Applied Mathematics at the educational-scientific level is a high-tech and methodological field that serves as a bridge between fundamental mathematical science, computer technology (Computer Science / Artificial Intelligence), and the practical solution of complex problems in business, engineering, physics, medicine, economics, and the defense sector.
A modern Doctor of Philosophy (PhD) in Applied Mathematics is a research scientist, an architect of mathematical models and complex algorithms, and a specialist in Data Science, ML/AI, numerical methods, and optimization capable of formalizing previously unsolved or unstructured problems and developing new mathematical theories, algorithms, and computational software for them.
The research activities of postgraduate students in this specialty are based on studying the following objects:
- mathematical methods and theories: new and adapted mathematical methods of differential equations, probability theory, mathematical statistics, discrete mathematics, graph theory, and optimization;
- mathematical models of complex systems: conceptual, analytical, probabilistic, stochastic, and computational models of physical, biological, socio-economic, ecological, and technical processes;
- algorithms and machine execution: development, analysis of convergence, stability, and time and space complexity of novel numerical algorithms, optimization methods, high-performance computing, and parallel computing;
- software and data-driven systems: development of specialized software suits, application of machine learning and deep learning methods (Machine Learning / Deep Learning), neural networks, mathematical methods for processing Big Data and knowledge;
- modeling under uncertainty: decision-making methods under the influence of fuzzy data, stochastic factors, interval uncertainty, and incomplete information.
Goals of postgraduate (PhD) study — training highly qualified scientific and pedagogical personnel capable of carrying out original fundamental and applied scientific research, producing new knowledge in the field of applied mathematics, as well as:
- formulating, solving, and generalizing new scientific and practical problems using fundamental and specialized applied methods of mathematical and computer sciences;
- solving complex problems of mathematical modeling of processes and phenomena under conditions of high uncertainty, risks, and incomplete initial information regarding the functioning of objects or systems;
- constructing, researching, and applying cutting-edge mathematical models based both on fundamental laws (Physics-Informed models) and on large volumes of data and knowledge (Data-Driven / AI models), creating and operating corresponding high-performance software.
Key competencies and training focuses:
- fundamental and applied modeling — construction of complex mathematical models of diverse nature (hydrodynamic, biomedical, economic, cryptographic, etc.) and analysis of their adequacy;
- algorithmization and numerical methods — creation of new supercomputer, parallel, and adaptive numerical algorithms, proving theorems on convergence and stability of methods;
- Data Science and Machine Learning — mathematical foundation of machine and deep learning models, development of new neural network architectures, reinforcement learning (RL) methods, and LLMs;
- optimization and operations research — solving multi-objective optimization problems, stochastic programming, game theory, and optimal control of complex systems;
- scientific and pedagogical activity — writing scientific papers for leading specialized publications (Scopus / Web of Science Q1–Q2), preparing grant proposals, teaching higher mathematics and Data Science in higher education institutions.
Doctors of Philosophy (PhD) in Applied Mathematics possess the highest level of analytical and computational skills and are highly sought after both in academia and in the leading R&D departments of global IT and engineering corporations:
- research and development (R&D): Applied Mathematician, Quantitative Researcher, Lead AI/ML Scientist, R&D Engineer in global IT companies (Google, Microsoft, OpenAI, NVIDIA, Meta) and domestic product/outsource businesses;
- academic sphere and education: researcher at institutes of the National Academy of Sciences of Ukraine (Glushkov Institute of Cybernetics, Institute for Applied Analysis, etc.), senior lecturer, associate professor, professor at leading Ukrainian and foreign universities;
- financial and investment sector (Quant Finance): quantitative analyst (quant), risk evaluator, developer of high-frequency trading (HFT) algorithms in hedge funds, investment banks, and financial technologies (FinTech);
- high-tech, defense, and aerospace industries: specialist in flight trajectory modeling, physical process simulation, signal and image processing, cryptographic data protection, autonomous systems, and robotics;
- bioinformatics and medicine: analyst of complex medical and genetic data, developer of mathematical models for disease propagation and tissue dynamics.
Training is provided by the Postgraduate and Doctoral Studies Department.
Education is provided under the following educational programs:
| Educational Program | Degree | Mode of Study | Duration of Study |
|---|---|---|---|
| Applied Mathematics | Doctor of Philosophy | Full-time and Part-time | 4 years |