Insegnamento a.a. 2025-2026

30449 - MATHEMATICS - MODULE 2 (APPLIED MATHEMATICS)

Department of Decision Sciences

code 30448 Mathematics - Module 1 (Theory and methods) and code 30449 Mathematics - Module 2 (Applied mathematics) are respectively the first and the second module of the course code 30447 Mathematics

Class timetable
Exam timetable

Course taught in English
Go to class group/s: 13
BESS (9 credits - II sem. - OB  |  SECS-S/06)
Course Director:
SIMONE CERREIA VIOGLIO

Classes: 13 (II sem.)
Instructors:
Class 13: MAURO D'AMICO


Suggested background knowledge

The content of MATHEMATICS – MODULE 1 (THEORY AND METHODS), or an equivalent course, constitutes a relevant foundation of background knowledge for this course.

Mission & Content Summary

MISSION

Mathematics is the language in which most modern economics is written. This course aims to provide the basic mathematical tools that students need to complete their undergraduate studies in economics. In addition, it develops the analytical thinking skills that students will need throughout their academic careers.

CONTENT SUMMARY

  • Integration: Riemann Integral, Improper Integrals, Parametric and Stieltjes Intergrals.
  • Financial mathematics: Contingent Claims, Completeness, Arrow Security, Arbitrage, Fundamental Theorem of Finance.

  • Linear algebra: Symmetric Matrix, Spectral Theorem, Eigenvalues, Quadratic Form, Positive Definite Matrices, Principal Minors.

  • Multivariate calculus and optimization: Jacobian, Hessian, Taylor Expansion, Lagrange Multipliers, Constrained Optimization, Implicit Function Theorem.


Intended Learning Outcomes (ILO)

KNOWLEDGE AND UNDERSTANDING

At the end of the course student will be able to...
  • Carry out a formal mathematical proof.
  • Recognize the abstract mathematical structures that underlie modern economic theories.
  • Have an understanding of the foundations of the modern theory of Finance.
  • Solve constrained optimization problems.

APPLYING KNOWLEDGE AND UNDERSTANDING

At the end of the course student will be able to...
  • Apply calculus' methods to solve an optimization problem and to compute integrals.
  • Apply to economics and to the social sciences the techniques of contemporary mathematics.

Teaching methods

  • Lectures
  • Practical Exercises

DETAILS

Throughout the course, the exercise sessions and theoretical lectures are interconnected.


Assessment methods

  Continuous assessment Partial exams General exam
  • Written individual exam (traditional/online)
   x x

ATTENDING AND NOT ATTENDING STUDENTS

The exam is written. Each student can choose whether to take:

General Exam: a single final exam. The General Exam is worth 100% of the final grade.

Partial Exams: 2 partial written exams. Each partial written exam is worth 50% of the final grade (100% in total).


Teaching materials


ATTENDING AND NOT ATTENDING STUDENTS

  • S. CERREIA-VIOGLIO, M. MARINACCI, E. VIGNA, Principles of Mathematics and Economics, draft version (March 2024). Available on BBoard in PDF format.

Last change 30/11/2025 14:57