COURSE CONTENT:
Approximate numbers: sources of errors, significant figures, rounding numbers, errors of arithmetic operations and functions, error progression. Nonlinear equations: root isolation, bisection method, NewtonRaphson method, secant method, method of successive approximations. Interpolation: interpolation problem, finite differences, Newton's method, Lagrange's method, spline method. Numerical differentiation and integration: numerical differentiation of continuous and discrete functions, numerical integration, trapezoidal formula, Simpson's formula. Ordinary differential equations: Euler's method, RungeKutta methods, finite difference method. Optimization: nonderivative and derivative minimisation methods, simplex, steepest descents algorithm, conjugate gradients algorithm, NewtonRaphson method, global search, Monte Carlo method, genetic algorithm. Probability theory: classical definition of probability, axiomatic definition of probability, conditional probability, total probability, Bayes formula, basics of combinatorics, fundamental theorem of counting, variations, permutations, combinations. Basic statistics: descriptive statistics, measures of central tendency and dispersion, sampling and graphical representation of data. Discrete randrom variables: random variables, probability function, cumulative distribution function, moments of distribution, uniform distribution, Bernoulli trials, binomial distribution, Poisson distribution, hypergeometric distribution, estimate of distribution parameters. Continuous distribution function: probabiltiy density function, cumulative distribution function, moments of distribution, continuous uniform distribution, Gauss distribution, exponential distribution, estimate of distribution parameters. Statistical hypothesis testing: nullhypothesis, statistical model checking, location and dispersion tests. Regression: linear regression and correlation, confidence intervals, nonlinear regression.
LEARNING OUTCOMES:
 to discriminate the exact and the approximate numbers
 to calculate the relative and the absolute error
 to solve nonlinear equations using adequate numerical methods
 to use numerical methods for interpolation
 to use numerical methods for differentiation and integration
 to discriminate numerical methods for optimisation of functions
 to explain basic principles of probability theory
 to explain basic principles of statistics
 to discriminate discrete and continuous variables
 to explain probability density function and cumulative distribution function
 to use binomial, Poisson, and hypergeometric distributions
 to use normal (Gaussian) distribution and uniform distribution
 to define statistical tests and hypothesis
 to use regression analysis

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