The course will provide the students with basic knowledge of one-variable calculus and linear algebra, illustrating the main ideas and tools through examples, exercises and theoretical discussions.

Knowledge and understanding: The course will introduce basic quantitative mathematical tools together with examples of applications and their theoretical discussion. Applying knowledge and understanding: The students will learn to formally write and discuss mathematical results, with a level of abstraction that will allow them to connect different empirical problems (as those they will meet in subsequent courses) to the same mathematical understanding. They will be able to apply the tools learned during the course to non-standard exercises, suitably adapting them. The students will also be able to discuss main ideas and motivations that stand behind the introduction of the mathematical techniques they learned. 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 problems in computer science and economics. 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, both in written and oral communication, using the English language. They will also gain a sufficient level of abstraction to understand how different concrete problems can be studied using similar techniques. Learning skills: Students will broaden their mathematical knowledge and their competence in abstract reasoning, and become able to work independently with basic mathematical concepts and tools.

Basics of mathematical logic and set theory. Number sets. Sequences and their limits. Functions of one real variable: limits, continuity, derivatives, approximation by Taylor’s polynomials. Integrals of functions of one real variable. Vectors, matrices, systems of linear equations. Vector spaces and subspaces. Linear transformations. Coordinate systems.

Notes on every topic in the course will be given by the instructor. A good book containing the topics of the first part of the course is: J. Stewart, "Calculus, Early Transcendentals", Brooks/Cole, Seventh Edition or later. Good texts for the second part of the course are: D.C. Lay, "Linear Algebra and Its Applications", Addison-Wesley, 5th Edition and Ron Larson, “Elementary Linear Algebra”, Cengage, 8th edition. A basic level book containing most (but not all) the topics in this course is Lorenzo Peccati, Sandro Salsa, Annamaria Squellati Mathematics for Economics and Business, Egea.

Lectures, exercise classes on campus and online. Weekly multiple-choice tests self-evaluation. Weekly exercises assigned to groups; every week some groups have to provide their solutions to the teacher, and they will then be shared with the whole class. Optional presentations by the students on additional topics.

Written and oral exam. The written part consists in multiple choice questions (possibly also about theoretical aspects as discussed during the course) and exercises (similar to those explained during the course). The oral part consists in the discussion of two (small) topics chosen by the instructor at the moment of the exam from a list of topics given to the students at least one week before the exam; this can be substituted, at the student’s choice, with an oral presentation of an additional topic chosen by the student from a list of arguments that have been discussed briefly in class but whose in-depth analysis is left to students. The exam commission can ask questions on this part, to verify the student’s comprehension of the topic. Complete references and material will be given by the instructor about such topics. There is the possibility for partial evaluation during the course, that, if positive, results in a shorter final written exam.

Discussion with the instructor

No