CHRIST (Deemed to University), Bangalore DEPARTMENT OF sciences-and-humanities-(engineering) faculty-of-engineering
Syllabus for Master of Philosophy (Mathematics) Academic Year (2019)

1 Semester - 2019 - Batch
Course Code	Course	Type	Hours Per Week	Credits	Marks
RES131	FOUNDATIONS OF RESEARCH	Core Courses	4	4	100
RES132	RESEARCH PUBLICATION	Core Courses	4	4	100
RSC131	METHODS IN RESEARCH FOR SCIENCE	Discipline Specific Elective Courses	4	4	100
RSC132	RESEARCH WRITING FOR SCIENCE	Discipline Specific Elective Courses	4	4	100

Introduction to Program:

The Master of Philosophy Programme in Mathematics is being offered based on a credit system similar to the other programmes offered by the University. The M. Phil. programme has two semesters with each semester spreading through 15 weeks. The candidate has to submit the dissertation within two months after the second semester ends. It can be extended by two more months on specific request. Those who fail to submit the dissertation within the extended time period can register for a further extension of four more months with a payment of 50% of the course fee. There will be only two repeat chances (within three years after registration) for the course work papers and no revaluation of papers at any stage of the program. The time taken from the admission till the submission of the dissertation shall be considered as the duration of the M. Phil. Program.

Assesment Pattern

Each paper of the semester will be assessed upon 100 marks (Continuous Internal Assessment (CIA) – 45 marks, Attendance –5 marks and End Semester Examination - 50 marks).

The internal assessment (comprising various components such as seminar, literature survey, presentation, class test and so on) will be done periodically and the CIA marks will be sent to the Controller of Examination through Dean of Science and a copy forwarded to the General Research Coordinator as per the following guidelines:

CIA 1: 10 Marks assessment

CIA 2: 25 Marks assessment

CIA 3: 10 Marks assessment

The end semester examination will be conducted at the end of second semester for Research Methodology and for each elective paper. The Maximum marks for each paper will be 100 and the duration is three hours.

Adjudication of the M. Phil Dissertation

The dissertation submitted by the candidate under the guidance of the guide will be assessed by two experts (one internal and one external).

The candidates also have to appear for final viva-voce. Assessment based on the viva-voce and the dissertation, along with the assessment of theory papers of both I & II semesters will be considered to declare the results.

Examination And Assesments

Sl. No.	Subject	Marks
1	Research Methodology	100
2	Paper 1 (Common Paper)	100
3	Paper 2 (Specialization Paper)	100
4	Dissertation & Viva-Voce
Components
Presentation on the research proposal		50
Double valuation of the dissertation		100
Viva-Voce examination		50
Total		500

RES131 - FOUNDATIONS OF RESEARCH (2019 Batch)
Total Teaching Hours for Semester:60	No of Lecture Hours/Week:4
Max Marks:100	Credits:4
Course Objectives/Course Description
Philosophical foundations of research are the scenario of higher education provided. Various approaches to research, review of literature and application of theory are also included.
Course Outcome
Reflections on the hilosophical foundations of research Knowledge of the history and context of higher education Knkowledge about various approaches to research Review of literature Application of theory

