Course Syllabus
This syllabus outlines the modules of Research Methodology and Scientific Writing.
- Meaning of research in mathematics; pure, applied and computational research
- mathematical problems, conjectures and theorems; proof as method
- examples and counterexamples; abstraction and generalization
- formulation of research questions; objectives and methodology
- structure of a research proposal
- distinction between exposition, survey, review and original research
- Sources of mathematical literature; textbooks, monographs, research papers, conference proceedings and preprints
- university libraries
- MathSciNet, zbMATH, arXiv, Google Scholar, DOAJ and institutional repositories
- reading a mathematical paper
- preparing summaries, notes and annotated bibliographies
- identifying research gaps
- Principles of mathematical writing; definitions, examples, theorems, lemmas, propositions, corollaries, remarks and proofs
- writing clear proofs
- introduction to LaTeX; document classes; mathematical symbols; equation environments
- matrices; theorem environments; tables and figures; cross-referencing
- BibTeX and bibliography management
- preparation of assignments, seminar reports and dissertation chapters
- Academic integrity; plagiarism and self-plagiarism
- paraphrasing and acknowledgement; citation ethics
- authorship and contributorship
- peer review process; preprints and journals
- predatory journals and conferences
- copyright and open access; intellectual property rights
- ethical use of artificial intelligence and digital tools