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M-SC in Mathematics at Manipur University
Imphal West, Manipur
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About the Specialization
What is Mathematics at Manipur University Imphal West?
This M.Sc. Mathematics program at Manipur University focuses on advanced mathematical concepts, preparing students for research, higher studies, and diverse careers in India and globally. It provides a strong theoretical foundation in both pure and applied mathematics, emphasizing analytical thinking and problem-solving skills which are highly demanded in various Indian sectors like IT, finance, and academia, differentiating itself with a comprehensive curriculum and research opportunities.
Who Should Apply?
This program is ideal for Bachelor of Arts or Science graduates with Honours in Mathematics, or those with Mathematics as a subject, who possess a strong aptitude for abstract reasoning and logical problem-solving. It suits individuals aspiring to become researchers, educators, data scientists, or quantitative analysts in India. It is also suitable for working professionals looking to upskill in advanced mathematical techniques or career changers transitioning into analytical roles.
Why Choose This Course?
Graduates of this program can expect diverse career paths in India, including roles as mathematicians, statisticians, data scientists, operations research analysts, or lecturers. Entry-level salaries can range from INR 3-6 LPA, growing significantly with experience. Opportunities exist in government research organizations, IT firms, and educational institutions, with potential for advanced certifications in data science, actuarial science, or financial modeling aligning with industry needs.
Student Success Practices
Foundation Stage
Build Strong Foundational Concepts- (Semester 1-2)
Dedicate significant time to thoroughly understand core subjects like Abstract Algebra, Real Analysis, and Complex Analysis. Actively participate in lectures, solve all assigned problems, and review advanced topics immediately after class. Form study groups to discuss complex theories and proofs.
Tools & Resources
NPTEL courses on foundational mathematics, Standard textbooks by Walter Rudin, Serge Lang, Online problem-solving platforms like Stack Exchange Mathematics, Peer study groups
Career Connection
A solid grasp of fundamentals is crucial for qualifying NET/GATE exams, essential for academic careers and research positions in India, and forms the basis for advanced analytical roles in industry.
Develop Rigorous Problem-Solving Skills- (Semester 1-2)
Beyond textbook problems, seek out challenging problems from previous year question papers and competitive mathematics exams, such as NBHM Ph.D. Scholarship Test questions. Focus on understanding the underlying principles and various approaches to a problem, not just memorizing solutions.
Tools & Resources
Previous year question papers, Reference books on problem-solving in mathematics, Online forums dedicated to mathematical puzzles, Faculty consultation
Career Connection
Enhances critical thinking and analytical capabilities, highly valued in research, data science, and quantitative finance roles, significantly improving employability in analytical positions across Indian companies.
Engage in Early Academic Exploration- (Semester 1-2)
Actively attend departmental seminars and workshops on diverse mathematical topics. Reach out to professors to discuss their research interests and explore potential for small research projects or guided reading assignments. This helps in identifying areas of specialization for later semesters and future academic pursuits.
Tools & Resources
University department website for seminar schedules, Faculty profiles, Academic journals accessible through university library, Networking with senior students and alumni
Career Connection
Early exposure to research helps in identifying suitable areas for specialization and future Ph.D. studies, and develops a research-oriented mindset beneficial for R&D roles in India''''s academic and industrial sectors.
Intermediate Stage
Advanced Stage
Program Structure and Curriculum
Eligibility:
- B.A./B.Sc. with Honours in Mathematics or B.A./B.Sc. with Mathematics as one of the subjects with at least 50% marks in aggregate or equivalent grade points.
