The aim of the course is to provide working knowledge of techniques and tools of linear algebra that will be needed in the study of economics, management and finance. At the end of the course students should be able to solve problems adapting all the techniques learned and to discuss the importance of the main theoretical results presented during the course.

Knowledge and understanding: The course will provide many basic mathematical tools, together with their theoretical interpretation and with examples of their possible applications to quantitative analysis in Economics, Finance, Statistics, with the help of the MATLAB software when needed. Applying knowledge and understanding: Students will be able to adapt and apply a variety of techniques to solve non-standard mathematical problems, as well as to discuss the arguments that justify usage of such techniques. Making judgements: Students are expected to be able to choose properly the best solution strategy for each mathematical problem and to understand how to apply concepts and tools to economics and financial problems. This ability will be evaluated via exercises and exams. Communications Skills: Students will learn how to properly formulate and communicate mathematical concepts and logical reasoning, using the English language. They will also understand how different concrete problems can be studied using similar techniques. Learning skills: Students will broaden their mathematical knowledge and reasoning and they will become able to work independently with advanced mathematical concepts and tools; they will also learn basics of the MATLAB language.

An introduction to linear algebra, with applications to economics. Matrices, Systems of Linear Equations, Vector Spaces, Subspaces and Bases, Eigenvalues and Eigenvectors, Orthogonality, Least-squares, linear programming.

Main text: R.Larson, Elementary Linear Algebra, 8th edition, Cengage Other required readings: D.C. Lay, S.R. Lay and J.J. McDonald, Linear Algebra and Its Applications, 5th Edition, Pearson. S.J. Leon, Linear Algebra with Applications, 8th Edition, Pearson. K.Sydsaeter, P.J.Hammond, A.Strom, A.Carvajal, Essential Mathematics for Economic Analysis, 6th Edition, Pearson. W.H.Green, Econometric Analysis, 8th Edition, Pearson

Lectures on the main theoretical aspects of each topic, with examples and short exercises. Weekly exercise sessions: written exercises + MatLab.

Student assessments in this course will be determined by individual performance, active participation in class activities, and consistent engagement with assigned tasks. Throughout the semester, students will complete MATLAB evaluations, which together will account for 20% of the final grade. These evaluations will be conducted during the course as well as in the final exam. A midterm exam will be held after the sixth week of classes and will contribute 10% of the final grade, but only if it improves the student’s overall average. The exact date of the midterm will be announced no later than the third week of the semester. It is important to note that retakes will not be permitted. Final performance will also reflect active class participation and the completion of weekly assignments, which may earn students bonus points, or fractions of them, to be added to their final grade. The weight of the final exam will vary depending on whether the midterm grade is applied: if the midterm grade counts, the final exam will represent 70% of the overall grade; if not, it will represent 80%. The final exam will therefore include both the written component and the completion of the MATLAB exam. In all written examinations, students are expected to present solutions clearly and systematically, providing appropriate explanations and justifications, and using precise technical language. Answers should demonstrate not only theoretical understanding but also the ability to apply the course material in practical contexts. After each written exam, and before final grades are officially recorded, students will be offered the opportunity to review their work in a dedicated meeting with the instructors. Special Conditions: Students who do not participate in class activities or have absences will have the percentage normally attributed to these components added to the weight of the final exam, ensuring that the final evaluation constitutes a total of 100%.

Interview with the instructor.