The Ph.D. (Doctor of Philosophy) Program in the Department of Pure and Applied Mathematics is a research-orientated program designed to provide advanced training in both theoretical and applied aspects of mathematics. The programme offers scholars the opportunity to explore fundamental mathematical theories as well as address complex real-world problems through analytical, computational, and applied approaches. The programme encourages rigorous research in core areas of pure mathematics, such as algebra, analysis, and topology, as well as in applied mathematics, including differential equations, mathematical modelling, numerical analysis, optimisation, and operations research. Scholars are also encouraged to engage in interdisciplinary and multidisciplinary research, connecting mathematics with fields such as engineering, computer science, data science, finance, and emerging technological domains. Through a strong emphasis on logical reasoning, abstract thinking, and advanced mathematical techniques, the programme equips researchers with the skills needed to develop new mathematical theories, design innovative models, and contribute to solving scientific, technological, and industrial challenges.
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• Applicants holding a master’s degree with a minimum of 55% marks or an equivalent grade in a point scale as prescribed by the UGC from time to time, wherever the grading system is followed.
• Applicants whose results of the final examination of a programme leading to a master’s degree are awaited may be granted provisional admission, subject to fulfilling all other admission requirements. Such candidates must submit proof of completion of the master’s degree with a minimum of 55% marks within three months of admission, failing which the admission shall stand cancelled.
• Applicants holding foreign degrees equivalent to a master’s degree with a minimum of 55% marks or an equivalent grade in a point scale as prescribed by the UGC may be admitted to the Ph.D. programme, subject to clearance by the Equivalence Committee of Alliance University.
• Applicants who have completed M.Phil. coursework with a minimum of 55% marks in aggregate or its equivalent grade in the UGC point scale, and those whose M.Phil. dissertation has been evaluated but whose viva-voce is pending, may also be admitted to the Ph.D. programme.
• Applicants possessing a degree approved as equivalent to the M.Phil. degree in India and obtained from a foreign educational institution accredited by the UGC may be admitted to the Ph.D. programme, subject to clearance by the Equivalence Committee of Alliance University.
• Admission of candidates belonging to SC/ST/OBC and other reserved categories shall be governed by the Karnataka State Rules and applicable regulations in force from time to time.
• Students from a four-year undergraduate programme (with Honors) may enroll directly in the Ph.D. programme if they have secured 75% marks or above, with a 5% relaxation for specified categories as per UGC regulations.
• Students from a four-year undergraduate programme who have secured between 55% and 75% marks may qualify after completing either a one-year master’s programme or a bridging programme of 36–40 credits. (Refer National Credit Framework (NCrF) 2024).
• For students from a three-year undergraduate programme, Ph.D. eligibility requires completion of a bridging programme of 36–40 credits along with the necessary coursework. (Refer National Credit Framework (NCrF) 2024).
| Entry Level | Program Duration |
|---|---|
| Entry Level | 3–6 years full-time |
| Particulars | Indian Nationals | Foreign Nationals |
|---|---|---|
| Registration Fee | ₹50,000 | $600 |
| program Fee (Per Annum) | ₹1,00,000 | $1,400 |
| Comprehensive Exam Fee | ₹20,000 | |
| Thesis Submission Fee | ₹30,000 | |
| Doctoral Scroll Free | ₹5,000 | |
| Convocation Fee | ₹3,000 | |
| Alumni Association Fee | ₹3,000 |
| Category | Eligibility / Scope | Grant Amount / Benefits |
|---|---|---|
| Research Fellowship | Full-time scholars | ₹35,000 per month |
| Contingency Grant | Full-time scholars | ₹25,000 per year |
| International Conference Funding | Case-by-case basis; once during the program | Up to ₹1,00,000 |
| National Workshop Funding | Scholars not receiving other funding support | ₹30,000 per year |
| Inclusion & Special Provisions | Women scholars and differently-abled scholars | Special provisions and relaxations; access to Centres of Excellence and entrepreneurial fund of ₹10 Crores |
| Policy | Conditions | Awards and funding are subject to review by the Scholarship / Research Committee; limited availability on a first-come-first-served basis |
| Steps | Description |
|---|---|
| Step 1 | Submit online application |
| Step 2 | Pay Application Fee — ₹3,000 |
| Step 3 | Alliance Research Aptitude Test (ARAT) |
| Step 4 | Personal Interview |
| Step 5 | Evaluation of research synopsis on proposed dissertation |
| Step 6 | Consideration of scholastic record, work experience, and extracurricular achievements; final selection based on overall performance |
Comfort, safety, and community form the foundation of campus living. Our residential halls are thoughtfully designed to create a sense of belonging—offering a welcoming environment where students can study, unwind, and build lifelong friendships.
