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PHD in Mathematics at Malaviya National Institute of Technology Jaipur
Jaipur, Rajasthan
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About the Specialization
What is Mathematics at Malaviya National Institute of Technology Jaipur Jaipur?
This PhD in Mathematics program at Malaviya National Institute of Technology Jaipur focuses on advanced research in diverse mathematical areas, including pure and applied mathematics, statistics, and computational techniques. It caters to the growing demand for highly skilled researchers and academicians who can contribute to scientific advancements and solve complex problems across various Indian industries, from IT and finance to engineering and defense.
Who Should Apply?
This program is ideal for candidates holding a Master''''s degree in Mathematics or a related field, as well as exceptional B.Tech/B.E graduates with a strong mathematical aptitude. It targets aspiring researchers, university lecturers, and scientists seeking to contribute original knowledge. Working professionals in R&D or analytics who wish to deepen their theoretical foundations and pursue advanced problem-solving can also benefit.
Why Choose This Course?
Graduates of this program can expect to pursue esteemed careers as faculty in IITs/NITs/universities, research scientists in DRDO/ISRO, data scientists in leading IT firms, or quantitative analysts in financial institutions in India. Entry-level salaries range from INR 7-15 LPA, with experienced professionals earning significantly more. The program fosters critical thinking and advanced analytical skills, essential for high-impact roles.
Student Success Practices
Foundation Stage
Master Core Mathematical Foundations- (undefined)
Dedicate initial semesters to thoroughly grasp advanced concepts in core areas like analysis, algebra, and topology. Engage with recommended textbooks and research papers. This strong foundation is crucial for identifying novel research problems and excelling in comprehensive exams.
Tools & Resources
NPTEL courses, Standard graduate textbooks, Departmental seminars
Career Connection
A solid theoretical base enables students to identify niche research areas and develop the analytical rigor required for impactful publications and strong thesis defense.
Proactively Engage with Faculty and Research Groups- (undefined)
Attend departmental research presentations, actively participate in discussions, and seek out faculty members whose research aligns with your interests. Early engagement helps in identifying a research supervisor and project, setting the trajectory for your PhD journey.
Tools & Resources
Departmental research colloquia, Faculty profiles on MNIT website, Research group meetings
Career Connection
Building strong mentor relationships and networking within research groups can lead to collaborative projects, publications, and future academic/industry recommendations.
Develop Advanced Problem-Solving Skills- (undefined)
Regularly solve complex problems from coursework and advanced texts. Participate in problem-solving sessions and mathematical competitions. This sharpens analytical abilities and prepares you for the rigor of independent research and theoretical contributions.
Tools & Resources
Graduate-level problem books, Online platforms like Project Euler for mathematical challenges, Peer study groups
Career Connection
Enhanced problem-solving skills are directly transferable to research, data analytics roles, and competitive exams for government research positions.
Intermediate Stage
Deep Dive into Specialization and Literature Review- (undefined)
Once coursework is complete, focus intensely on your chosen research area. Conduct an exhaustive literature review, understanding current trends, open problems, and methodologies. This stage is critical for formulating your research proposal and identifying your unique contribution.
Tools & Resources
JSTOR, MathSciNet, arXiv.org, Google Scholar, EndNote/Zotero for reference management
Career Connection
A thorough understanding of your specialization positions you as an expert, making you attractive to research institutions and R&D divisions in India and globally.
Attend and Present at National/International Conferences- (undefined)
Actively seek opportunities to present your preliminary research findings at relevant conferences and workshops within India and abroad. This helps in gaining feedback, networking with peers, and staying abreast of the latest research. Many Indian institutions offer travel grants.
Tools & Resources
Departmental travel grants, Conference websites (e.g., those organized by Indian Mathematical Society), Professional networking platforms
Career Connection
Conference participation boosts your academic profile, leads to potential collaborations, and enhances visibility for post-doctoral positions or academic roles.
Publish Early and Strategically- (undefined)
Aim to publish initial research findings in peer-reviewed journals. Start with national journals and gradually target international journals. Early publications demonstrate research productivity and are crucial for academic career progression in India.