Unit-1	Teaching Hours:14
Philosophical foundations of Research
Ethics and values in Research, Scope of Interdisciplinary, multi-disciplinary and cross disciplinary research, Doctoral Supervision and supervisory styles, Types of Doctoral Research and implications, Pedagogy and Research: Research Informed teaching and Problem Based learning
Unit-2	Teaching Hours:16
Higher Education
History of Higher Education, The notion of University, Disciplines and Domain knowledge, Accreditations and Educational Policy, The Public Intellectual
Unit-3	Teaching Hours:16
Approaches to Research & Review of literature
Quantitative, Qualitative and mixed methods, Relationship between Research Paradigms, Designs and methods, Research Designs and its types, Research methods, Conceptualisation of Research problem in different research approaches, Research questions, Review of literature: Research Topic, Review of Literature in quantitative, qualitative and mixed methods, Steps in conducting Literature Review, Literature map, Abstracting studies, Literature Summary matrix, , Types of Reviews, Identification of Research Gap, Overview of Style manuals, Operational and Theoretical Definitions
Unit-4	Teaching Hours:14
Application of theory
Theory in quantitative research, Writing a Quantitative theoretical framework, Theory in Qualitative and mixed methods, Research proposals format for quantitative, Qualitative and mixed methods (Practical)
Text Books And Reference Books: Creswel, J. W. (2009). Research design: Qualitative, quantitative, and mixed methods approaches. Los angeles: University of Nebraska–Lincoln.
Essential Reading / Recommended Reading Altbach, P. G., Reisberg, L., & Rumbley, L. E. (2019). Trends in global higher education: Tracking an academic revolution. BRILL. Denzin, N.K. and Lincoln, Y.S. (eds.). (2011). The Sage handbook of qualitative research. Thousand Oaks: Sage. Fink, A. (2019). Conducting research literature reviews: From the internet to paper. Sage Fuller, S. (2019). Philosophy of science and its discontents. Routledge. Herr, K. and Anderson, G.L. (2005). The action research dissertation. Thousand Oaks, CA: Sage. Johnson, A.P. (2005). A short guide to action research. Boston: Pearson Education. Kindon, S., Pain, R., and Kesby, M. (eds). (2007). Participatory action research approaches and methods. NY: Routledge. McNiff, J. and Whitehead, J. (2006). All you need to know about action research. Thousand Oaks, CA: Sage. Reason, P. and Bradbury, H. (eds.). (2006). Handbook of action research. Thousand Oaks, CA: Sage. Stringer, E.T. (2007). Action Research. Thousand Oaks, CA: Sage.
Evaluation Pattern Internal Assessements are designed to improve knowledge of and skill in all sections of the course Each unit is evaluated separately and all units have equal weightage Not attending more than four hours of lectures of each unit will require the scholar to repeat the unit
RES132 - RESEARCH PUBLICATION (2019 Batch)
Total Teaching Hours for Semester:60	No of Lecture Hours/Week:4
Max Marks:100	Credits:4
Course Objectives/Course Description
This course introduces the candidates to various journals, proceedings, books and conferences. It also helps them in collaborating with the scholars of various fields. Learning Objectives To provide the researchers the information, knowledge, and skills to identify academic journals of various quality To be able to know about the industry of publishing journals To teach the researchers how to submit articles to journals To understand the advantages, disadvantages, responsibilities and ethics of collaborative publishing
Course Outcome
On Successful completion of this course, research scholars will be able to: choose journals based on their quality work in different processes in journal publishing submit research articles independently collaborate with scholars and researchers

Unit-1	Teaching Hours:15
Quality Measures of Journals
The concept and history of indexing Indexing Agencies Various Review Methods Indexing Parameters Open Access Publications,
Unit-2	Teaching Hours:15
Journal Publishing
Types of Journals Domain based Journals University Publications Private Publications Individual Publications Regional Publications Society/Association Publications Economics of Journal Publishing Article Processing Charges
Unit-3	Teaching Hours:15
Article Submission
Journal Databases Journal Template Plagiarism Submission Processes: Editorial Manager, OJS, Referee List
Unit-4	Teaching Hours:15
Academic Collaboration
Collaboration in Research Collaboration in Research Publication Merits of Collaboration Authorship preferences Tools of Collaboration Types of Authors
Text Books And Reference Books: Coser, L. A., Kadushin, C., & Powell, W. W. (1982). Books: The culture and commerce of publishing (p. 22). New York: Basic Books.
Essential Reading / Recommended Reading Cross, R., Taylor, S & Zehner, D (2018). Collaboration Without Burnout, Harvard Business Review, July–August, pp.134–137. Ferris LE & Winker MA, (2017). Ethical issues in publishing in predatory journals, Biochem Med (Zagreb). 27(2):279-284. doi: 10.11613/BM.2017.030. Habibzadeh, F., & Simundic, A.-M. (2017). Predatory journals and their effects on scientific research community. Biochemia Medica, 27(2), 270–272. http://doi.org/10.11613/BM.2017.028 Laine, C., & Winker, M. A. (2017). Identifying predatory or pseudo-journals. Biochemia Medica, 27(2), 285–291. http://doi.org/10.11613/BM.2017.031 Lippi, G. (2017). How do I write a scientific article?—A personal perspective. Annals of Translational Medicine, 5(20), 416. http://doi.org/10.21037/atm.2017.07.43 Prater, C. 8 Ways to Identify a Questionable Open Access Journal, https://www.aje.com/en/arc/8-ways-identify-questionable-open-access-journal/ accessed on July 3, 2018 Saha, I & Paul, B (2017). Research submission: Some technicalities and vital links, Med J Armed Forces India. 74(2): 165–168. doi: 10.1016/j.mjafi.2017.10.006 Shewan, L. G., & Coats, A. J. (2010). Ethics in the authorship and publishing of scientific articles.
Evaluation Pattern Internal Assessements are designed to improve knowledge of and skill in all sections of the course Each unit is evaluated separately and all units have equal weightage Each unit has about 12 lecture hours and 3 library/practical hours Not attending more than four hours of lectures of each unit will require the scholar to repeat the unit
RSC131 - METHODS IN RESEARCH FOR SCIENCE (2019 Batch)
Total Teaching Hours for Semester:60	No of Lecture Hours/Week:4
Max Marks:100	Credits:4
Course Objectives/Course Description
This course introduces scholars to the Python Programming, MATLAB, Origin, Tikz and LaTeX Draw, thus enabling them to develop skills of numeric computation, data analysis and visualization, programming and algorithm development and application development. Course Learning Objectives To provide the knowledge of MathLab, Origin and Python. To explore the possibilities of using Python language as a tool for learning Mathematics. To develop the skill of preparing documents using LaTeX also to develop the skill of drawing figures using Tikz
Course Outcome
On successful completion of the course, the students should be able to: Explore and visualize data using MATLAB and ORIGIN commands and functions Import data from heterogeneous sources Build predictive models using MATLAB and ORIGIN Toolbox Prepare documents using LaTeX Draw mathematical figures using Tikz