Separate hostels
for boys and girls
Student-friendly
common areas
Spacious rooms
(single, double, or triple occupancy)
Dedicated wardens
and support teams
The overall teaching and learning experience at Alliance University has been very enriching. With a strong academic environment that inspires growth, the doctoral program is giving me exposure to new ideas and connecting me with leading experts in the field of research.
A doctoral research program focused on advanced mathematical modeling, analytical research, and applied problem-solving across science, technology, engineering, and industry.
Applied Statistics, Artificial Intelligence, Big Data Analytics, Graph Theory, Numerical Methods, Machine Learning, Stochastic Processes, Differential Equations, and more.
Master’s degree with ?55% marks (or equivalent); direct entry for eligible four-year Honors graduates as per UGC/NCrF norms.
Typically 3–6 years, depending on research progress.
Fellowships, contingency grants, and funding for national and international academic engagements.
Through application review, entrance evaluation, interview, and research proposal assessment.
AU-STIC central instrumentation facility, global databases, Centers of Excellence, and international research networks.
Yes, subject to equivalence approval by Alliance University.
Yes, in accordance with Karnataka State Rules and UGC guidelines.
Yes, subject to approval.
Research Methodology, Research & Publication Ethics, Advanced Mathematical Papers, Academic Writing, and Research Practicum.
| Course Type | Course Name | Credits |
|---|---|---|
| University Core | Research and Publication Ethics | 2 |
| University Core | Learning and Development | 1 |
| University Core | Academic Writing | 1 |
| Department Core | Research Methodology | 4 |
| Department Elective | Directed Course | 4 |
| Total Credits | 12 |
• Research Competence & Knowledge Creation – Demonstrate proficiency in applying advanced research methodologies, analytical techniques, and experimental designs to produce high-quality research and contribute to knowledge creation.
• Research Ethics & Integrity – Uphold ethical research practices by ensuring compliance with academic integrity, plagiarism standards, and responsible data management.
• Effective Communication & Knowledge Dissemination – Demonstrate proficiency in academic writing, presentations, publications, and scholarly discourse for effective dissemination of research outcomes.
• Societal Impact – Align research with societal needs and the Sustainable Development Goals (SDGs), contributing to policy development, industry advancement, and community-driven solutions.
• Lifelong Learning & Continuous Professional Development – Commit to continuous learning and professional growth by staying updated with emerging trends, theories, technologies, and best practices in the field.
• Structured Coursework – A semester-long coursework with a special focus on Research Methodology and Academic Writing, enabling scholars to develop a concrete research proposal by the end of the coursework.
• Problem-Driven Research – Research aligned with national priorities such as sustainability, healthcare, energy, water, and digital transformation, with a strong emphasis on real-world impact.
• Advanced Research Facilities – Access to shared state-of-the-art laboratories and research facilities across departments to support experimental, computational, and translational research.
• International Research Collaboration – Opportunities for joint research projects, visiting researcher programmes, and co-authored publications with leading global institutions.
• Innovation and Technology Transfer – Strong focus on innovation, intellectual property creation, patent filing, product development, and commercialization of research outcomes.
• Publication-Oriented Research Culture – Encouragement and support for high-impact journal publications, conference presentations, and interdisciplinary dissemination of research findings.
• Research Fellowship – Monthly fellowship of Rs.35,000 along with applicable benefits for full-time research scholars.
• Customized Directed Courses – Directed courses specifically designed for each scholar based on their chosen research area and academic interests.
• Rigorous Doctoral Evaluation – Ph.D. awarded upon successful completion of coursework, qualifying examination, and original research work evaluated by the competent authority.
• Pure and Applied Mathematics – Advanced research in theoretical and applied mathematical concepts addressing contemporary scientific and engineering challenges.
• Dynamical Systems and Mathematical Modelling – Research focused on modelling, analysis, and prediction of complex dynamic systems across interdisciplinary domains.
• Probability, Statistics, and Reliability Theory – Investigation of stochastic processes, statistical methodologies, risk assessment, and reliability analysis.
• Computational Mathematics and Scientific Computing – Development of numerical methods, algorithms, and computational techniques for solving complex mathematical and scientific problems.
• Mathematical Foundations of Data Science and AI – Research on mathematical principles underpinning data analytics, machine learning, artificial intelligence, and computational intelligence systems.