Tools & Resources
Scopus, Web of Science, JournalFinder tools, Mendeley for collaborative writing
Career Connection
High-quality publications are a primary metric for academic recruitment (Assistant Professor roles) and research grants in India, establishing your credibility as a researcher.
Advanced Stage
Focus on Thesis Writing and Defense Preparation- (undefined)
Systematically structure and write your doctoral thesis, ensuring clarity, coherence, and originality. Regularly discuss progress with your supervisor and incorporate feedback. Prepare rigorously for your pre-submission and final thesis defense.
Tools & Resources
LaTeX for typesetting, Grammarly/Turnitin for proofreading, Mock defense presentations
Career Connection
A well-written and defended thesis is the cornerstone of your PhD, opening doors to academic positions, research fellowships, and expert roles in R&D.
Develop Teaching and Mentoring Skills- (undefined)
Utilize opportunities to assist in teaching undergraduate or master''''s courses, conduct tutorials, and mentor junior students. These experiences are vital for aspiring academicians in India to build their pedagogical profile and communication skills.
Tools & Resources
Departmental teaching assistantships, Teaching workshops, Feedback from students/faculty
Career Connection
Strong teaching experience significantly enhances your application for faculty positions in Indian universities and colleges, demonstrating readiness for academic responsibilities.
Plan Post-PhD Career Paths and Network Actively- (undefined)
Explore various post-PhD options, including post-doctoral fellowships, faculty positions, or industry research roles. Network with senior academics, industry experts, and alumni. Attend career fairs and workshops tailored for PhD graduates in India.
Tools & Resources
LinkedIn, Professional mathematical societies (e.g., IMS, Ramanujan Mathematical Society), University career services
Career Connection
Proactive career planning and networking ensure a smooth transition from PhD to a successful professional career, whether in academia, government research, or specialized industry roles.
Program Structure and Curriculum
Eligibility:
- Master''''s Degree in Science (Mathematics) or equivalent with 6.5 CGPA or 60% marks. OR Bachelor''''s Degree in Engineering/Technology/Architecture/Planning with 8.0 CGPA or 75% marks AND Master''''s Degree by Research with 6.5 CGPA or 60% marks. OR Bachelor''''s Degree in Engineering/Technology/Architecture/Planning with 8.0 CGPA or 75% marks. Valid GATE/NET/CSIR-JRF/INSPIRE fellowship etc. often required for institute fellowship.
Duration: Minimum 3 years (Full-Time), Minimum 4 years (Part-Time) for PhD. Maximum 6 years (Full-Time), Maximum 7 years (Part-Time).
Credits: Minimum 8 credits (for M.Tech/M.E/M.Arch/M.Plan. or equivalent entrants) or Minimum 16 credits (for B.Tech/B.E/B.Arch/B.Plan. or equivalent entrants) for coursework. Credits
Assessment: Assessment pattern not specified
Semester-wise Curriculum Table
Semester 1
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| MAM 701A | ADVANCED DISCRETE MATHEMATICS | Elective (Coursework) | 3 | Advanced counting techniques, Graph theory (matching, coloring, planarity), Coding theory (linear codes, cyclic codes), Cryptography (public key, secret key), Boolean algebra |
| MAM 702A | ADVANCED OPTIMIZATION TECHNIQUES | Elective (Coursework) | 3 | Linear programming (duality, revised simplex), Non-linear programming (KKT conditions, quadratic programming), Dynamic programming, Geometric programming, Multi-objective optimization |
| MAM 703A | ADVANCED NUMERICAL ANALYSIS | Elective (Coursework) | 3 | Solution of ODEs (Runge-Kutta, multistep methods), Solution of PDEs (finite difference, finite element), Iterative methods for linear systems, Eigenvalue problems, Error analysis |
