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M-SC-MASTER-OF-SCIENCE in Mathematics at Dibrugarh University
Dibrugarh, Assam
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About the Specialization
What is Mathematics at Dibrugarh University Dibrugarh?
This M.Sc Mathematics program at Dibrugarh University focuses on building a robust theoretical foundation combined with practical application skills. It emphasizes core mathematical disciplines such as algebra, analysis, and differential equations, while also introducing areas like computational mathematics and financial mathematics. The program is designed to meet the growing demand for analytical professionals in India''''s technology, finance, and research sectors, offering a balanced curriculum for comprehensive skill development.
Who Should Apply?
This program is ideal for Bachelor of Science or Arts graduates with a strong foundation in Mathematics, seeking to deepen their understanding of advanced mathematical concepts. It caters to individuals aspiring for careers in academia, research, data science, financial analytics, or computational fields. Students with a keen interest in problem-solving and abstract reasoning, aiming for a career in diverse Indian industries, will find this program highly beneficial.
Why Choose This Course?
Graduates of this program can expect diverse career paths in India, including roles as mathematicians, data scientists, quantitative analysts, research associates, and educators. Entry-level salaries typically range from INR 4-7 LPA, with experienced professionals earning INR 10-20+ LPA depending on sector and expertise. The program prepares students for NET/SET examinations, PhD pursuits, and specialized roles in growing sectors like FinTech and AI in leading Indian and multinational companies.
Student Success Practices
Foundation Stage
Master Core Concepts and Problem-Solving- (Semester 1-2)
Dedicate significant time to understanding the foundational theories in Abstract Algebra, Real Analysis, and Linear Algebra. Actively solve a wide range of problems from textbooks and previous year question papers. Collaborate with peers to discuss challenging concepts and different approaches to solutions.
Tools & Resources
Standard Textbooks (e.g., Dummit & Foote for Algebra, Rudin for Analysis), NPTEL courses for conceptual clarity, Peer study groups, University library resources
Career Connection
A strong grasp of fundamentals is crucial for higher studies, competitive exams (NET/SET), and analytical roles requiring deep mathematical reasoning.
Develop Computational Skills with C and MATLAB/Python- (Semester 1-2)
Actively participate in the computer programming labs. Beyond assignments, practice coding mathematical algorithms in C and then transition to MATLAB/Python for numerical methods and data visualization. Develop small projects demonstrating mathematical concepts using code.
Tools & Resources
Online coding platforms (HackerRank, LeetCode for C), MATLAB/Python documentation and tutorials, Coursera/edX courses on scientific computing, GitHub for project hosting
Career Connection
Proficiency in computational tools is highly valued in data science, quantitative finance, and scientific research roles in India, complementing theoretical knowledge.
Engage in Academic Discussions and Seminars- (Semester 1-2)
Actively participate in departmental seminars, workshops, and classroom discussions. Present short topics to peers to enhance communication skills and deepen understanding. Seek feedback from professors and peers to refine your presentation and analytical abilities.
Tools & Resources
Departmental seminar series, Academic journals (e.g., J. Indian Math. Soc.), Presentation software (PowerPoint, LaTeX Beamer)
Career Connection
Strong communication and critical thinking are essential for academic roles, research positions, and effectively conveying complex ideas in any professional setting.
Intermediate Stage
Explore Electives for Specialization & Industry Relevance- (Semester 3)
Carefully choose elective subjects like Differential Geometry, Fuzzy Set Theory, Mathematical Modelling, or Applied Statistics based on your interest and career aspirations. Dive deep into these areas by reading advanced texts and exploring their real-world applications.
Tools & Resources
Specialized textbooks for chosen electives, Research papers (Google Scholar, MathSciNet), Online forums and communities related to the elective topics
Career Connection
Electives provide specialized knowledge, opening doors to niche roles in areas like actuarial science, data analytics, or computational geometry within Indian companies.
Undertake Mini-Projects or Research Internships- (Semester 3)
Seek opportunities for mini-projects with faculty members or explore short-term internships, if available, at local research labs, analytics firms, or educational institutions during semester breaks. Focus on applying theoretical knowledge to solve practical problems.
