Argomenti dell'insegnamento
M1: Sets, relations, functions. Basic algebra, numbers, approximations, sequences and their limits, series, geometric series. Real functions (polynomial, rational, irrational, exponential and logarithmic functions), limits of functions, differentiation,Taylor approximations, Newton’s method, convexity, single variable optimization, integration. M2: 1. Matrix calculus, rank and linear independence, systems of linear equations, Gaussian elimination, applications. 2. Functions of several variables: gradients, Hesse matrices, Taylor approximation, convexity. 3. Multivariable optimization, Lagrange method and economic applications. Simple least square regression. 4. If enough time remains: Basics of probability theory.

Insegnamenti propedeutici
none

Modalità di insegnamento
Lectures and exercise sessions

Modalità d'esame
M1: A written final exam (questions and problems to solve) which counts 100% for the M1 partial grade. M2: A written final exam (questions and problems to solve) which counts 100% for the M2 partial grade. The final mark is the average of the marks of M1 and M2 - There is no different assessment for attending and non-attending students.

Criteri di valutazione
Final grade: 50% grade for M1 partial grade, 50% for M2 partial grade. The results of assignments and partial exams are only valid for the academic year in question. They cannot be carried over beyond that time frame.