Mathematics and Statistics

Numerical sets.: N, Z, Q e R. The coordinate plane: straight lines, parabolas, circles. Outline of trigonometry. Elementary functions and their graph. Equations, inequalities and system of algebraic and irrational inequalities. Generalities about real funcion: domain, range, injective and surjective functions, composed functions, inverse functions, geometric transforms of elementary functions. Limits: computing limits, comparison of infinites and infinitesimals, indeterminate forms. Continuity. Asymptotes: vertical, horizontal and slant. Differential calculus: first derivative, tangent line, monotonicity, global and local maxima and minima. Second derivative: convexity and concavity, inflection points. Integral calculus. Computation of plane areas.

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.