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.

Some basic notions 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 , homework

A written midterm worth 40% of the total grade, a final written exam worth 50% of the total grade, and a Python exam worth 10% of the total grade. If students are unable to attend the midterm or are not satisfied with their grade, they may reject it and take a larger final exam worth 90% of the total grade.

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