Unit-1	Teaching Hours:16
Origin: Data Analysis and Technical Graphics Software
Introduction to ORIGIN, Introduction to ORIGIN Graphing Elements, Creating Simple Graphs, Graph Customization and Technicalities, Workbook, Worksheets and Columns, Graphical Exploration of Data, Themes and Templates, Graphing Data from multiple sheets, Row Statistics, Data Analysis [Peak Analysis, Curve Fitting, Statistics].
Unit-2	Teaching Hours:14
Python Programming
Installation, IDES, Introduction, Hardware components, Software components, The Operating system, Programming in Python, formatted printing, Visualizing data with graphs, Algebra and symbolic math with Symphy, Graphs as a python class, Graph Density, Distance and diameter of a graph, The complete python graph class.
Unit-3	Teaching Hours:14
Data analysis using MATLAB
Introduction to MATLAB [Variables, Matrices, Built-in Functions, Arrays, Structure, Cell], MATLAB Programming [Inline functions, control structures, Programming syntax, Script files and Functions files], solution of Differential equations, Data Visualization and Data Exploration Techniques [Data import/export, Plots, Statistics basics], Models for Data Analysis [Regression Models, Classification Models [Using of Statistic Toolbox].
Unit-4	Teaching Hours:16
Latex and Tikz
Introduction, Preparing an input file, The document, Document class, The title page, Changing the type style, Mathematical formulas, Mathematical Symbols, Defining commands and environments, Other document classes, Pictures and colors, Erros, The bibliography database, Reference manual, Drawing lines and curves using Tikz, Filling up areas, Putting labels in Pictures, Integration with beamer.
Text Books And Reference Books: A very minimal introduction to TikZ, Jacques Cremer, Toulouse School of Economics. D. M. Etter, Introduction to MATLAB, 3rd ed., Prentice Hall, 2014. Doing Maths with Python Amit Saha, no starch press:San Fransisco, 2015. Origin 9.1 User Guide – OriginLab.
Essential Reading / Recommended Reading Deng, E., & Huang, L. (2019). An Elegant LATEX Template for Books. Johansson, R. (2019). Introduction to computing with python. In Numerical Python (pp. 1-41). Apress, Berkeley, CA. Lode, C. (2019). Better Books with LaTeX: Self-Publish Your Book on Amazon and Google. Clemens Lode Verlag eK. Origin: Data Analysis and Technical Graphics Software, Microcal Software, Microcal Software Incorporated, 1999 Payne, J. R. (2019). Introduction to Computer Programming and Python. In Python for Teenagers (pp. 1-16). Apress, Berkeley, CA. S. Attaway, MATLAB: A Practical Introduction to Programming and Problem Solving, 3rd Edition, 3rd ed., Elsevier Inc., 2013. W. L. Martinez et. al., Exploratory Data Analysis with MATLAB, 2nd ed., CRC Press, 2010.
Evaluation Pattern Internal Assessements are designed to improve knowledge of and skill in all sections of the course Each unit is evaluated separately and all units have equal weightage Not attending more than four hours of lectures of each unit will require the scholar to repeat the unit
RSC132 - RESEARCH WRITING FOR SCIENCE (2019 Batch)
Total Teaching Hours for Semester:60	No of Lecture Hours/Week:4
Max Marks:100	Credits:4
Course Objectives/Course Description
The course aims to enable researchers to use their reading ability and the material they read to develop the writing skills their work requires. It will serve as a foundation for publications and thesis writing later on during the course of the PhD programme. Course Learning Objectives To provide the researchers the information, vocabulary and skills you need quickly and easily so that they can write confidently using the style and structure they see in the journals they read. To discover the conventions of structure, organization, grammar and vocabulary in science writing in the field of the researchers and will provide them with the tools to write in a similar way and at a similar level. To teach the researchers how to turn their research into a paper that can be submitted to a professional journal. To be able to get the information, the language and vocabulary for writing a dissertation in English.
Course Outcome
On Successful completion of this course, research scholars will be able to: write their scientific papers using a conventional structure of writing for Mathematics acquire academic vocabulary for their Mathematics writing/dissertations/theses read research articles critically and evaluate the contents in terms of English language publish scientific papers in peer-reviewed journals emanating from countries that have English as the first language acquire subject specific communication skills that serve the purpose of conferences / seminars / workshops / colloquia / symposia / teaching / viva voce

