M.Sc. Mathematics – SF

The M.Sc. Mathematics programme is designed to provide advanced training in mathematics with emphasis on analytical thinking, logical reasoning, problem-solving skills, computational techniques, and research aptitude. The programme offers a balanced blend of theoretical foundations and interdisciplinary exposure, enabling students to develop intellectual competence, creativity, and independent learning abilities.
The curriculum is designed to equip students with the knowledge and skills required to address contemporary challenges in academia, research, industry, and emerging technological fields. The programme also aims to foster scientific curiosity, professional excellence, ethical values, and lifelong learning.
The programme prepares graduates for higher studies, research, teaching, and diverse career opportunities in areas such as information technology, analytics, finance, scientific computing, and other mathematics-oriented professions.
OBJECTIVES OF THE M.SC. MATHEMATICS PROGRAMME
The M.Sc. Mathematics programme is designed to nurture analytically strong, computationally skilled, and research-oriented graduates capable of addressing challenges in academia, industry, and emerging technologies. The programme aims to:
- Build a strong foundation in advanced areas of pure and applied mathematics.
- Develop logical reasoning, analytical thinking, and innovative problem-solving abilities.
- Integrate computational tools and programming techniques with mathematical learning.
- Explore modern applications of mathematics in Machine Learning, Cryptography, Optimization, Data Science, and Scientific Computing.
- Foster research aptitude, creativity, and independent learning through projects and interdisciplinary studies.
- Prepare students for higher studies and careers in research, education, analytics, finance, information technology, and other mathematics-driven professions.
Promote scientific curiosity, professional excellence, and lifelong learning
STRUCTURE OF M.SC MATHEMATICS
The programme shall include two types of courses, Core Courses and Elective Courses. There shall also be a Project/Dissertation and Comprehensive Viva Voce as core courses. The programme also includes assignments, seminars, class tests, and project work as part of the continuous evaluation process. The total credit for the programme is fixed at 80.
THEORY COURSES
There are nineteen theory courses spread in four semesters in the M.Sc. Programme. Distribution of theory courses is as follows. There are sixteen core courses common to all students. Semester I, Semester II and Semester III will have five core courses each and Semester IV will have one core course, three elective core courses and a project. The three elective core courses can be chosen as per the interest of the students, availability of faculty and academic infrastructure.
PROJECT
The project of the PG program should be relevant and innovative in nature. The type of project can be decided by the student and the guide (a faculty of the department or other department/ college/ university/ institution). The project work should be taken up seriously by the student and the guide. The project should be aimed to motivate the inquisitiveness and research aptitude of the students. The students may be encouraged to present the results of the project in seminars/symposia. The conduct of the project may be started at the beginning of Semester III, with its evaluation scheduled at the end of Semester IV. The project is evaluated by one external and one internal examiner.
COMPREHENSIVE VIVA VOCE
A comprehensive viva voce examination will be conducted by one external and one internal examiner at the time of evaluation of the project. The components of viva consist of subjects of special interest, fundamental concepts, topics covering all semesters and awareness of current and advanced topics.
CORE COURSES
| Semester | Course Code | Course Title |
| I | MT1C01TM25 | Linear Algebra |
| MT1C02TM25 | Basic Topology | |
| MT1C03TM25 | Real Analysis | |
| MT1C04TM25 | Abstract Algebra | |
| MT1C05TM25 | Graph Theory | |
| II | MT2C06TM25 | Complex Analysis |
| MT2C07TM25 | Functional Analysis | |
| MT2C08TM25 | Field Theory | |
| MT2C09TM25 | Numerical Analysis with Python | |
| MT2C10TM25 | Research Methodology | |
| III | MT3C11TM25 | Spectral Theory |
| MT3C12TM25 | Measure Theory and Integration | |
| MT3C13TM25 | Linear Algebra for Machine Learning | |
| MT3C14TM25 | Partial Differential Equations | |
| MT3C15TM25 | Advanced Graph Theory | |
| IV | MT4C16TM25 | Optimization Techniques |
| Elective 1 | ||
| Elective 2 | ||
| Elective 3 | ||
| MT4PRM25 | Project/Dissertation | |
| MT4VM25 | Viva-Voce |
ELECTIVE COURSES
| Course code | Course Title |
| MT4E01TM25 | Advanced Complex Analysis |
| MT4E02TM25 | Number Theory and Cryptography |
| MT4E03TM25 | Differential Geometry |
| MT4E04TM25 | Multivariate Calculus and Integral Transforms |
| MT4E05TM25 | Combinatorics |
| MT4E06TM25 | Analytic Number Theory |
| MT4E07TM25 | Operations Research |
| MT4E08TM25 | Probability Theory |
| MT4E09TM25 | Coding Theory |








