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MA-MASTER-OF-ARTS in Mathematics at Dibrugarh University
Dibrugarh, Assam
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About the Specialization
What is Mathematics at Dibrugarh University Dibrugarh?
This MA (Master of Arts) in Mathematics program at Dibrugarh University, Dibrugarh, Assam, focuses on providing a strong foundation in both pure and applied mathematics. It covers advanced topics essential for research, academia, and various analytical roles in the Indian industry. The program emphasizes rigorous analytical thinking and problem-solving, making graduates highly sought after in sectors requiring data analysis, modeling, and quantitative skills.
Who Should Apply?
This program is ideal for Bachelor of Arts or Science graduates with a Major in Mathematics who possess a strong aptitude for abstract reasoning and a passion for deep mathematical inquiry. It caters to fresh graduates aspiring for higher studies or a career in research and development, and also to educators seeking to enhance their qualifications. Individuals looking to transition into data science, finance, or IT sectors requiring robust quantitative skills will also find this program beneficial.
Why Choose This Course?
Graduates of this program can expect diverse career paths in India, including roles as mathematicians, statisticians, data scientists, quantitative analysts, research associates, and educators. Entry-level salaries can range from INR 4-6 LPA, growing significantly with experience to INR 8-15 LPA in analytical and research roles. The program provides a solid foundation for NET/SET examinations, PhD studies, and competitive examinations for government and public sector undertakings.
Student Success Practices
Foundation Stage
Master Core Concepts and Problem Solving- (Semester 1-2)
Dedicate significant time to understanding fundamental theorems and proofs in Abstract Algebra, Real Analysis, and Complex Analysis. Practice solving a wide variety of problems from textbooks and previous year question papers rigorously. Engage in group study sessions to discuss challenging concepts and different problem-solving approaches.
Tools & Resources
Standard textbooks (e.g., Dummit & Foote for Algebra, Rudin for Analysis), NPTEL lectures, Online problem-solving forums like StackExchange, Peer study groups
Career Connection
A strong conceptual foundation is crucial for competitive exams (NET/SET) and for building advanced skills required in quantitative roles and research.
Develop Mathematical Software Proficiency- (Semester 1-2)
Begin familiarizing yourself with mathematical software relevant to topics like ODEs and Numerical Analysis. Tools like MATLAB, Octave, or Python with libraries such as NumPy and SciPy can significantly aid in visualizing concepts and solving computational problems. Start with basic exercises and gradually apply them to course assignments.
Tools & Resources
MATLAB Academic License (if available), GNU Octave (free), Anaconda Distribution for Python (with NumPy, SciPy, Matplotlib), Online tutorials
Career Connection
Proficiency in computational tools is highly valued in data science, scientific computing, and research roles across various Indian industries.
Engage in Departmental Seminars and Workshops- (Semester 1-2)
Actively participate in seminars, colloquia, and workshops organized by the Department of Mathematics. These events expose students to current research trends, specialized topics, and networking opportunities with faculty and guest speakers, fostering a broader understanding beyond the curriculum.
Tools & Resources
University notice boards, Department website, Faculty announcements
Career Connection
Builds intellectual curiosity, provides insights into potential research areas, and helps in identifying areas of specialization for future career paths in academia or R&D.
Intermediate Stage
Strategic Elective Selection and Deep Dive- (Semester 3)
Carefully choose elective courses (e.g., Measure Theory, Operations Research, Discrete Mathematics) based on your career interests, whether it''''s pure research, data science, or finance. Once chosen, dive deep into these subjects by reading advanced texts, exploring related research papers, and attempting complex problems beyond the syllabus.
Tools & Resources
University''''s elective course descriptions, Faculty advisors, Research journals (e.g., JSTOR, Springer), Specific advanced textbooks for chosen electives
Career Connection
Specialization through electives makes you more competitive for specific roles in the Indian job market, demonstrating focused expertise.
Pursue Research Internships/Projects- (Semester 3 & inter-semester breaks)
Look for opportunities to undertake short-term research internships during semester breaks or engage in faculty-guided projects. This practical exposure to research methodology, problem formulation, and data analysis is invaluable. Institutions like IITs, IISc, TIFR, or even internal departmental projects are good options.
Tools & Resources
Institute''''s research portal, Faculty contacts, National research internship programs (e.g., SERB-SURE), Various university summer research programs
Career Connection
Builds a strong research profile for higher studies (PhD) and quantitative research roles, enhancing critical thinking and independent problem-solving skills.