Tools & Resources
Departmental notice boards for research opportunities, University career services, Networking with alumni on LinkedIn
Career Connection
Practical experience enhances your resume, builds a professional network, and provides insights into industry expectations, crucial for placements in India.
Prepare for National Level Exams (NET/SET)- (Semester 3)
Start dedicated preparation for national-level eligibility tests like UGC NET or state-level SET examinations. Regularly solve previous year question papers and take mock tests. Join coaching or online groups for structured study if needed.
Tools & Resources
UGC NET/SET syllabus and past papers, Online test series platforms, Specialized coaching institutes (online/offline)
Career Connection
Clearing NET/SET is mandatory for lectureship positions in Indian universities and colleges, and for Junior Research Fellowship (JRF) leading to PhD opportunities.
Advanced Stage
Undertake a Comprehensive Research Project/Dissertation- (Semester 4)
For your final semester project, choose a topic that aligns with your career goals and involves significant research or application. Focus on a clear problem statement, methodology, analysis, and present your findings effectively in a dissertation.
Tools & Resources
Access to academic databases (JSTOR, Scopus), Statistical software (R, Python libraries), LaTeX for professional document formatting
Career Connection
A strong project demonstrates research capabilities and specialized knowledge, enhancing your profile for advanced research roles or competitive industry positions.
Focus on Placement Preparation and Interview Skills- (Semester 4)
Actively attend campus recruitment drives and workshops. Practice quantitative aptitude, logical reasoning, and communication skills. Prepare for technical interviews by reviewing core mathematical concepts and practicing problem-solving under time pressure.
Tools & Resources
University placement cell services, Online aptitude test platforms, Mock interview sessions, Industry-specific interview guides
Career Connection
Effective preparation is key to securing placements in leading Indian companies in sectors like finance, analytics, IT, and education.
Network and Seek Mentorship- (Semester 4)
Connect with alumni, faculty, and industry professionals through university events, conferences, and platforms like LinkedIn. Seek their advice on career paths, skill development, and job opportunities. A strong network can open doors to internships and jobs.
Tools & Resources
LinkedIn profiles of alumni, Professional mathematical societies (e.g., IMS), University alumni network events
Career Connection
Networking is invaluable for career guidance, discovering hidden job markets, and gaining insights into industry trends in the competitive Indian job landscape.
Program Structure and Curriculum
Eligibility:
- B.A./B.Sc. with Mathematics as a major/honours subject or with 300 marks in Mathematics, from Dibrugarh University or any other recognized University. Minimum 45% marks in Mathematics.
Duration: 4 semesters / 2 years
Credits: 96 Credits
Assessment: Internal: 40%, External: 60%
Semester-wise Curriculum Table
Semester 1
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| MMA 101 | Abstract Algebra | Core | 4 | Groups and Subgroups, Normal Subgroups and Quotient Groups, Rings, Integral Domains, Fields, Polynomial Rings, Isomorphism Theorems |
| MMA 102 | Real Analysis | Core | 4 | Metric Spaces, Completeness and Compactness, Connectedness, Sequences and Series of Functions, Riemann-Stieltjes Integral |
| MMA 103 | Complex Analysis | Core | 4 | Complex Numbers and Functions, Analytic Functions and Cauchy-Riemann Equations, Complex Integration and Cauchy''''s Theorem, Singularities and Residues, Conformal Mappings |
| MMA 104 | Linear Algebra | Core | 4 | Vector Spaces and Subspaces, Linear Transformations, Eigenvalues and Eigenvectors, Inner Product Spaces, Diagonalization and Canonical Forms |
| MMA 105 | Differential Equations | Core | 4 | First and Second Order Linear Equations, Series Solutions, Existence and Uniqueness of Solutions, Sturm-Liouville Problems, Partial Differential Equations Introduction |
