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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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