX) * Presentation (Beamer).

1.3.1. Piracy and Plagiarism.
1.3.2. Morality and ethics.
1.3.3. Rules and regulations – IPR.