PhD courses
Speciality Name:
Pure and Applied Mathematics
Faculty:
Mechanics and Mathematics
Qualification:
- Scientific and pedagogical direction - Doctor of Philosophy (PhD)
- Model of graduating student
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Mandatory
disciplines
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Elective
disciplines
- Professional
1.To use innovative pedagogical technologies, methods for teaching mathematical disciplines; develop assessment tools, guidelines, methodological manuals;
2.On the basis of deep system knowledge in the field of model theory, algebra, differential equations, mathematical physics, create forecasting techniques, modeling complex systems;
3.Formulate tasks and hypotheses that create interest in the global scientific community;
4.Conduct research work, solve problems, prove theorems, creating competition to the advanced scientific community
5.Lead (or be in the forefront) of a scientific school in the direction of Algebra. Actively working with leading foreign scientists in this direction.
6.Lead (or be in the forefront) scientific school in the direction of mathematical logic. Actively working with leading foreign scientists in this direction.
7.Lead (or be in the forefront) scientific school in the direction of Differential Equations. Actively working with leading foreign scientists in this direction.
8.Lead (or be in the forefront) scientific school in the direction of Mathematical Physics. Actively working with leading foreign scientists in this direction.
9.Organize and manage scientific conferences. Management of scientific seminars.
10.To conduct expert opinions on scientific works in the following directions: theory of models, algebra, differential equations, mathematical physics. And also to do a review on the work of undergraduates, doctoral candidates, theses and scientific articles.
11.Advise commercial organizations on mathematical modeling of processes and forecasting their behavior.
12.To own and use linguistic and linguistic knowledge for communication and publications in multilingual and multicultural society in the international arena
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Academic writing
- Number of credits: 2
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: Academic writing is characterized by presentation in an impersonal and unemotional tone, academic writing is aimed at a critical and informed audience based on carefully substantiated and proven knowledge; and is intended to reinforce or challenge concepts or arguments.
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Algebraic questions of differential operators
- Number of credits: 5
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The ability to use differential operators to solve algebraic problems is being formed. In particular, for a Lie group over a field K, operators act on a smooth manifold over K. This course will allow doctoral students to combine different areas of research.
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Main problems of differential equations, geometry and mathematical logic
- Number of credits: 5
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The actual most important mathematical problems are formulated. There is a discussion of world problems, approaches and results. In particular, the problems: the Navier-Stokes equations, the Riemann hypothesis, the Poincaré conjecture, P = NP problem. This course allows doctoral students to understand the prospects and directions of development of modern mathematics. As well as methods of teaching mathematical disciplines.
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Scientific Research methods
- Number of credits: 3
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: General methods of scientific knowledge are usually divided into two large groups: a) methods of empirical research (observation, comparison, measurement, experiment); b) methods of theoretical research (abstraction, analysis and synthesis, idealization, induction and deduction, mental modeling, ascent from the abstract to the concrete, etc.).
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PhD thesis writing and defence
- Number of credits: 12
- Type of control: Докторская диссертация
- Description: The main purpose of "PhD thesis writing and defence": of a doctoral dissertation is the formation of the doctoral students' ability to disclose the content of research work for the defense of the thesis.
During the study of course, doctoral student's should be competent in:
1. to substantiate the content of new scientifically grounded theoretical and experimental results that allow to solve a theoretical or applied problem or are a major achievement in the development of specific scientific directions;
2. explain the assessment of the completeness of the solutions to the tasks assigned, according to the specifics of the professional sphere of activity;
3. they can analyze alternative solutions for solving research and practical problems and assess the prospects for implementing these options;
4. apply the skills of writing scientific texts and presenting them in the form of scientific publications and presentations.
5. to plan and structure the scientific search, clearly highlight the research problem, develop a plan / program and methods for its study, formalize, in accordance with the requirements of the State Educational Establishment, the scientific and qualification work in the form of a thesis for a scientific degree Doctor of Doctor of Philosophy (PhD) on specialty «8D07502 – Standardization and certification (by industry)».
During the study of the discipline doctoral student will learn following aspects: Registration of documents for presentation of the thesis for defense. Information card of the dissertation and registration-registration card (in the format Visio 2003). Extract from the minutes of the meeting of the institution, in which the preliminary defense of the thesis took place. Cover letter to the Higher Attestation Commission. Expert conclusion on the possibility of publishing the author's abstract. Expert opinion on the possibility of publishing a dissertation. Minutes of the meeting of the counting commission. Bulletin for voting. A shorthand record of the meeting of the dissertational council. List of scientific papers. Response of the official opponent. A review of the leading organization. The recall of the scientific adviser.
Data for 2021-2024 years
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Commutative algebra
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: To form the ability to use modern methods of commutative algebra. The content of the discipline is aimed at studying the following questions in algebra: commutative rings, polynomial rings over rings without zero divisors. Quadratic forms. Application of Hilbert's theorems on zeros and a basis to problems of algebraic geometry. Basis in an algebraically closed field.
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Spectral theory of ordinary differential operators
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: For linear operators defined by an ordinary differential expression and boundary conditions, many spectral problems have now been solved. The classes of boundary conditions are distinguished under which the operator has no eigenvalues. Theorems on completeness and basicity of the system of eigenfunctions and associated functions are proved. This course introduces the modern state of the spectral theory of differential operators on a segment.
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Modern methods of differential equations of mathematical physics
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The ability to use modern methods to solve problems of equations of mathematical physics is being formed. The content of the discipline is aimed at the study of various equations and their application to specific tasks. The knowledge gained helps to create methods for modeling complex systems.
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Countable models of complete theories
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: To acquaint students with the concepts of countable atomic, simple, homogeneous, countably saturated and unsaturated models of the full theory. The theory of types, theorems on lowering and the implementation of types have been developed. The knowledge gained allows us to assess the importance of work on similar topics.
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Representation Theory
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: To form the ability to use representation theory to the problems of algebras, not necessarily associative. In algebra, group representations play an important role. The content of the discipline is aimed at studyingdifferent bases of commutative rings, theorems on passage to the limit, uniform decomposition of homomorphisms
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The Theory of Stability
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: Provide a classification of complete stable theories. To this end, it is proposed to study the ranks of the formulas (Morley, Laskar, Shelah). Introduce the concepts of lambda stability, definability of types. Prove Shelah's theorem that a theory is stable if and only if each type is stable. Equivalently infinite indistinguishable sequence is an infinite indistinguishable set.
Data for 2021-2024 years
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Pedagogical
- Type of control: Защита практики
- Description: Aim оf discipline: formation of the ability to carry out educational activities in universities, to design the educational process and conduct certain types of training sessions using innovative educational technologies.
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Research
- Type of control: Защита практики
- Description: The purpose of the practice: gaining experience in the study of an actual scientific problem, expand the professional knowledge gained in the learning process, and developing practical skills for conducting independent scientific work. The practice is aimed at developing the skills of research, analysis and application of economic knowledge.
Data for 2021-2024 years
