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Matematica per EPE

Semestre 1-2 · 27279 · Corso di laurea in Economia, Politica ed Etica · 12CFU · EN


Mathematics A
This course introduces the fundamental concepts of mathematical analysis, starting from the basic language of sets, functions, and numbers. It develops tools for the study of single-variable functions, including limits, derivatives, Taylor expansions, and other properties. Optimization in one dimension and basic notions of convexity are also covered, together with an introduction to integral calculus.


Mathematics B
This course builds on the foundations of Mathematics A and extends them to multivariable contexts. It covers linear algebra techniques and the study of functions of several variables, including gradients and other properties. Topics also include convexity/concavity and optimization methods, with special emphasis on the Lagrange method and applications in economics. Time permitting, a short introduction to probability theory is provided.

Docenti: Luciano Marzufero, Martin Meier, Paolo Maraner

Ore didattica frontale: 72 (36 + 36)
Ore di laboratorio: 72 (36 + 36)
Obbligo di frequenza: Suggested, but not mandatory

Argomenti dell'insegnamento
MATHEMATICS A: 1. Basic mathematical concepts: sets, relations, functions, numbers, limits, absolute values. 2. Functions of one variable: basic properties, derivatives and their calculus, Taylor approximations, Newton’s method. 3. Convexity and single-variable optimization (Fermat’s rule and sufficient optimality conditions). 4. Elements of integration (indefinite, definite and improper). MATHEMATICS B: 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 and concavity. 3. Multivariable optimization, Lagrange method and economic applications. 4. If enough time remains: Basics of probability theory.

Insegnamenti propedeutici
None

Modalità di insegnamento
Lectures and exercise sessions

Modalità d'esame
A written final exam (questions and problems to solve) covering both M1 and M2 parts (M1 partial exam and M2 partial exam, respectively). Written exam of maximal 120min at the end of each module. There is no different assessment for attending and non-attending students.

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

Bibliografia obbligatoria
  • Lecture notes provided in due course (available in the Reserve Collection)
  • L. Peccati, S. Salsa, A. Squellati, "Mathematics for Economics and Business", Bocconi University Press, 2016.
  • Further readings will be announced at the beginning of the course.



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Obiettivi di sviluppo sostenibile
Questa attività didattica contribuisce al raggiungimento dei seguenti Obiettivi di Sviluppo sostenibile.

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Modules

Semestre 1 · 27279A · Corso di laurea in Economia, Politica ed Etica · 6CFU · EN

Module A — Matematica A per EPE

The course "Mathematics A for EPE M1" deals with basic mathematical concepts like sets, relations, functions, numbers, limits and absolute values. Moreover we will introduce functions of one variable by studying their basic properties, derivatives and their calculus, Taylor approximations and the Newton's method. We will also address the single-variable optimization (Fermat's rule and sufficient optimality conditions) and the elements of integration.

Docenti: Martin Meier, Luciano Marzufero

Ore didattica frontale: 36
Ore di laboratorio: 36

Modalità di insegnamento
Lectures and exercise sessions

Bibliografia obbligatoria

Lecture notes provided in due course (available in the Reserve Collection)

L. Peccati, S. Salsa, A. Squellati, Mathematics for Economics and Business, Bocconi University Press, 2016.



Semestre 2 · 27279B · Corso di laurea in Economia, Politica ed Etica · 6CFU · EN

Module B — Matematica B per EPE

Matrix calculus, rank and linear independence, systems of linear equations, Gaussian
elimination, applications.
• Functions of several variables: gradients, Hesse matrices, Taylor approximation, convexity
and concavity.
• Multivariable optimization, Lagrange method and economic applications.
• If enough time remains: Basics of probability theory.

Docenti: Paolo Maraner, Martin Meier

Ore didattica frontale: 36
Ore di laboratorio: -

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