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, 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. The study material is given to the students some days before the session.

Students will be evaluated through a written and an oral exam. Each written exam will consist of quizzes and written exercises. Students are required to solve exercises with suitable explanations and arguments, proving knowledge of the necessary instruments and using proper mathematical language. The written exam is sufficient with a grade of 18 or higher and gives aces to the oral exam. In place of the final written exam, students may take two midterm exams during the course. Each midterm exam is passed with a grade of 18 or higher and the grade for the written exam is given by the average of the two midterm exams. The oral exam is compulsory for students who get a grade of 27 or higher. The students in this situation who do not take the oral exam will have a final grade of 26. The oral exam will also be required upon request from the teacher. All the students who obtained a grade between 18 and 26 and who are not asked by the teacher to sit for the oral exam can register the grade for the written exam by stating their intention to register the grade on a questionnaire tool of the course’s Moodle page. In order to register the exam students must book the written and the oral exam in all cases Students who participate to the oral exam will be given a matlab exercise the day prior to the exam. Students must complete the assignment and they must be prepared to discuss it in the oral exam. The oral exam may then continue with a discussion of all the topics described in class and contained in the syllabus. In particular, the following may be asked: definitions, properties, descriptions, examples, and mathematical exercises. The final grade can be higher or lower than the grade obtained in the written exam. Students who obtained a grade between 16 and 18 in the written exam can take the oral exam. No assignment will be given to them, but they must demonstrate a good command of the subject, better than that resulting from the written exam.

Interview with the instructor.