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ÚSI-ESMATAcad. year: 2019/2020
Basic mathematical notions. Concept of a function, sequences, series. Vector spaces (linear combination of vectors, linear dependence, independence vectors, base, dimension of a vector space). Matrices and determinants. Systems of linear equations and their solution. Differential calculus of one variable, limit, continuity, derivative of a function. Derivatives of higher orders, l´Hospital rule, behavior of a function. Integral calculus of fuctions of one variable, indefinite integral. Integration by parts, substitution methods. Definite integral and its applications. Introduction to descriptive statistics. Introduction to probability. Some probability models (classical, discrete, geometrical), conditional probability, dependence and independence of random events. Total probability rule and Bayes theorem. Discrete random variables (probability mass function, cumulative distribution function, mean and variance). Discrete probability distributions (binomial, geometric, hypergeometric, Poisson, uniform). Continuous random variables (probability density function, distrubution function, mean, variance, quantiles). Exponencial distribution. Normal distribution. Central limit theorem. Testing of statistical hypotheses (t-test).
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