Department of
MATHEMATICS






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

 
1 Semester - 2019 - Batch
Paper Code
Paper
Hours Per
Week
Credits
Marks
RES131 FOUNDATION OF RESEARCH 4 4 100
RES132 RESEARCH PUBLICATION 4 4 100
RSC131 METHODS IN RESEARCH FOR SCIENCE 4 4 100
        

  

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

Department Overview:
Department of Mathematics, Christ University is one of the oldest departments of the University. It offers programmes in Mathematics at the undergraduate level, post graduate level as well as M.Phil and Ph.D. The department aims to * enhance the logical, reasoning, analytical and problem solving skills of students. * cultivate a research culture in young minds. * foster aesthetic appreciation for mathematical thinking. * encourage students for pursuing higher studies in mathematics. * motivate students to uphold scientific integrity and objectivity in professional endeavors.
Mission Statement:
Vision: Excellence and Service Mission: To organize, connect, create and communicate mathematical ideas effectively, through 4D?s; Dedication, Discipline, Direction and Determination.
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.
Program Objective:
Programme Objective: POBJ1. To provide learners with an in-depth knowledge, abilities and insight in specialized topics in Mathematics. POBJ2. Research Methodology in Mathematics. POBJ3. To encourage collaborative learning through dissertation and research activities so that they can pursue research programmes. POBJ4. To provide a platform for the learner to engage in various academic activities independently or in a group. Programme Outcomes: PO1. To be able to explain mathematical principle to formulate, model and hence find solutions to practical problems. PO2. To be able explain the advantages, limitations, importance of mathematics and its techniques to solve problems in specialized topic. PO3. To acquire the skills which are necessary to do research/higher studies in the areas of the specialized topic. PO4. The learner will be able to become a good teacher or researcher in mathematics so that he/she can communicate the subject with others in an efficient way.

RES131 - FOUNDATION 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.

Learning 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

Learning 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

Learning 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