Research Methodology — DU B.Sc. (Hons.) Mathematics Previous Year Question Papers

Parts of the question are to be attempted together. 1. (a) Complete the following sentences, that describe the rules that must be observed for avoiding errors and for the betterment of a mathematical writing. (i) Begin sentences with words, not . (ii) Adopt a notation. (iii) Use a balance of and while writing mathematical sentences or statements. (iv) Write words fully, without . (v) Write sentences in style, not style. (vi) Use math symbols within math expressions, not as_______ between math expressions and words. (b) List out the basic techniques that successful mathematicians have found useful in discovering mathematics and that are central part of the mathematical thought process. (c) What is the general sequence of components of a research/review paper. Explain each component in detail. 2. (a) Write short notes on the following terms, with reference to mathematical writing, giving an example in each case: (ii) Otiose Symbols (iii) Different kinds of ellipsis (b) What points should be kept in mind, while writing the ‘Introduction’ section of a research paper? (c) Explain the key factors that a researcher should consider, to choose an appropriate journal for publication of his/her research paper? 3. (a) Describe how mathematical expressions are written in LaTeX, explaining the LaTeX environments for producing, an in-text formula and a displayed formula. Give one example each, for a fraction, an integral, and matrix, to show how each of these is written using LaTeX commands. (b) Write a code in LaTeX software to obtain the following output : 1.1 Importance of LaTeX LaTeX is widely weed for professional documents. 1. High-quality typesetting 2. Easy equations 3. Auto-numbering x + y = 10 x – y = 4 (1) (c) What is cross-referencing in LaTeX? Explain the steps to add a figure, give it a label, and refer to it in the text 4. (a) What is the advantage of giving a presentation of the research work? Write a short note on poster presentation. Give the general format of a poster. (b) Make a Beamer presentation on the topic ‘The Mathematical Research’ with at least one bullet list and one equation. (c) Explain the use of the PSTricks commands \begin{pspicture}, \pscircle, and psline, and describe how coordinates are used in PSTricks. 5. (a) Describe the following web resources for mathematics, with reference to research in Mathematics: (b) (c) What is Impact Factor of a journal? Who introduced Impact Factor and when? Which database can be used to find the impact factor of a journal? Explain in detail, the journal metrics SJR and MCQ. 6. (a) Describe research ethics concerning : (i) the participants (ii) the researchers. (b) (c) Explain the key features of the databases ‘MathSciNet and ‘Scopus’. Write the official websites for accessing these databases. What do you mean by plagiarism with reference to a mathematical writing?