## Annotation of lecture courses

## Courses read by the members of the department:

**Mathematical analysis**- mathematical analysis standard course for students of the first and second years of mathematics specialty. Part 1. Part 2.**Mathematical analysis**– separate multimedia lectures. Lecture 16.**Mathematical analysis**– mathematical analysis course for students of the first and second years of applied mathematics specialty.**Mathematical analysis**– mathematical analysis short course for students of the first year of economic theory specialty.**Measure and integral theory**– basic attention in this course is paid to measure construction and Lebesgue integral. Some aspects of measure and integral construction in general case are also viewed.**Function analysis**– annual lectures for students of universities’ mathematical faculties, where metrical theories, linear rationed and Euclid spaces, linear functional and operators and their application to the decision of statement equations are stated.**Chances theory and mathematical statistics**- annual lectures for students of universities’ mathematical faculties. Main conceptions and facts are firstly entered for discrete case. Expected value is stated as Lebesgue integral, but any preliminary knowledge of Lebesgue integral is not assumed. Course sections: independent tests and Markov chains, Moivre-Laplace and Poisson maximum theorems, casual sizes, productive and characteristic functions, the law of large numbers, central limit theorem, basic concepts of mathematical statistics, statistical estimations, statistical hypotheses verification, confidence intervals, cross-correlation and regression analysis.**Chances theory and mathematical statistics**– half-hear course for students of theoretical mechanics specialty.**Chances theory and mathematical statistics**– short course for students-psychologies.**Theory of the even approaching of function by polynomials**– special course, where Weierstrass theorem and its various generalization, Stone theorem are studied; classic lines and reverse theorems.**Fourier series**– along with classic results Fourier series in Hilbert space, convergence and summability problems almost everywhere of Fourier series and trigonometric series utility are examined.**Adding up of numerical series theory**– half-year course, where classic methods of Cesaro and Abel’s adding up, regular matrix methods and results, reflecting “force” and “weakness” of these methods, are contained.**Multiple series**– half-year special course, where convergence of multiple numeral and sedate series theorem are stated.**Functions with the limited middle vibration**– special course, where functions properties with the limited middle oscillation and some near classes are studied.**Functions classes, determined in terms of middle vibrations**– special course, where functions middle integral vibration and their properties, function properties, expressed in term of middle vibrations, functions classes, determined through middle vibrations are studied.**Gravimetric estimations for Hardy-Littlewoods maximally operator**– special course, where gravimetric estimations for Hardy-Littlewoods maximally operator are considered and properties of types of Makenhaupt, Gering classes, satisfying reverse Gilder inequality are studied.**Financial mathematics bases**– special course which acquaint students with simple and complex interests, simplest streams of payment cost, rents basic types, credits repayment, capital investment efficiency and cost of securities evaluation.**Casual processes and their application in insurance and financial mathematics**– annual course which consist of two parts: basic theories of random processes (36 hours) and probabilistic models in insurance and stochastic financial mathematics (24 hours).**Life-insurance**– half-year course which gives simple and concise summer of main mathematical models and methods that are required for determination of life-span descriptions, valid for one occasion and periodic bonuses, insurance raises, backlogs for different types of insurance and pension charts. Course’s material forms basic theoretical base of insurance business.**Mathematical bases of economic risk**– special course which acquaints students with mathematical risks analysis in insurance and stochastic models of prices changing and forming.**Queuing systems**– one of the section of the course “Operations analysis”. It requires knowledge of chances theory. The course is oriented on practical issues which can ba described by mathematical methods.**Mathematical methods in biology**– course which acquaints students with mathematical concepts and data analyzing popular methods, forms skills in statistic application package.