Passports of specialty
Doctor of Philosophy (PhD) – Specialty Doctor
6D070500 – Mathematical and Computer Modeling
(6D070502 – Mathematical Modeling, Numerical Methods, and Software Complexes)
(Approved by the Resolution of the Presidium of the Supreme Attestation Commission under the President of the Republic of Tajikistan dated January 31, 2024, №41/шд)
SPECIALTY CODE:
6D070500 – Mathematical and Computer Modeling (PhD program) establishes the foundation for research in mathematical and computer modeling, numerical methods, software complexes, and applied problems.
I. SCIENTIFIC FIELD FOR WHICH ACADEMIC DEGREES ARE AWARDED:
Technical Sciences, Physical and Mathematical Sciences
II. DEFINITION OF THE SPECIALTY:
The main components of this specialty involve the development of fundamental principles and application of mathematical modeling, numerical methods, and software complexes for addressing scientific, technical, fundamental, and applied problems. A crucial aspect is that the research must present original results simultaneously in three areas: mathematical modeling, numerical methods, and software complexes.
III. AREAS OF RESEARCH:
1. Development of new mathematical modeling methods for objects and phenomena.
2. Development of qualitative and approximate analytical methods for investigating mathematical models.
3. Development, justification, and testing of efficient computational methods using modern computer technologies.
4. Implementation of effective numerical methods and algorithms as problem-oriented software complexes for computational experiments.
5. Comprehensive studies of scientific and technical problems utilizing modern mathematical modeling and computational experimentation.
6. Development of mathematical methods and algorithms for validating the adequacy of mathematical models using experimental data.
7. Development of mathematical methods and algorithms for interpreting experimental data via mathematical models.
8. Development of computer and simulation modeling systems.
9. Models, methods, and algorithms for designing, analyzing, transforming, verifying, and testing software and software systems.
10. Models, methods, algorithms, languages, and software tools for organizing interactions between programs and software systems.
11. Symbolic computation software systems.
12. Human-machine interfaces; models, methods, algorithms, and software tools for computer graphics, visualization, image processing, virtual reality systems, and multimedia communication.
13. Models and methods for developing programs and software systems for parallel and distributed data processing; parallel programming languages and tools.
14. Models, methods, algorithms, and software infrastructure for globally distributed data processing.
15. Methods and algorithms for forecasting and evaluating the effectiveness, quality, and reliability of complex systems.
16. Development of methods and algorithms for system analysis, optimization, management, decision-making, and information processing.
17. Criteria and models for evaluating the effectiveness of solutions in system analysis, optimization, management, decision-making, and information processing.
18. Intelligent decision-support methods and algorithms for technical, economic, biological, medical, and social systems.
19. Methods for pattern recognition, cluster analysis, neural networks, fuzzy technologies, decision rules, and soft computing in database analysis.
20. Computer methods and models for describing, assessing, and optimizing information processes and resources.
21. Technical support for information systems and processes, including data collection, storage, transmission, and presentation hardware.
22. Linguistic support for information systems and processes.
23. Decision support systems based on databases and knowledge bases for predictive modeling.
24. Requirements for hardware and software solutions for modern telecommunication systems.
25. Principles and technologies for database and knowledge management systems.
26. New internet technologies, including secure information search, analysis, and filtering methods.
27. Automated information systems, resources, and technologies for various fields (scientific, technical, economic, educational, humanitarian).
28. Document management systems and information security measures.
29. Principles and solutions for information protection and security.
30. Automation of control and testing.
31. Methods and models for describing, assessing, and optimizing information flows; cognitive models for human-machine interaction.
32. Quality and efficiency evaluation methods for algorithms and software in AI and machine learning systems.
33. Specialized mathematical, algorithmic, and software solutions for AI and machine learning.
34. Methods and tools for forming data arrays and case studies, including big data, for AI and machine learning.
35. Mathematical research in statistics, logic, algebra, topology, functional analysis, and other areas focused on AI and machine learning problems.
36. Application of neural networks and artificial intelligence for non-destructive testing and diagnostics.
37. Application of artificial intelligence in brain and cognitive research.
IV. RELATED SPECIALTY CODES AND NAMES:
6D060100 – Mathematics; 6D060200 – Informatics; 6D070300 – Information Systems (by industry); 6D070400 – Computing Equipment and Software.
V. DISTINCTIONS FROM RELATED SPECIALTIES:
A dissertation relates to other specialties if it predominantly covers:
- Methods from function theory and functional analysis – specialty "Real, Complex, and Functional Analysis";
- Existence and uniqueness of solutions in differential equations – specialty 01.01.02 "Differential Equations, Dynamical Systems, and Optimal Control";
- Mathematical physics equations research – specialty "Mathematical Physics";
- Theoretical aspects of numerical methods – specialty "Computational Mathematics";
- Programming and calculation automation – specialty "Mathematical and Software Support for Computers and Information Systems";
- Automation theory, models, methods, algorithms, and systems structures for technological processes and production – specialty "Automation and Control of Technological Processes";
- Physical, chemical, technical, economic, or other aspects – corresponding specialties in the official nomenclature.
FIELD OF SCIENCE:
- Technical Sciences (research corresponding to at least three points of this passport);
- Physical and Mathematical Sciences (research corresponding to at least three points, predominantly using mathematical methods and yielding results as new mathematical methods, computational algorithms, or new laws characterizing the studied objects).