Prepare for National Level Examinations- (Semester 3-4)
Begin dedicated preparation for national-level examinations like CSIR NET, GATE (Mathematics), and SET, which are crucial for lectureship positions and PhD admissions in India. This involves solving previous year papers, joining coaching, or forming dedicated study groups.
Tools & Resources
Previous year question papers, Official exam websites, Coaching institutes (online/offline), Dedicated study materials
Career Connection
Success in these exams directly opens doors to academic careers, research fellowships, and faculty positions in Indian universities and colleges.
Advanced Stage
Excel in Project/Dissertation Work- (Semester 4)
Treat your Semester IV project as a capstone experience. Choose a topic aligned with your career aspirations, engage deeply with your supervisor, and aim for original contributions or a comprehensive review. Focus on clarity in problem statement, methodology, results, and presentation.
Tools & Resources
University library resources, Research databases, Academic writing guides, Continuous feedback from project supervisor
Career Connection
A well-executed project demonstrates independent research capability, analytical rigor, and communication skills, highly attractive to employers and PhD committees.
Network and Attend Conferences/Workshops- (Semester 4)
Expand your professional network by actively attending national or regional mathematics conferences, symposiums, or workshops. Presenting your project work (if applicable) or simply engaging with researchers and faculty from other institutions can lead to future collaborations and opportunities.
Tools & Resources
Professional mathematical societies in India (e.g., Indian Mathematical Society), University funding for conference travel, Academic event listings
Career Connection
Essential for career progression in academia and research, opening doors to post-doctoral positions, joint projects, and broader recognition within the mathematical community.
Develop Interview and Presentation Skills- (Semester 4)
Focus on honing your communication and presentation skills, which are vital for academic interviews, job placements, and public speaking. Participate in mock interviews, practice presenting your project work concisely, and articulate your mathematical understanding clearly to diverse audiences.
Tools & Resources
Career counseling cells, University placement services, Peer feedback, Online public speaking courses, Mock interview sessions with faculty
Career Connection
Strong communication skills are universally valued, ensuring you can effectively convey your expertise during job interviews, research presentations, or teaching assignments.
Program Structure and Curriculum
Eligibility:
- A Bachelor degree with Major in Mathematics from Dibrugarh University or any other recognized university/institution with at least 45% marks in Major or equivalent Grade Point. Candidates having B.A./B.Sc. without Major in Mathematics must have at least 50% marks in Mathematics and 45% marks in aggregate or equivalent Grade Point.
Duration: 4 semesters
Credits: 80 Credits
Assessment: Internal: 30%, External: 70%
Semester-wise Curriculum Table
Semester 1
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| MMA C 101 | Abstract Algebra | Core | 5 | Groups, Normal subgroups, Isomorphism theorems, Rings, Integral domains, Fields, Polynomial rings, Unique factorization domains, Module theory basics, Group actions |
| MMA C 102 | Real Analysis | Core | 5 | Metric spaces, Completeness, Compactness, Connectedness, Sequences and series of functions, Uniform convergence, Riemann-Stieltjes Integral, Functions of several variables, Inverse and Implicit function theorems, Measure theory introduction |
| MMA C 103 | Complex Analysis | Core | 5 | Complex plane, Analytic functions, Cauchy-Riemann equations, Complex integration, Cauchy''''s Integral Formula, Liouville''''s Theorem, Maximum Modulus Principle, Taylor and Laurent Series, Singularities, Residue Theorem, Argument Principle |
| MMA C 104 | Ordinary Differential Equations | Core | 5 | First order ODEs, Exact equations, Integrating factors, Second order linear ODEs, Wronskian, Variation of parameters, Series solutions, Legendre and Bessel functions, Boundary value problems, Sturm-Liouville theory, Laplace Transforms applications |
Semester 2
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| MMA C 201 | Advanced Abstract Algebra | Core | 5 | Vector spaces, Linear transformations, Dual spaces, Eigenvalues, Canonical forms (Jordan, Rational), Bilinear forms, Quadratic forms, Module over principal ideal domain, Field extensions, Galois theory |
