Mathematics and Statistics

Mathematics
· Number sets;
· Set operations;
· Direct and reverse proportionality;
· Percentages;
· Radicals;
· Logarithms;
· Exponential;
· Integer and fractional first-degree equations;
· Integer and fractional second-degree equations;
· Equations above the second degree;
· Systems of integer and fractional first degree equations;
· Systems of integer and fractional second-degree equations;
· Whole and fractional first-degree inequalities;
· Whole and fractional second degree inequalities;
· Whole and fractional systems of first-degree inequalities;
· Whole and fractional systems of second-degree inequalities;
· Trigonometry elements;
· Limits;
· Derivatives;
· Elements of mathematical logic;
· Algorithms

Statistics

Samples and populations. Types of variables: qualitative, quantitative. Absolute and relative frequency
Diagrams and histograms, frequency distribution, cumulative frequencies, quantiles and percentiles. Box-plot.
Measures of central tendency: mean, median, mode. Measures of dispersion: range of variation, deviance, variance, standard deviation, coefficient of variation
Probability. Basic rules of probability. Discrete and continue probability distribution
Binomial distribution. Poisson distribution
Normal distribution. Standardization of a variable. Normalized standard distribution. Asymmetry and kurtosis
The central limit theorem. The sampling distribution of an estimate: the standard error. The confidence interval. Student's t-distribution
Verifying hypotheses. Null hypothesis and alternative statistical significance and P-value Error types I and II
Comparison between a sample mean and a population mean. Comparison between two sample means
The chi-square test. The chi-square distribution. The 2x2 contingency table
Relationship between variables: covariance. Correlation and linear regression. Regression analysis
Analysis of variance: the comparison between means of several groups:. The F-distribution