93095 - Mathematics

Learning outcomes

At the end of Mathematics course, the student will be able to apply all the basic elements of Calculus in one variable and some relevant topics in several variables. Also the basic elements of Linear Algebra will be approached together with eigenvalues and eigenvectors theory.

Course contents

The numerical sets N, Z, Q, R and their structures.

The real function of a real variable: basic definitions, elementary functions and examples of mathematical models in Finance.

The discrete Mathematics: sequences, limits and series.

Limits for real functions: properties and theorems related to the continuous property, local and global.

The concept of derivatoive and its geometric meaning. Derivatives properties, computation rules and theorems: Rolle, Lagrange and Cauchy.

Unconstrained optimization in one variable. Convexity and concavity Taylor formula and Taylor-MacLaurin formula.

The concept of anti-derivative and its properties. Integrability methods and theorems. Generalized integrals.

N-dimensional vector spaces; matrices, determinat and rank.

Linear systems, Cramer and Rouchè-Capelli theorems.

Eigenvalues, eigenvectors and their meaning.

Introductory elements of several variables unconstrained optimization. Gradient vector and Hessian matrix.

Readings/Bibliography

K. Sydsaeter, P. Hammond, A. Strom (a cura di D. La Torre), Metodi Matematici per l'Analisi Economica e Finanziaria, Pearson.

The book can also be found in English.

A booklet based on solved exam exercises will be downloadable from the present page.

Teaching methods

The active participation of students during traditional lectures is encouraged by the proposal of open problems whose solutions are shared collegially.

The individual training path is verified through two tools: at the end of each lesson, applications related to the theoretical aspects illustrated are assigned, the solutions of which are illustrated at the beginning of the next lesson. Furthermore, at the end of each macro topic, tests consisting of 30 questions to be solved as part of personal study are distributed. Students are invited to present short optional case studies on the financial applications of mathematics using material provided by the teacher or found in authoritative sources; every week, groups of 2-3 students are organized for the presentations to be given in class.

The weekly exercises held by the tutor provide students with a further opportunity to verify the acquisition of the knowledge illustrated in class.

Assessment methods

The individual training path and learning are verified through two tools: at the end of each lesson, applications related to the theoretical aspects illustrated are assigned, the solutions of which are illustrated at the beginning of the next lesson. Furthermore, at the end of each macro topic, tests consisting of 30 questions are distributed to be solved within the scope of personal study and which are then corrected in class.

The final written test in Mathematics is divided into two partial tests whose score is expressed in thirtieths.

The final score is therefore given by the average of the two partial written tests and allows you to pass the exam if this average is greater than or equal to 18. Each of the two written tests is organized into 10-12 independent exercises, each exercise assigns a score written clearly in the test. In the event that the result of the first partial written test is not satisfactory, the student can repeat it on the occasion of the second partial written test. The oral test is optional and the final grade of the exam is given by the average of the written and oral grades.

The written tests are open-book, so the student can consult notes and texts during the exams, he/she cannot use the programmable calculator.

Students who present a case study on the applications of mathematics in the classroom in an effective and clear manner are awarded an additional point to be added to the average of the written tests.

Teaching tools

The attendance of the crash course MATH&FIN is strongly recommended, together with the attendance of the exercises based course.

Students with learning disorders and\or temporary or permanent disabilities: please, contact the office responsible (https://site.unibo.it/studenti-con-disabilita-e-dsa/en/for-students ) as soon as possible so that they can propose acceptable adjustments. The request for adaptation must be submitted in advance (15 days before the exam date) to the lecturer, who will assess the appropriateness of the adjustments, taking into account the teaching objectives.

Office hours

See the website of Maria Letizia Guerra