Duration: 4 semesters / 2 years
Credits: 90 Credits
Assessment: Internal: 30%, External: 70%
Semester-wise Curriculum Table
Semester 1
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| MTH 401C | Advanced Abstract Algebra I | Core | 4 | Permutation groups, Sylow''''s Theorems, Solvable and Nilpotent groups, Field extensions, Splitting fields |
| MTH 402C | Real Analysis I | Core | 4 | Riemann-Stieltjes integral, Functions of Bounded Variation, Improper integrals, Uniform convergence, Weierstrass Approximation Theorem |
| MTH 403C | Ordinary Differential Equations | Core | 4 | Linear equations, Series solutions, Legendre and Bessel functions, Picard''''s method, Existence and uniqueness theorems |
| MTH 404C | Complex Analysis I | Core | 4 | Complex numbers, Analytic functions, Cauchy-Riemann equations, Contour integration, Cauchy''''s integral formula, Power series |
| MTH 405C | Classical Mechanics | Core | 4 | Constraints, D''''Alembert''''s Principle, Lagrange''''s equations, Hamilton''''s Principle, Central force problem, Hamilton-Jacobi theory |
Semester 2
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| MTH 406C | Advanced Abstract Algebra II | Core | 4 | Galois theory, Solvability by radicals, Modules, Noetherian and Artinian modules, Tensor products |
| MTH 407C | Real Analysis II | Core | 4 | Functions of several variables, Inverse function theorem, Implicit function theorem, Riemann integration in Rn, Lebesgue measure, Measurable functions |
| MTH 408C | Partial Differential Equations | Core | 4 | First order PDEs, Charpit''''s method, Second order PDEs classification, Wave, Heat, Laplace equations, Green''''s functions |
| MTH 409C | Complex Analysis II | Core | 4 | Residue theorem, Rouche''''s Theorem, Open Mapping Theorem, Maximum Modulus Principle, Conformal mappings, Schwarz-Christoffel transformation |
| MTH 410C | Operations Research | Core | 4 | Linear Programming, Simplex method, Duality theory, Transportation problem, Assignment problem, Game theory, Queueing theory |
Semester 3
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| MTH 501C | Functional Analysis | Core | 4 | Normed linear spaces, Banach spaces, Hahn-Banach Theorem, Open Mapping Theorem, Hilbert spaces, Orthonormal bases |
| MTH 502C | Differential Geometry | Core | 4 | Curves in R3, Serret-Frenet formulae, Surfaces, First and second fundamental forms, Gaussian curvature, Geodesics |
| MTH 503C | Number Theory | Core | 4 | Divisibility, Congruences, Euler''''s totient function, Quadratic residues, Primitive roots, Diophantine equations |
| MTH 504C | Topology | Core | 4 | Topological spaces, Open and closed sets, Continuous functions, Connectedness, Compactness, Product and Quotient topology |
| MTH 505E | Advanced Discrete Mathematics | Elective | 4 | Lattices, Boolean algebra, Graph theory, Trees and Planar graphs, Generating functions, Recurrence relations |
| MTH 506E | Mathematical Modeling | Elective | 4 | Types of models, Dimensional analysis, Compartmental models, Population dynamics, Epidemic models, Optimization models |
| MTH 507E | Financial Mathematics | Elective | 4 | Interest rates, Present and future value, Annuities, Bonds, Options pricing, Black-Scholes model, Portfolio theory |
| MTH 508E | Mathematical Methods | Elective | 4 | Fourier series and transforms, Laplace transforms, Green''''s functions, Integral equations, Calculus of variations |
| MTH 509P | Practical I (MATLAB / Mathematica / Python) | Practical | 2 | Basic commands, Data visualization, Numerical methods, Symbolic computation, Programming for mathematical tasks |
Semester 4
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| MTH 510C | Fluid Dynamics | Core | 4 | Equation of continuity, Euler''''s and Bernoulli''''s equation, Stream function, Viscous flows, Navier-Stokes equations, Boundary layer theory |
| MTH 511C | Abstract Measure Theory | Core | 4 | Measure spaces, Outer and Lebesgue measure, Measurable functions, Integrability, Product measures, Fubini''''s Theorem |
| MTH 512C | Advanced Graph Theory | Core | 4 | Connectivity, Matchings, Network flows, Coloring problems, Hamiltonian cycles, Eulerian circuits, Digraphs |
| MTH 513E | Advanced Functional Analysis | Elective | 4 | Spectral theory, Compact operators, Self-adjoint operators, Unbounded operators, Banach algebras |
| MTH 514E | Cryptography | Elective | 4 | Classical ciphers, Symmetric and Asymmetric key cryptography, RSA algorithm, Elliptic curve cryptography, Hash functions |
| MTH 515E | Fuzzy Set Theory | Elective | 4 | Fuzzy sets, Membership functions, Fuzzy operations, Fuzzy relations, Fuzzy logic, Fuzzy inference systems, Applications of fuzzy sets |
| MTH 516E | Wavelet Analysis | Elective | 4 | Fourier transform review, Continuous and Discrete wavelet transform, Multiresolution analysis, Daubechies wavelets, Wavelet applications |
| MTH 517E | Biomathematics | Elective | 4 | Population dynamics, Logistic growth, Predator-prey models, Epidemic models, Enzyme kinetics, Mathematical ecology |
| MTH 518E | Stochastic Processes | Elective | 4 | Random variables, Markov chains, Poisson processes, Birth-death processes, Brownian motion, Martingales |
| MTH 519E | Computational Fluid Dynamics | Elective | 4 | Finite difference method, Finite volume method, Grid generation, Navier-Stokes equations discretization, Turbulence modeling |
| MTH 520P | Project | Project | 6 | Problem identification, Literature review, Methodology design, Data analysis and interpretation, Report writing and presentation, Original research contribution |
| MTH 521V | Viva-Voce | Viva | 2 | Comprehensive assessment of mathematical knowledge, Understanding of project work, Communication and presentation skills, Clarity of concepts |