Unit-1	Teaching Hours:15
How to Write an Introduction
Structure of Introduction Section Grammar and Writing Skills for Introduction Section Writing Task: Build a Model Vocabulary for Introduction Section Writing an Introduction Section
Unit-2	Teaching Hours:15
Writing about Methodology
Structure, Grammar and Writing Skills Writing Task: Build a Model Vocabulary for Writing a Results Section
Unit-3	Teaching Hours:15
Writing about Results
Structure, Grammar and Writing Skills Writing Task: Build a Model Vocabulary for Writing a Results Section
Unit-4	Teaching Hours:15
Writing the Discussion/Conclusion and Abstract
Structure, Grammar and Writing Skills Writing Task: Build a Model, Vocabulary for Discussion / Conclusion Section Writing a Discussion / Conclusion Section Structure, Grammar and Writing Skills Writing Task: Build a Model Vocabulary for Abstract Writing an Abstract.
Text Books And Reference Books: H. Glasman-Deal, Science research writing: for non-native speakers of English. World Scientific, 2010.
Essential Reading / Recommended Reading S. Bailey, Academic writing a handbook for international students. Routledge, 2018. M. Cargill and P. O'Connor, Writing Scientific Research Articles: Strategy and Steps, 2nd Edition. John Wiley and Sons, 2013. H. G. Danner, Thesaurus of english word roots. Rowman and Littlefield, 2014. R. B. Maddox and R. B. Maddox, A transition to abstract mathematics: mathematical thinking and writing. Academic Press/Elsevier, 2009. A. Meyers, Longman academic writing series. Pearson Education, Inc., 2014. J. Morley,Academic phrasebank. Manchester: University of Manchester.[online], Available at: http://www.phrasebank.manchester.ac.uk R. Murray and S. Moore, The Handbook of academic writing: a fresh approach. Open University Press, 2006. D. K. Pugalee, Writing to develop mathematical understanding. Christopher-Gordon Publishers, Inc., 2005. A. Ramet, Creative writing: how to unlock your imagination and develop your writing skills. How To Books, 2010.
Evaluation Pattern Internal Assessements are designed to improve knowledge of and skill in all sections of the course Each unit is evaluated separately and all units have equal weightage Not attending more than four hours of lectures of each unit will require the scholar to repeat the unit

CHRIST (Deemed to University), Bangalore

DEPARTMENT OF sciences-and-humanities-(engineering)

faculty-of-engineering

Syllabus for Master of Philosophy (Mathematics) Academic Year (2019)

Syllabus for
Master of Philosophy (Mathematics)
Academic Year (2019)