Mathematics and Statistics

1. Basic concepts:- Number sets (N, Z, Q, R), ordering of the real line and the symbol of infinite.- Absolute value, powers and roots.- The Cartesian plane: coordinates, straight lines, parabolas, circles, equilateral hyperbolas.- Properties of elementary functions: powers with real exponent, exponentials, logarithms and trigonometric functions.- Equations and inequalities: algebraic of first and second degree, rational, with roots, exponential and logarithmic. 2. Real functions of one real variable:- Maps. Domain, codomain, graph of a function.- Limits. Indeterminate forms and limits of special interest.- Continuity and properties of continuous functions.- Derivatives: definition and geometrical meaning, tangent lines. Computation of derivatives. Monotony and search for extremal points of a function. - Second derivative, concavity and inflection points.- Horizontal, vertical and oblique asymptotes.- Qualitative study of the graph of a function. 3. Integrals:- Indefinite integrals: definition, antiderivatives of elementary functions, methods of computation of the antiderivative of a function.- Definite integrals: geometrical meaning and basic properties, the fundamental theorem of calculus, improper integrals.- Computation of the area of a plane region.

1 - Statistic language; 2 - Organization and graphical representations of the data; 3 - data descriptors: measures of central tendency (mean, median and mode), measures of dispersion and variation; 4 - bivariate analysis with qualitative and quantitative data; 5 - Analysis of the dependence between two statistical variables. Correlation and interpolation (linear and not linear) 6 - Probability; 7 - Random variables and distribution of probability. The Normal distribution; 8 - Sampling distributions and point estimation. Desirable properties of point estimators. Distribution of sample mean. Central Limit Theorem. Confidence intervals for mean. 9 - Fundamentals on Hypothesis testing; 10 - Test on a single population. Hypothesis test on mean. Hypothesis test on proportion. 11 - Comparing two population. Hypothesis test on the difference between means of two populations (with paired and non-paired samples).