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Mathematics and Computer Science is a doctoral study aimed at producing a high level of research on mathematical theories and methods as well as their application in computer science. Most Ph.D. programs take 4-6 years and involves credit courses, seminars, individual research under faculty supervision, comprehensive examinations to assess mastery of fundamental contents, and preparation and defense of a dissertation that contributes knowledge to the discipline.
People pursue a Ph.D. after they finish their undergraduate studies and apply for the program. Standardized tests that are considered for admission depend on the program, but most popular options are the Graduate Record Examination (GRE) general test that proved quantitative scores meant to establish mathematical skills. Certain programmes also have standardised tests such as GRE mathematics or computer science subject tests required or recommended. Accepted tests might be the GATE or other national tests that may be mandatory for the applicant in the country of origin for postgraduate studies. Recommendations, declaration of purpose, letters of recommendation, academic transcripts, and prior experience in research are also considered in evaluating Ph.D. aspirants by the programs. Mathematics and Computer Science is a doctoral study aimed at producing a high level of research on mathematical theories and methods as well as their application in computer science. Most Ph.D. programs take 4-6 years and involves credit courses, seminars, individual research under faculty supervision, comprehensive examinations to assess mastery of fundamental contents, and preparation and defense of a dissertation that contributes knowledge to the discipline.
| Feature | Description |
|---|---|
| Full Form | Doctor of Philosophy (Mathematics & Computer Science) |
| Also Known As | Ph.D. in Computational Mathematics, Ph.D. in Mathematical Computer Science |
| Duration | 4-6 years (full-time), may vary depending on the program |
| Course Level | Doctoral Level |
| Eligibility | Master's degree in Mathematics, Computer Science, or a related field with strong foundations in both disciplines |
| Top Universities (World) | Massachusetts Institute of Technology (MIT), Stanford University, Carnegie Mellon University, University of California Berkeley, ETH Zurich |
| Top Universities (US) | Courant Institute (NYU), California Institute of Technology (Caltech), University of Chicago, Princeton University, University of Toronto |
| Entrance Exam | University-specific entrance exams (GRE Subject Tests in Math & CS possible), research proposal evaluation, and interview rounds |
1. Possess a master’s degree in Mathematics, Computer Science or related discipline with the minimum grade requirements from an accredited university.
2. Have a valid score in PhD entrance tests like that GATE/NET or a test conducted by the university or the institute in question.
3. Clear any interviews or other conditions added by the respective institute or department for determining the eligibility.
4. Have former teachers or research supervisors write the recommendation letters.
5. Submit a provisional title of the paper to be written based on the faculty research interest areas.
6. Minimum passing marks for the previous academic credentials such as bachelors, masters etc., should be attained.
| Subject | Important Topics |
|---|---|
| Mathematical Foundations of Computer Science | Complexity theory, algorithmic analysis, Computability theory, Discrete mathematics for computer science |
| Numerical Analysis | Numerical methods for solving linear and nonlinear equations, Numerical differentiation and integration, Optimization algorithms |
| Scientific Computing | High-performance computing, Parallel and distributed computing, Numerical methods for scientific simulations |
| Algebraic Combinatorics | Combinatorial optimization problems, Graph theory and network analysis, Coding theory and cryptography |
| Mathematical Logic and Formal Methods | Model theory and automated reasoning, Formal verification of software systems, Logic programming languages |
| Elective Courses (Depending on the University) | Machine Learning and Optimization, Computer Vision and Image Processing, Natural Language Processing, Mathematical Modeling and Simulation, Bioinformatics and Computational Biology |
| Specialization | Job Title | Average Salary |
|---|---|---|
| Scientific Computing | Scientific Computing Researcher, High-Performance Computing Specialist, Computational Scientist | $80,000 - $140,000+ |
| Computational Mathematics | Applied Mathematician, Cryptographer, Operations Research Analyst | $75,000 - $130,000+ |
| Machine Learning & Optimization | Machine Learning Researcher, Algorithmic Engineer, Optimization Specialist | $90,000 - $150,000+ |
| Computer Vision & Image Processing | Computer Vision Scientist, Image Processing Engineer, Robotics Engineer | $85,000 - $145,000+ |
| Natural Language Processing (NLP) | NLP Scientist, Computational Linguist, Speech Recognition Engineer | $80,000 - $135,000+ |
