Introduction and review of basic mathematical notions. Natural numbers, sum and product of natural numbers. Neutral element and inverses. Relative numbers and rational numbers. Irrational and real numbers. Consistency and density of the real numbers. Units of measurement and conversion factors. Intervals. Operations. Scientific notation. Approximations. Equations and inequalities. Sets, inclusion relation, set representation with Eulero-Venn diagrams. Intersection, union, difference. Complement operation and cartesian product. Properties of the set operations.
Functions and Properties of function. Injective, surjective, bijective functions. Real Functions of a Real Variable and their Geometrical Representation: graph, domain, codomain and image. Symmetry. Increasing and decreasing functions. Dependent and independent variables. Functional notation. Range and domain. The graph of a function. Function transformations: shifting, stretching, reflecting, sum, product and composition. Inverse functions. One-to-one and invertible functions. Determining the graph and equation of the inverse.
Algebraic functions. Linear functions, quadratic functions, polynomial, power and rational functions. Transcendental functions: exponential and logarithmic functions. Introduction to trigonometric functions. Function composition. The inverse function.
Limits and Continuity. Definition of limits, properties and calculating the limits. Limits of functions, continuity and asymptotes.
Derivatives The Tangent to a Curve and the Derivative of a Function. Definition and calculation of derivative: algebraic and transcendental functions. The First and Second Derivatives. Left and right derivatives, higher order derivatives. Necessary condition of differentiability (with proof). Non differentiable functions.. Global and local maximum and minimum. Extreme value theorem. Differentiability and monotonicity. Differentiability and local extremes. Concavity and inflection points (with proofs). Necessary and sufficient conditions for the existence of inflection points (with proofs). De l’Hospital Theorem.
Integration. Definite integration. Integrable and non integrable functions. Properties of the definite integral. Indefinite integration and antiderivatives. The fundamental theorem of calculus. Integration formulas. Integration by part and substitution.

Linear algebra. Vectors, vector spaces, geometric representation of vectors, linear dependence and independence. Matrices and properties. Determinants. Properties of determinants. Rank of a matrix. Matrix operations. Systems of linear equations. Rouché-Capelli theorem. Cramer rule. Eigenvalues and eigenvectors.
Statistics. Notions of descriptive statistics: variables, categories and statistical units. Frequency distribution and graphical representations. Position measures: mean, median and mode. Variability and shape of a distribution. Analysis of the association between two characters, the ordinary least squares (OLS) estimator. Introduction to the linear regression models.
Introduction to probability. Notion of event. Probability distributions. Axioms of probability. Independent events and incompatible events. Conditional probability. Bayes theorem. Random variables and probability distributions. Introduction to statistical inference and the theory of hypothesis testing.

REFERENCE TEXTS:

- Bodine et al (2017) Matematica per le scienze della vita. UTET
-Slides of the course and exercises made available in the student's portal.