| MMA C 202 | Topology | Core | 5 | Topological spaces, Open and closed sets, Bases, Continuous functions, Homeomorphisms, Connectedness, Path-connectedness, Compactness, Local compactness, Product topology, Quotient topology |
| MMA C 203 | Partial Differential Equations | Core | 5 | Formation of PDEs, First order linear and quasi-linear PDEs, Charpit''''s method, Jacobi''''s method, Classification of second order PDEs, Canonical forms, Wave equation, Heat equation, Laplace equation, Separation of variables, Boundary value problems |
| MMA C 204 | Fluid Dynamics | Core | 5 | Kinematics of fluids, Lagrangian and Eulerian descriptions, Equation of continuity, Equations of motion of a fluid, Bernoulli''''s equation, Vortex motion, Two-dimensional irrotational motion, Complex potential, Viscous incompressible flow, Navier-Stokes equations |
Semester 3
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| MMA C 301 | Functional Analysis | Core | 5 | Normed linear spaces, Banach spaces, Hahn-Banach Theorem, Bounded linear operators, Open Mapping Theorem, Closed Graph Theorem, Hilbert spaces, Orthonormal bases, Riesz Representation Theorem, Spectral Theory in Normed Spaces, Compact operators |
| MMA C 302 | Numerical Analysis | Core | 5 | Error analysis, Floating point arithmetic, Solutions of algebraic and transcendental equations (Bisection, Newton-Raphson), Interpolation (Lagrange, Newton, Hermite), Numerical differentiation and integration (Trapezoidal, Simpson''''s, Gauss), Numerical solutions of ODEs (Euler, Runge-Kutta) |
| MMA E 301 | Measure Theory and Integration | Elective | 5 | Lebesgue Outer Measure, Measurable sets, Non-measurable sets, Measurable functions, Littlewood''''s Three Principles, Lebesgue Integral, Monotone Convergence Theorem, Dominated Convergence Theorem, Fatou''''s Lemma, Lp spaces, Riesz-Fischer Theorem |
| MMA E 302 | Advanced Complex Analysis | Elective | 5 | Entire functions, Weierstrass product theorem, Meromorphic functions, Mittag-Leffler''''s theorem, Elliptic functions, Weierstrass''''s and Jacobi''''s elliptic functions, Conformal mapping, Riemann mapping theorem, Analytic continuation |
| MMA E 303 | Operations Research | Elective | 5 | Linear programming problem, Simplex method, Duality theory, Dual Simplex Method, Transportation problem, Assignment problem, Network analysis (CPM/PERT), Queuing theory basics |
| MMA E 304 | Discrete Mathematics | Elective | 5 | Mathematical Logic, Propositional and Predicate Logic, Set theory, Relations, Functions, Pigeonhole Principle, Graph Theory (Paths, Cycles, Connectivity, Planar Graphs), Trees, Spanning Trees, Minimum Spanning Trees, Combinatorics, Recurrence Relations, Generating Functions |
Semester 4
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| MMA C 401 | Advanced Topology | Core | 5 | Countability axioms, Separation axioms (T0 to T4), Urysohn''''s Lemma, Tietze Extension Theorem, Nets and Filters, Compactification (Stone-Cech), Product spaces, Metrization theorems, Introduction to Homotopy and Fundamental Group |
| MMA P 401 | Project/Dissertation | Project | 5 | Research methodology, Problem identification and formulation, Literature review and survey, Mathematical modeling and analysis, Results, Discussion and Conclusion, Dissertation writing and Oral presentation |
| MMA E 401 | Advanced Functional Analysis | Elective | 5 | Banach Algebras, Gelfand-Mazur Theorem, Spectral theory for compact operators, Unbounded operators, Closed operators, C*-algebras and Von Neumann Algebras, Quantum Mechanics formalisms |
| MMA E 402 | Advanced Numerical Analysis | Elective | 5 | Numerical solutions of PDEs (Finite Difference Method, Finite Element Method), Finite volume method, Approximation Theory, Chebyshev approximation, Spline functions, B-splines, Numerical solutions for integral equations |
| MMA E 403 | Optimization Techniques | Elective | 5 | Nonlinear Programming, Kuhn-Tucker conditions, Quadratic Programming, Convex Programming, Dynamic Programming, Bellman''''s principle of optimality, Integer Programming, Branch and Bound method, Metaheuristics (Genetic Algorithms, Simulated Annealing) |
| MMA E 404 | Cryptography | Elective | 5 | Basic Number Theory (Primality, Modular Arithmetic), Symmetric-key Cryptography (DES, AES), Asymmetric-key Cryptography (RSA, ElGamal), Hash functions, Message Authentication Codes (MACs), Digital Signatures, Key exchange (Diffie-Hellman) |
| MMA E 405 | Relativity and Cosmology | Elective | 5 | Special Theory of Relativity, Lorentz Transformations, Four-vectors, Energy-momentum tensor, General Theory of Relativity, Equivalence Principle, Schwarzschild solution, Black holes, Friedmann-Robertson-Walker metric, Big Bang Cosmology |
