00679 - Foundations of Mathematics

Learning outcomes

At the end of the course, the student will have a basic knowledge of the mathematical concepts and techniques that are of central importance for economics, finance, statistics and econometrics. The student will be able, in particular, to apply fruitfully tools and concepts from linear algebra, differential calculus and integral calculus to a wide range of topics and models in economics, finance and management.

Course contents

· Linear functions and linear models

· Systems of linear equations

· Matrix algebra and applications

· Mathematics of finance

· Nonlinear functions and models

· Introduction to derivatives and differentiation techniques

· Application of derivatives

· Introduction to integral calculus and integration techniques

· Applications of integral calculus

· Multivariable functions

· Introduction to optimization

Readings/Bibliography

· Stefan Waner, Steven R. Costenoble, ”Strumenti quantitativi per la gestione aziendale” (a cura di Marzia De Donno, Paola Modesti, Simona Sanfelici), 2018 (Seconda Edizione), Apogeo Education, Maggioli Editore, ISBN: 978-8891621207.

(or: Stefan Waner, Steven R. Costenoble, ”Strumenti quantitativi per la gestione aziendale” (a cura di Marco Li Calzi), 2006 (1 Edizione), Apogeo Education, Maggioli Editore, ISBN: 9788838785764)

· Knut Sydsaeter, Peter Hammond, Arne Strøm, “Metodi matematici per l'analisi economica e finanziaria” (a cura di D. La Torre e C. Pellizzari), Pearson, 2015. ISBN: 978-8865189535.

· Peccati, Salsa, Squellati, “Matematica per l’economia e l’azienda”, 2018 (Quarta Edizione), Egea, ISBN: 978-8823822696.

Teaching methods

Class lectures. During the class lectures (as well as in the additional exercise classes) each topic will be illustrated by examples, worked-out exercises and applications to Economics and Finance.

Assessment methods

Written examination.

The exam of the first (winter) session can be taken in two steps: a midterm exam (at the end of the first half of the course) and a final exam (also called second midterm or second partial exam). Each part is weighted 50% in the final grade.

The written exam aims at testing the student's ability to understand and effectively apply the basic and advanced concepts and techniques learned in the course to specific problems in calculus, linear algebra and their economic applications.

Grade rejection

Students can reject the grade obtained at the exam once. To this end, students must email a request to the instructor within the date set for registration. The instructor will confirm reception of the request within the same date.

Rejection is intended with respect to the grade of the whole exam (which can be, in particular, a weighted average of the grades obtained in the midterm exam and the final exam). If the grade is rejected, the student must retake the full exam (consisting of both parts). The only "grade" that can be rejected without any communication from the student is the one of the first mid-term: in fact, at the end of the course, the student can either take the second mid-term or opt for the full exam (thus automatically losing the grade obtained in the first mid-term).

Students sitting the first mid-term can take the second mid-term only on the first examination date after the end of the course. If a student fails or rejects the grade obtained, he/she will have to resit the full exam and will lose the grade obtained in the first mid-term.

Teaching tools

Blackboard, slides.

Prior to the beginning of the course, a Crash Course in Mathematics will cover a number of introductory topics (so-called precalculus).

Office hours

See the website of Roberto Dieci