Research Methodology
MATH17-R01 : Research Methodology (M.Phil/Ph.D. coursework)
Syllabus. Scientific research and literature survey. History of mathematics, finding and solving research problems, role of a supervisor, survey of a research topic, publishing a paper, reviewing a paper, research grant proposal writing, copyright issues, ethics and plagiarism.
Research tools. Searching google (query modifiers), MathSciNet, ZMATH, Scopus, ISI Web of Science, Impact factor, h-index, Google Scholar, ORCID, JStor, Online and open access journals, Virtual library of various countries
Scientific writing and presentation. Writing a research paper, survey article, thesis writing; LaTeX, PSTricks, Beamer, HTML and MathJaX
Software for Mathematics. Mathematica/Matlab/Scilab/GAP
Reference:
J. Stillwell, Mathematics and its History, Springer International Edition, 4th Indian Reprint, 2005
L. Lamport, LaTeX, a Document Preparation System, 2nd ed, Addison-Wesley, 1994.
Norman E. Steenrod, Paul R. Halmos, Menahem M. Schiffer, Jean A. Dieudonne, How to Write Mathematics, American Mathematical Society, 1973.
Nicholas J. Higham, Handbook of Writing for the Mathematical Sciences, 2ed, SIAM, 1998.
Donald E. Knuth, Tracy L. Larrabee, and Paul M. Roberts, Mathematical Writing, Mathematical Association of America, Washington, D.C., 1989.
Frank Mittelbach, Michel Goossens, Johannes Braams, David Carlisle, Chris Rowley, The LaTeX Companion, 2nd edition (TTCT series), Addison-Wesley, 2004.
Michel Goossens, Frank Mittelbach, Sebastian Rahtz, Denis Roegel, Herbert Voss, The LaTeX Graphics Companion, 2nd edition (TTCT series), Addison-Wesley, 2004
Martin J. Erickson and Donald Bindner, A Student's Guide to the Study, Practice, and Tools of Modern Mathematics, CRC Press, Boca Raton, FL, 2011.
Mathtools documentation (http://mirrors.ctan.org/macros/latex/contrib/mathtools/mathtools.pdf)
Pstricks documentation (http://tug.org/PSTricks/main.cgi?file=doc/docs)
MathJax documentation (http://tug.org/PSTricks/main.cgi?file=doc/docs)
USEFUL LINKS
A Course on Research Methodology by Palash Sarkar, ISI Calcutta
History of Mathematics
TeX Related
Writing Mathematics
Writing Mathematics Papers, by J Trzeciak (IMPAN)
Jean-Pierre Serre: How to write mathematics badly (Youtube) / PDF
“Mathematical Writing” – notes from a lecture course by Don Knuth, Tracy Larrabee, and Paul Roberts.
Paul Halmos’ “How to write mathematics” (the book also contains similar pieces by Dieudonné, Schiffer, and Steenrod); the article can be found here.
Ethics
Plagiarism
Some links to retracted articles: CVEE; IJMMS; JMAA, AML(1); AML(2); AMC
Interesting articles by Denis Bouyssou, Silvano Martello, Frank Plastria (i) Plagiarism again: Sreenivas and Srinivas, with an update on Marcu, 4OR-Q J Oper Res (2009) 7: 17 (ii) A case of plagiarism: Dănuţ Marcu 4OR (2006) 4: 11
Softwares