Learning objectives
The goal of the course is to provide freshmen students in Mathematics and Physics a gentle introduction to mathematical thinking and a correct use of the mathematical language. The first week of the course will focus on the basic notions of mathematics such as functions between sets and functions in a real variable. During this time, the students are strongly encouraged to self-assess their knowledge on these topics and if necessary act swiftly to fill the gaps, for instance by taking advantage of the tutoring service offered by the Department.
During the second and third week, the course will revolve around basic notions of combinatorics, probability, and discrete mathematics.
Prerequisites
- - -
Course unit content
Overview of the basic notions of mathematics, focusing in particular on functions between sets and functions in one real variable. Cardinalities, partial and total orders, foundations of mathematics. Basics of combinatorics, probability, and discrete mathematics.
Full programme
Lecture 1 - 4h.
Logic and set theory.
Lezioni 2, 3 e 4a - 13h.
Functions. Definitions. Examples. Functions in one real variable. Operation on functions. Graphs. Implicit functions. Conic sections.
Lezioni 4b e 5 - 7h. (only for students in Mathematics).
Cardinalities. Partial and total orders. Relations. Modular arithmetics.
Lezione 6 - 4h.
Combinatorics and proofs. Permutations and combinations. Sums over multiple indices.
Lezione 7 - 4h. Revision session.
End of the course for the students in Physics.
Lezioni 8, 9 e 10a - 10h.
Introduction to Probability. Conditional probability and Bayes theorem.
Lezione 10b - 2h. Revision session.
Lezione 11 - 4h.
Practice exam and discussion of solutions.
Bibliography
Lecture notes will be provided on Elly together with exercises and solutions. Additional material:
• S. Lang, Basic Mathematics, 1970.
• G. Prodi, Analisi Matematica (Cap. 0), 1972.
• E. Acerbi, G. Buttazzo, Matematica Preuniversitaria di Base, 2003.
• S. Ross, Probabilit`a e statistica per l’ingegneria e le scienze, 2013.
• F.G. Alessio, C. de Fabritiis, C. Marcelli, P. Montecchiari, Matematica zero, 2016.
Teaching methods
The program of the course will be divided in "single-day" topics. This means that a given topic is discussed entirely from both a theoretical and practical point of view in the span of a morning and an afternoon sessions.
Assessment methods and criteria
There will be a final, 3 hours long, written exam with both multiple choices and open-ended questions.
Other information
- - -
2030 agenda goals for sustainable development
- - -
