Department of Applied Mathematics
Formulation of the problem of linear programming, transcription of some practical problems to the linear programming problems. Simplex and convex polyedra. Simplex method, basic solutions, duality principle in linear programming, stability of solution of linear programming problem. Traffic problem.
Department of Applied Mathematics
Formulation of the task of integer programming, branch and bound method of numerical solution, problems about knapsack, travelling salesman, sets, location of stores and post boxes, tasks of scheduling, heuristics, metaheuristics - genetic algorithms, ant colony optimization.
Department of Applied Mathematics
Stocastic modelling, estimation, prediction, filtration, control, methods of data analysis - k-means, DBSCAN, naive Bayes, decision trees, support vector machine.
Department of Applied Mathematics
Stocastic modelling, estimation, prediction, filtration, control, methods of data analysis: k-means, DBSCAN, naive Bayes, decision trees, support vector machine.
Department of Applied Mathematics
Stocastic modelling, estimation, prediction, filtration, control, methods of data analysis: k-means, DBSCAN, naive Bayes, decision trees, support vector machine.
Department of Applied Mathematics
• Introduction of basic notions: system, model • Stochastic model and its estimation (Bayes rule) • Normal and categorical models, estimation • Prediction with dynamic categorical and normal models • State filtration, Kalman filter • Basics of the dynamic programming method for minimization of quadratic criterion • Control of dynamic system with normal and categorical model • Estimation by the method Naive Bayes • Logistic and Poisson regresion • Clustering (data separation, fuzzy clustering, density clustering, hierarchical clustering) • Classification (K-nearest neighbour, Support vector machines) • Decision trees and their use for classification • Recollection and repetition
Department of Applied Mathematics
System. Regression, discrete and logistic models. Bayesian estimation of model parameters. Parameter estimation of normal regression, discrete and logistic models. Classification with logistic model. One-step and multi-step prediction with regression and discrete models. State model. State estimation. Kalman filter. Control with regression and discrete models.
Department of Applied Mathematics
Basics of probability Descriptive statistics Population and sample, limit theorem Point estimate, construction and properties Interval estimates Parametric tests Nonparametric tests Regression and correlation analysis
Department of Applied Mathematics
Definition of probability, random variable and its description, known distributions, random vector, function of random variable. Methods of point estimation. Testing of statistical hypothesis. Regression and correlation, linear regression, correlation coefficient, coefficient of determination, the general linear model, statistical inference in linear regression, analysis of variance, multiple regression, the use of matrices in regression.