PhD in Mathematics and Scientific Computing
Department
Mathematics
Level
Postgraduate
College
College of Computer Sciences & Information Systems
Course Detail
The PhD in Mathematics program is designed to provide advanced training in both theoretical and applied aspects of mathematics, preparing scholars to
contribute to research, innovation, and evidence-based problem solving across academia, industry, and government. The Department has a diverse faculty
with expertise spanning pure and applied mathematics, offering students a wide range of specialized subjects and research areas to choose from according to their
academic interests and career goals. The program aims to develop researchers capable of advancing mathematical theory, formulating innovative models and
methods, and conducting high-quality scientific investigations to address contemporary challenges. While individual researchers may pursue different areas
of specialization, the program emphasizes rigorous coursework and excellence in research, encouraging publications in reputable international conferences and
HEC-recognized journals. The coursework and research requirements are structured in accordance with HEC criteria to ensure the highest academic standards.
Eligibility
Applicants seeking admission to the PhD in Mathematics program must possess an M.Phil./M.S. in Mathematics or an equivalent qualification from an HECrecognized institution and meet the following criteria:
• A minimum CGPA of 3.00 on a scale of 4.00, or at least 60% marks, or an equivalent qualification.
• A minimum of 18 years of education corresponding to an M.S./M.Phil.
degree or an equivalent qualification in Mathematics or a closely related discipline from an HEC-recognized institution.
• A valid score of at least 60% in the GRE (Subject), GAT (Subject) conducted by NTS, or an equivalent test in the relevant discipline, as prescribed by HEC.
• Successful completion of an interview conducted by the Department.
• Fulfillment of all other admission requirements stipulated by the Higher Education Commission (HEC) of Pakistan.
Degree Requirements
The PhD in Mathematics requires the successful completion of coursework and a dissertation/thesis. The minimum duration of the program is three years, while the maximum duration is five years.
• The coursework component consists of six graduate-level courses carrying a total of 18 credit hours.
• Upon successful completion and defense of the dissertation/thesis, the student is awarded 30 credit hours.
Additional PhD Requirements
In addition to the completion of coursework and dissertation/thesis credits, a PhD student must fulfill the following requirements:
• Pass the Comprehensive Examination.
• Develop and submit a PhD Proposal/Synopsis.
• Successfully defend the PhD Proposal/Synopsis.
• Obtain approval of the PhD Proposal/Synopsis from the Board of Advanced Studies and Research (BASR).
• Maintain continuous enrollment in supervised research courses to satisfy the full-time residency requirements.
• Complete the PhD Dissertation/Thesis under the supervision of the assigned research supervisor(s).
• Obtain BASR approval for the selection of external evaluators.
• Publish at least one research paper in an ISI-indexed or HEC-recognized
journal, or provide an official acceptance letter for publication.
• Secure evaluation of the PhD Dissertation/Thesis by two foreign experts from developed countries in accordance with HEC criteria.
• Incorporate the recommendations of the evaluators and finalize the Dissertation/Thesis.
• Successfully defend the Dissertation/Thesis in an open public defense.
• Fulfill any other requirements stipulated by the Higher Education Commission (HEC) from time to time.
• Submit the final approved version of the Dissertation/Thesis to BASR
Program Learning Outcomes
Upon successful completion of the PhD in Mathematics program, graduates will be able to:
• Demonstrate an in-depth understanding of advanced mathematical theories and conduct high-quality, original research.
• Lead and manage independent and collaborative research projects effectively.
• Support and actively participate in academic, governmental, and industrial research and development projects.
• Apply mathematical theories, models, and analytical techniques to address and solve real-world problems.
Career Opportunities
• Faculty positions in universities.
• Industrial research and development (R&D) roles
• Scientific consulting and interdisciplinary research careers.
• Computational mechanics expert.
• Specialist in mathematical analysis for multidisciplinary applications.
• Specialist in algorithm design and computational mathematics.
• Data scientist and machine learning researcher.
• Specialist in computational fluid dynamics (CFD) and simulation
Course Structure
Core Course
Courses Credit Hours
Research Methodology 3+0
Elective Courses
| Elective Courses | Credit Hours |
|---|---|
| MAT701 Convex and Stochastic Optimization | 3 |
| MAT702 Mathematical Analysis of Machine Learning Algorithms | 3 |
| STS802 Advanced Mathematical Statistics | 3 |
| MAT703 Continuum Mechanics | 3 |
| MAT704 Advanced Numerical Computing | 3 |
| MAT804 Advanced Partial Differential Equations | 3 |
| MAT805 Advanced Topics in Number Theory | 3 |
| MAT706 Linear Algebra and Lie Algebra | 3 |
| MAT706 Applied Matrix Theory | 3 |
| MAT707 Numerical Methods for PDEs | 3 |
| MAT708 Topics in Inverse Problems | 3 |
| MAT709 Topics in Numerical Differential Equations | 3 |
| STS801 Advanced Statistical Computing & Graphics | 3 |
| STS702 Nonlinear and Integer Programming | 3+0 |
| MAT710 Stochastic Differential Equations (SDEs) | 3+0 |
| MAT801 Advanced Fluid Dynamics | 3+0 |
| MAT802 Advanced Modeling and Simulation | 3+0 |
| MAT711 Mathematical Economics | 3+0 |
| MAT712 Quantum Finance | 3+0 |
| MAT713 Mathematics of Fuzzy Sets and Fuzzy Logic | 3+0 |
| MAT714 Topological Data Analysis | 3+0 |
| MAT803 Advanced Dynamical Systems | 3+0 |
| MAT715 Calculus of Variations | 3+0 |
| MAT716 Optimization Methods | 3+0 |
| MAT921 Research Thesis (3 Units) | |
| MAT922 Research Thesis (6 Units) | |
| MAT923 Research Thesis (9 Units) | 30 |