**Fundamentals of** **WEB** **programming**

For 3rd year students of specialties

APPLIED MATHEMATICS, MATHEMATICS

Semester 6

**Lecturer** : associate professor *Rudnev Yuriy Illich*

**Course structure** : 2 years. ( **Lectures** ) + 2 hours ( **lectures / practice** )

**Basic knowledge:** computer science and programming

**Reporting form** : exam / credit (optional)

**Tentative content:**

- Overview of development tools: IDE, browser tools, version control systems.
- Client-server interaction. HTTP data transfer protocol.
- Layout basics (HTML, CSS). Adaptive layout.
- Use Javascript scripts to give interactivity a web page.
- Frontend Frameworks – Jquery, Bootstrap.
- ASP.NET based on C #.
- Basics of using databases on an example of MS SQL Server.
- MVC programming pattern and its use in web programming.

**Analytical Mechanics**

(Continuation of the course “Theoretical mechanics”)

For 3rd year students of specialties

APPLIED MATHEMATICS, MATHEMATICS

Semester 6

**Lecturer** : candidate of physical and mathematical sciences, associate professor *Poslovsky Sergey Alexandrovich*

**Course structure** : 2 years. ( **Lectures** ) + 2 hours. ( **Practice)** for a week

**Basic knowledge:** theoretical mechanics, mathematical analysis, ordinary differential equations, linear algebra.

**Reporting form** : exam / credit (optional)

**Tentative content:**

- Elements of celestial mechanics.
- Solid state dynamics.
- The variational principle of Hamilton-Ostrogradsky.
- The first integrals of the Lagrange equations.
- Conditions of equilibrium of the mechanical system.
- The Lagrange-Dirichlet theorem on the stability of the conservative system’s equilibrium.
- Small variations of conservative systems.
- Forced oscillations. Resonance.
- Canonical Hamilton equations. Poisson’s toes.
- The Liouville theorem on the preservation of the phase volume.

**Steering and stabilization**

For 3rd year students of specialties

APPLIED MATHEMATICS, MATHEMATICS

Semester 6

**Lecturer** : candidate of physical and mathematical sciences, associate professor *Smortsov Tatyana Ivanivna*

**Course structure** : 2 years. ( **Lectures** ) + 2 years ( **practice** ) per week

**Basic knowledge:** ordinary differential equations, linear algebra

**Reporting form** : exam / credit (optional)

**Tentative content:**

- Control of linear systems without management constraints.
- Stabilization of linear systems.
- Display of managed systems on the canonical system.
- The management of nonlinear triangular systems. Korobov’s theorem.
- Stabilization of triangular systems.
- Tasks of optimal control. Linear task of speed.
- The control of linear systems on a subspace.
- Geometric criterion of controllability.

**Markov chains – forecasting, games, genetics**

For 3rd year students of a specialty

APPLIED MATHEMATICS, MATHEMATICS

Semester 6

**Lecturer** : Doctor of Physical and Mathematical Sciences, Professor *Anatoliy G. Rutaks*

**Course structure** : 2 years. ( **Lectures** ) + 2 years ( **practice)** per week

**Basic knowledge:** linear algebra, discrete mathematics

**Reporting form** : exam / credit (optional)

**Tentative content**

Structural and spectral properties of inseparable matrices, Frobenius and Perron theorems. Stochastic vectors and matrices, Markov chains. Regular ergodic and absorbing chains. The use of Markov chains in prediction and game theory. Application in ecology, biology, sociology, economics, genetics.

**Mathematical modeling with** **Python** **.**

For 3rd year students of specialties

APPLIED MATHEMATICS, MATHEMATICS

Semester 6

**Lecturer** : candidate of physical and mathematical sciences, associate professor *Ignatovich Svetlana Yurievna*

**Course structure** : 2 years. ( **Lectures** **/** **practice** ) + 2 years ( **practice** ) every week

**Basic knowledge:** programming, elementary mathematics

**Reporting form** : credit

**Tentative content:**

- Basic Python language constructs.
- Functional programming.
- Object-Oriented Programming.
- Workshop on solving various levels of mathematical modeling tasks in Python language (with emphasis on style and means of programming).

**The theory of graphs** **and** **their applications**

For 3rd year students of specialties

APPLIED MATHEMATICS, MATHEMATICS

Semester 5

**Lecturer** : Doctor of Physical and Mathematical Sciences, Professor *Anatoliy G. Rutaks*

**Course structure** : 2 years. ( **Lectures** ) + 2 years ( **practice** ) per week

**Basic knowledge:** linear algebra, discrete mathematics

**Reporting form** : credit

**Tentative content**

Study of geometric and algebraic properties of graphs. Typical tasks of discipline, coloring of graphs, enumeration of graphs and trees, Hamiltonian cycles and paths. Infinite graphs and their matrix and numerical characteristics. Application of graphs to the development of network models, mathematical models of radio engineering circles, the construction of mathematical models in sociology, economics, the use of graphs in computer engineering, forecasting and production activities.

**Numerical Analysis**

For 3rd year students of a specialty

MATH

(In conjunction with the students of the specialty “Applied Mathematics”)

Semester 5

**Lecturer** : Doctor of Physical and Mathematical Sciences, Professor *Valery I. Korobov*

**Course structure** : 2 years. ( **Lectures** ) + 2 hours. ( **Practice** ) for a week

**Basic knowledge:** linear algebra, mathematical analysis

**Reporting form** : credit

**Tentative content:**

- The task of interpolation.
- Interpolation of functions by polynomials.
- Interpolation of functions by splines.
- Approximation of functions. Smallest squares method.
- Quadrature formulas (numerical calculus of integrals).
- Numerical differentiation.

**Numerical analysis from** **Maple** **and** **Mathematica**

(Continuation of the course “Numerical analysis”)

For 3rd year students of specialties

APPLIED MATHEMATICS, MATHEMATICS

Semester 6

**Lecturer** : candidate of physical and mathematical sciences, lecturer *Bebya Maxim Otaryovich*

**Course structure** : 2 years. ( **Lectures** ) + 2 hours ( **practice)** per week

**Basic knowledge:** linear algebra, mathematical analysis.

**Reporting form** : exam / credit (optional)

**Tentative content:**

- Using the Maple and Mathematica packages in character and numerical calculations.
- Solving systems of nonlinear equations.
- Solving systems of linear algebraic equations.
- Task for own values.
- Numerical solution of the Cauchy problem.