Mathematics and Statistics

Basics of set theory. Number sets (N, Z, Q, R), real numbers, Dedekind Axiom. Rational equations. Maps (domain, codomain, image, definition set, composition of maps), injective maps, invertible maps, absolute value, powers, exponentials, logarithms, trigonometric functions and their inverses. Exponential, logarithmic and trigonometric equations. Basics of analytic geometry: distance between two points in the plane, equation of a line, parallel and orthogonal lines; second degree curves (circle, ellipsis, hyperbole, parabola). Resolution of linear systems with Gauss method. Limits of sequences: definitions, operations with limits, some special limits. Limits of functions and continuity: definitions, examples, right and left limit, types of discontinuity, zeroes, intermediate values, Weierstrass Theorem. Derivatives: definition and geometrical meaning, derivatives of elementary functions; operations with derivatives; derivatives of composite and inverse maps. De L'Hopital Theorem. Analysis of the graph of a function: extremal points, Rolle and Lagrange Theorem, increasing and decreasing functions, convex functions, asymptotes. Integrals: geometrical meaning and basic properties. Linearity of integral. Average Theorem. Primitives and Fundamental Theorem of Calculus. Integrals of rational functions, some integration techniques.

1-The language of statistics. 2-Organization of data end graphical representation. 3-Position and variability indices (mean, mode, median), variance. 4-Bivariate analysis for qualitative or quantitive data. 5-Probability, probability rules. Independents events. Total probability theorem. Bayes theorem. 6-Random variables, distributions. Distributions: binomial, geometrical, Poisson, Gaussian. 7-Random samples. Confidence intervals. Estimation. Sample mean. Central Limit Theorem. Confidence interval for the mean. 8-Hypothesis tests: fundamentals, phases, simple test. 9-Hypothesis test on a single population proportion. 10- Test and confidence interval for the difference of two means using independent sample. 11-Correlation analysis. Univariate linear regression. Inference. 12-Analysis of variance.