MASSIMILIANO FREZZA

MATHEMATICS FOR ECONOMICS AND FINANCE A.Y. 2025-2026

Classes will start on September 22th 2025 with the schedule:

• Monday 16-18 (room 6c)
• Tuesday 10-12 (room 6b)
• Thursday 16-18 (room 6b)

All instructional materials (including slides and other resources), along with all pertinent information and communications, will be made available on the official platform of Classroom

Reference books:
-     J. Bergin, Mathematics for Economists with Applications, Routledge, 2015  (Chapters 2-10-11-12-16-17)
-    S. Lang, Linear Algebra, Springer-Verlag, 3rd Ed., 1987         (Chapters 1-2-3-4-6)
-    C. P. Simon, L. Blume, Mathematics for Economists, Norton, 1994  (Chapters 14-17-18)
-      Lecture support notes made available on the course platform  (Classroom)
 

SYLLABUS 

1) LINEAR ALGEBRA

• Vector spaces and subspaces
• Concepts of dimension and basis of a vector space
• Change of basis in a vector space and its effect on the components of a vector
• Linear transformations between two vector spaces
• Association of a matrix to a linear transformation
• Kernel and image of a linear application and their properties
• Basis of the image and kernel

Textbooks
1) Course materials uploaded on Classroom (p. 1-131). 
2) Serge Lang (Chapters 1-2-3-4)
3) Bergin (Chapter 2)

2) EIGENVALUES AND EIGENVECTOR - QUADRATIC FORMS

• Definitions and properties
• Eigenvalues and eigenvectors of symmetric matrices
• Diagonalization of a linear transformation
• Quadratic forms
• Positive and negative (semi) definiteness
• Criteria for positive and negative (semi) definiteness
• Canonical form of a quadratic form
• Definiteness with equality constraints

Textbooks
1) Course materials uploaded on Classroom (pp. 132-229). 
2) Serge Lang (Chapter 5)
3) Bergin (Chapter 10)

3) FUNCTIONS AND CALCULUS OF SEVERAL VARIABLES

• Functions between Euclidean spaces
• Basics from domain, limits and continuity
• Directional derivative: partial derivative as particular case
• Gradient vector and Hessian matrix
• Tangent plane
• Homogeneous functions and Euler´s theorem
• Multivariable Taylor Polynomial

Textbooks
1)Course materials uploaded on Classroom (pp. 230-304).
2) Simon and Blume( Chapter 14)

4) BASIC OF OPTIMIZATION

• Unconstrained optimization: first and second order conditions
• Constrained optimization: Lagrange’s multipliers

Textbooks
1)Course materials uploaded on Classroom (pp. 305-342)2) 
2) Bergin (Chapters 11-12)
3)Simon and Blume (Chapters 17-18.4)

5) DIFFERENTIAL EQUATIONS

• Linear differential equations of order n: homogeneous and non-homogeneous case
• First order linear differential equations: constant and variable coefficients
• Bernoulli differential equation
• Linear differential equations of order greater than 1 with constant coefficients

Textbooks
1) Course materials uploaded on Classroom (pp. 343-387)
2) Bergin (Chapter 16-17.4)

 
Matematica corso base (9 cfu) - Economia e Finanza (Canale: N-Z) (2024-2025)
Il corso inizierà il 18 settembre 2024.
Orario delle lezioni:
mercoledì   10:00-12:00 (aula Ezio Tarantelli)
giovedì    12:00-14:00 (aula Federico Caffè)
venerdì   10:00-12:00 (aula Federico Caffè)
 
Il corso sarà tenuto congiuntamente con la Prof.ssa Marconi
 
 
Matematica Finanziaria (9 cfu) - Scienze Aziendali  (2024-2025)
Il corso inizierà il 17 Febbraio 2025.
Orario delle lezioni:
lunedì   20:00-22:00 (auletta di Matematica, 1° piano)
martedì    20:00-22:00 (auletta di Matematica, 1° piano)
mercoledì   18:00-20:00 (auletta di Matematica, 1° piano)
 
 
Matematica applicata per la sostenibilità: modelli, calcoli, IA (9 cfu) (2024-2025)
Il corso inizierà il 23 settembre 2024.
Orario delle lezioni:
Lunedì   14:00-17:00 (aula 11)
Giovedì    09:00-12:00 (aula multimediale - Prof. Vitulano)

Il corso sarà tenuto congiuntamente con il Prof. Vitulano

Matematica per il machine learning (9 cfu) (2023-2024 e precedenti)
L´esame consiste in due prove relative rispettivamente alla prima parte (con me) ed alla seconda con il Prof. Vitulano. Entrambe le prove devono essere svolte nello stesso appello. Si consiglia di contattare i docenti per delucidazioni prima di iscriversi all´esame.