GEOMETRY: 1) LINEAR ALGEBRA (3 CFU):
Preliminary notions: sets, number sets, funcions; real line, cartesian plane. Vectors in R^n. Matrices. Rank. Gauss elimination. Detrminat of square matrices and applications. Lines, Planes and circles. Linear systems: study and resolution. Change of plane coordinates. Linear applications. Diagonalization.
2) COMBINATORICS AND DISCRETE PROBABILITY (2 CFU):
Induction. Binomial coefficient. Permutations, dispositions and combinations. Sample and probability space. Notion of probability. Conditional probability. Independence. Discrete random variables. Some important distributions.
ANALYSIS (7 CFU):
Real line; max and min, sup and inf in R; raw properties of functions of a real variable (monotonicity, boundedness, convexity). Elementary functions, graphical representation and properties. Limits and continuity. Derivatives (definitions, theorems, calculus, global properties). Study of the graph of a function. Approximation (Taylor's theorem). Integrals: definition, theorems, methods of integration. Improper integrals. Differential equations.