| MAM 704A | ADVANCED FUNCTIONAL ANALYSIS | Elective (Coursework) | 3 | Topological vector spaces, Hahn-Banach theorem, Open mapping theorem, Closed graph theorem, Spectral theory of operators |
| MAM 705A | ADVANCED TOPOLOGY | Elective (Coursework) | 3 | Compactness and connectedness, Separation axioms, Product and quotient spaces, Metrization theorems, Homotopy and fundamental group |
| MAM 706A | ADVANCED ALGEBRA | Elective (Coursework) | 3 | Group theory (Sylow theorems, solvable groups), Ring theory (Noetherian, Artinian rings), Field theory (Galois theory), Modules, Categories and functors |
| MAM 707A | ADVANCED NUMBER THEORY | Elective (Coursework) | 3 | Congruences, Quadratic residues, Diophantine equations, Algebraic number theory (number fields, integral bases), Analytic number theory (prime number theorem) |
| MAM 708A | ADVANCED COMPLEX ANALYSIS | Elective (Coursework) | 3 | Conformal mappings, Harmonic functions, Riemann surfaces, Elliptic functions, Entire functions |
| MAM 709A | THEORY OF FINITE ELEMENT METHODS | Elective (Coursework) | 3 | Variational formulations, Weighted residual methods, Shape functions, Isoparametric elements, Error estimation |
| MAM 710A | MATHEMATICAL MODELING | Elective (Coursework) | 3 | Principles of mathematical modeling, Dimensional analysis, Compartmental models, Difference and differential equations in modeling, Simulation techniques |
| MAM 711A | FUZZY MATHEMATICS AND ITS APPLICATIONS | Elective (Coursework) | 3 | Fuzzy sets and logic, Fuzzy relations, Fuzzy numbers, Fuzzy inference systems, Applications in control and decision making |
| MAM 712A | WAVELET ANALYSIS AND ITS APPLICATIONS | Elective (Coursework) | 3 | Fourier series, Continuous wavelet transform, Discrete wavelet transform, Multiresolution analysis, Applications in signal and image processing |
| MAM 713A | ADVANCED DIFFERENTIAL EQUATIONS | Elective (Coursework) | 3 | Existence and uniqueness of solutions, Stability theory, Boundary value problems, Green''''s functions, Perturbation methods |
| MAM 714A | ADVANCED OPERATIONS RESEARCH | Elective (Coursework) | 3 | Inventory models, Queuing theory, Network analysis (PERT/CPM), Game theory, Decision theory |
| MAM 715A | ADVANCED PROBABILITY AND STOCHASTIC PROCESSES | Elective (Coursework) | 3 | Measure theory, Random variables and distributions, Stochastic processes (Markov chains, Poisson process), Martingales, Ito''''s Lemma |
| MAM 716A | ADVANCED FLUID DYNAMICS | Elective (Coursework) | 3 | Navier-Stokes equations, Boundary layer theory, Compressible flow, Inviscid flow, Turbulence |
| MAM 717A | ADVANCED DIFFERENTIAL GEOMETRY | Elective (Coursework) | 3 | Manifolds, Tensors, Connections, Curvature (Riemannian, Ricci), Geodesics |
| MAM 718A | CRYPTOGRAPHY AND NETWORK SECURITY | Elective (Coursework) | 3 | Classical ciphers, Symmetric key cryptography (DES, AES), Asymmetric key cryptography (RSA, ECC), Hash functions, Digital signatures |
| MAM 719A | FINANCIAL MATHEMATICS | Elective (Coursework) | 3 | Interest rates, Derivatives (options, futures), Black-Scholes model, Stochastic calculus for finance, Portfolio optimization |
| MAM 720A | ACTUARIAL MATHEMATICS | Elective (Coursework) | 3 | Life contingencies, Survival models, Insurance pricing, Annuities, Risk theory |
| MAM 721A | IMAGE PROCESSING | Elective (Coursework) | 3 | Image enhancement, Image restoration, Image segmentation, Feature extraction, Image compression |
| MAM 722A | COMPUTATIONAL FLUID DYNAMICS | Elective (Coursework) | 3 | Finite difference method for fluid flow, Finite volume method, Grid generation, Turbulence modeling, CFD software |
