Part I
Upon completion of the program, the graduate will be able to:

• Thoroughly and systematically analyze concepts and problems in real and complex analysis and apply them to various fields of mathematics.
• Characterize and evaluate the nature of sets from two distinct perspectives, measure theory and topology, and apply these approaches in statistics and other areas of mathematics.
• Examine probability spaces, statistical experiments, random variables, numerical characteristics of probability distributions, and statistical estimators of parameters of various probability distributions, and apply appropriate estimation methods to specific problems.
• Explain concepts and methods of operator theory and operator algebras, as well as fundamental methods of function theory and functional analysis, and apply them to the investigation of various mathematical problems.
• Apply methods for studying differential equations and obtaining numerical approximations to their solutions, and develop algorithms by writing appropriate code in MATLAB.
• Explain and formulate fundamental methods and algebraic structures of abstract algebra and apply them to solving various theoretical and practical problems.
• Analyze initial data related to practical and applied problems through individual and collaborative work, validate the obtained results, and formulate them using mathematical language.
• Draw conclusions on discipline-specific issues using modern technologies, communicate effectively both in writing and orally, and present findings clearly, coherently, and in accordance with academic ethical standards to both specialist and non-specialist audiences.

Part II
Upon completion of the program, the graduate will be able to:

• Explain concepts and methods of operator theory and operator algebras, as well as fundamental methods of function theory and functional analysis, and apply them to the investigation of various mathematical problems.
• Explain and formulate fundamental methods and algebraic structures of abstract algebra and apply them to solving various theoretical and practical problems.
• Analyze significant issues in the field through individual and collaborative work and substantiate conclusions using relevant knowledge and logical reasoning.
• Draw conclusions on discipline-specific issues using modern technologies, communicate effectively both in writing and orally, and present findings clearly, coherently, and in accordance with academic ethical standards to both specialist and non-specialist audiences.
• Independently plan and conduct research at the master's level, formulate research aims and objectives, select appropriate mathematical methods, and evaluate the effectiveness of their application.
• Analyze theoretical and research problems using mathematical models and methods, critically evaluate the results obtained, substantiate conclusions, and identify opportunities for further development.
• Collaborate effectively in an academic environment, participate in research activities, and responsibly carry out both individual and collaborative research tasks.