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    SAS

    School of Arts & Science

    Ph.D. in Mathematics

    The School of Arts and Science at Vinayaka Mission’s Research Foundation offers a rigorous doctoral program in Mathematics.

    Ph.D. in Mathematics

    The Ph.D. in Mathematics at SAS (School of Arts and Sciences) is a research-intensive doctoral program designed to foster advanced scholarship, original contributions, and innovations in the mathematical sciences. The programme equips scholars with the knowledge, methodologies, and research skills necessary to pursue careers in academia, research institutions, and industries that demand high-level mathematical expertise.

    Program Options

    Full Time

    For those who want to focus only on research

    Part Time

    For working professionals

    International Students

    NRI/ Foreign Students can also apply for full time programme

    Admission Requirements

    • Master’s degree in Mathematics or allied discipline with minimum 55% marks (or equivalent CGPA).
    • Qualifying in SAS Ph.D. Entrance Exam and/or UGC-NET / CSIR-NET / GATE (as per regulations).
    • Personal interview to evaluate research aptitude and subject knowledge.

    Programme Structure

    • Duration: Minimum 3 years; Maximum 6 years (as per UGC regulations)
    • Credits: ~72+ credits (including coursework, seminars, and dissertation)
    • Mode: Full-time / Part-time (as per VMCC regulations)
    • Supervision: Each scholar will be guided by an approved Ph.D. supervisor with expertise in chosen research domains.

    Procedure

    Applicants must take a written test and appear for a personal interview (NET/SET cleared candidates are exempted from the written tests)

    Course Basket Overview

    Course Type Description
    Research Coursework Foundation courses in Research Methodology, Advanced Mathematical Techniques, and Computational Tools.
    Domain-Specific Papers Advanced topics in Pure Mathematics, Applied Mathematics, Statistics, or interdisciplinary mathematical sciences.
    Seminars & Colloquia Participation in departmental seminars, paper presentations, and conferences to build research communication skills.
    Dissertation / Thesis Original research work making a significant contribution to mathematics, defended in a viva voce.
    Course Type:
    Research Coursework
    Description:
    Foundation courses in Research Methodology, Advanced Mathematical Techniques, and Computational Tools.
    Course Type:
    Domain-Specific Papers
    Description:
    Advanced topics in Pure Mathematics, Applied Mathematics, Statistics, or interdisciplinary mathematical sciences.
    Course Type:
    Seminars & Colloquia
    Description:
    Participation in departmental seminars, paper presentations, and conferences to build research communication skills.
    Course Type:
    Dissertation / Thesis
    Description:
    Original research work making a significant contribution to mathematics, defended in a viva voce.

    Duration

    • Full Time: Minimum period 3 years and Maximum period 6 years
    • Part Time: Minimum period 4 years and Maximum period 8 years

    Career Prospects

    Academic Positions

    Professors, Lecturers, and Researchers in universities and colleges.

    Research Scientist Roles

    In national laboratories (ISRO, DRDO, CSIR, IISc, IITs, IISERs, etc.).

    Industry Roles

    Data Science, Cryptography, Quantitative Finance, Artificial Intelligence, and Analytics.

    Consultancy Opportunities

    In Operations Research, Risk Analysis, and Mathematical Modelling.

    Department of Mathematics - Research Supervisors

    Dr. Ananthan V
    Expertise in Nonlinear PDEs, Differential Geometry, and Applied Mathematics
    ananthan.v@math.ac.in
    Dr. Shankar R
    Expertise in Graph Theory, Operations Research, and Computational Mathematics
    shankar.r@math.ac.in

    Research Areas

    Research Methodology

    Foundation courses in Research Methodology, Advanced Mathematical Techniques, and Computational Tools.

    Domain-Specific Research

    Advanced topics in Pure Mathematics, Applied Mathematics, Statistics, or interdisciplinary mathematical sciences.

    Key Research Domains

    Nonlinear PDEs, Differential Geometry, Graph Theory, Probability, and more, tailored to the scholar's interests.

    Interdisciplinary Applications

    Integration of mathematics with physics, biology, computer science, and emerging fields for innovative solutions.

    Research Areas

    Areas of specialization may include, but are not limited to:

    Core Mathematical Sciences

    Nonlinear PDEs (Navier–Stokes, Reaction-Diffusion, Schrödinger Eq.)
    Differential Geometry & PDE applications in physics
    Advanced Difference Equations in population dynamics, epidemiology, and financial mathematics
    Hybrid models combining ODE + PDE + Difference equations
    Pure Mathematics (Algebra, Analysis, Topology, Number Theory)
    Applied Mathematics (Differential Equations, Mechanics, Mathematical Physics)
    Computational Mathematics & Numerical Analysis
    Probability, Statistics & Data Science
    Operations Research & Optimization
    Mathematical Modelling, Cryptography, and Emerging Interdisciplinary Fields

    Graph Theory and Applications

    Graph Theory with Applications
    Algebraic Graph Theory
    Spectral Graph Theory
    Graph Algorithms and Complexity
    Random Graphs & Probabilistic Methods
    Applications in Computer Science, Biology (gene networks), and Operations Research

    Why Choose SAS?

    Outcome-Based Curriculum

    Smart Classrooms & Innovation Labs

    Guaranteed Placement Support

    On-Campus Incubation Centre

    Access to Leading Research Networks

    Our Prestigious Recruiters

    Transforming Knowledge into Action

    Knowledge is only powerful when it’s applied. At our institution, we focus on transforming academic learning into real-world action. Our hands-on approach ensures that students don’t just understand theories—they learn how to make a difference in the world.
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