| MMA 106 | Computer Programming (C) | Core | 4 | C Language Fundamentals, Data Types, Operators, Expressions, Control Structures, Functions and Arrays, Pointers and Structures |
Semester 2
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| MMA 201 | Field Theory | Core | 4 | Field Extensions, Algebraic Extensions, Finite Fields, Galois Theory, Solvability by Radicals |
| MMA 202 | Topology | Core | 4 | Topological Spaces, Continuous Functions, Product and Quotient Spaces, Connectedness, Compactness |
| MMA 203 | Measure Theory | Core | 4 | Lebesgue Measure, Measurable Functions, Lebesgue Integration, Convergence Theorems, Product Measures |
| MMA 204 | Fluid Dynamics | Core | 4 | Kinematics of Fluid Flow, Equations of Motion, Bernoulli''''s Equation, Potential Flow, Boundary Layer Theory |
| MMA 205 | Classical Mechanics | Core | 4 | Lagrangian Mechanics, Hamiltonian Mechanics, Canonical Transformations, Hamilton-Jacobi Theory, Rigid Body Dynamics |
| MMA 206 | Computer Programming in MATLAB/Python | Core | 4 | MATLAB/Python Environment, Numerical Methods Implementation, Plotting and Visualization, Symbolic Computation, Data Handling |
Semester 3
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| MMA 301 | Functional Analysis | Core | 4 | Normed Linear Spaces and Banach Spaces, Hilbert Spaces, Bounded Linear Operators, Hahn-Banach Theorem, Open Mapping and Closed Graph Theorems |
| MMA 302 | Number Theory | Core | 4 | Divisibility and Congruences, Prime Numbers and Factorization, Quadratic Residues, Diophantine Equations, Arithmetic Functions |
| MMA 303 | Operations Research | Core | 4 | Linear Programming and Simplex Method, Duality Theory, Transportation and Assignment Problems, Queuing Theory, Game Theory |
| MMA 304(E)-I | Differential Geometry | Elective | 4 | Curves in Space, Surfaces, First and Second Fundamental Forms, Gaussian and Mean Curvature, Geodesics |
| MMA 304(E)-II | Fuzzy Set Theory | Elective | 4 | Fuzzy Sets and Operations, Fuzzy Relations, Fuzzy Numbers, Fuzzy Logic, Fuzzy Control Systems |
| MMA 305(E)-I | Mathematical Modelling | Elective | 4 | Principles of Mathematical Modelling, Modelling with Difference Equations, Modelling with Differential Equations, Population Dynamics Models, Compartment Models |
| MMA 305(E)-II | Applied Statistics | Elective | 4 | Probability Distributions, Sampling Theory, Hypothesis Testing, Analysis of Variance (ANOVA), Correlation and Regression Analysis |
| MMA 306 | Seminar | Core | 4 | Research Topic Selection, Literature Review, Presentation Skills, Technical Writing, Critical Analysis |
Semester 4
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| MMA 401 | Partial Differential Equations | Core | 4 | First Order Linear and Quasi-linear PDEs, Classification of Second Order PDEs, Wave Equation, Heat Equation, Laplace Equation |
| MMA 402 | Numerical Analysis | Core | 4 | Solutions of Non-linear Equations, Interpolation and Approximation, Numerical Differentiation and Integration, Numerical Solutions of ODEs, Numerical Solutions of PDEs |
| MMA 403 | Financial Mathematics | Core | 4 | Interest Rates and Annuities, Bonds and Derivatives, Options Pricing Models, Black-Scholes Model, Stochastic Calculus in Finance |
| MMA 404(E)-I | Advanced Abstract Algebra | Elective | 4 | Modules and Vector Spaces, Exact Sequences, Tensor Products, Homological Algebra, Commutative Algebra Basics |
| MMA 404(E)-II | Wavelets and Applications | Elective | 4 | Fourier Transform, Windowed Fourier Transform, Continuous Wavelet Transform, Discrete Wavelet Transform, Applications in Signal Processing |
| MMA 405(E)-I | Stochastic Processes | Elective | 4 | Random Walks, Markov Chains, Poisson Processes, Brownian Motion, Queuing Models |
| MMA 405(E)-II | Cryptography | Elective | 4 | Classical Ciphers, Number Theory for Cryptography, RSA Algorithm, Elliptic Curve Cryptography, Hash Functions |
| MMA 406 | Project/Dissertation | Core | 4 | Research Methodology, Problem Formulation, Data Analysis and Interpretation, Scientific Report Writing, Presentation of Findings |
