Discrete mathematics

A.Y. 2020/2021
6
Max ECTS
56
Overall hours
SSD
MAT/01 MAT/02 MAT/03 MAT/04 MAT/05 MAT/06 MAT/07 MAT/08 MAT/09
Language
Italian
Learning objectives
The objectives of the course include the basic notions of mathematical reasoning and their associated formalisms, with a particular focus in discrete mathematics (set theory, algebraic structures, linear algebra and geometry).
Expected learning outcomes
The ability of formalizing mathematical notions and reasonings, mastering basic notions of set theory and algebraic structures, knowing and properly applying the foundamentals of linear algebra and affine geometry.
Course syllabus and organization

Single session

Lesson period
First semester
Teaching will be given remotely using the Zoom platform.
Course syllabus
The course will cover the following topics:
- Basic operations between sets;
- Relations and their fundamental properties: transitivity, reflexivity, symmetry.
- Fundamental sets of numbers: natural, integers and rational numbers.
- Induction principle.
- Congruences, Chinese Remainder Theorem.
- Groups, homomorphisms between groups. Permutation groups.
- Fields and rings: definitions, examples, fundamental properties.
- Vectors, operations between vectors. Applications might include geometry in space (if time permits).
- Vector spaces: linear dependence, generators, bases, dimension, Grassman formula.
- Matrices: operations between matrices, relationship between matrices and linear systems, Gauss-Jordan method. Relationship with homomorphisms, search for eigenvalues ​​and eigenvectors, diagonalizability.
Prerequisites for admission
The ability to perform basic operations (sums, products, divisions), the ability to solve equations up to second degree, basic logical abilities.
Teaching methods
Lessons will be given synchronously from remote using the Zoom platform. Sometimes, during the lesson, Menti will also be used to test (but not to evaluate) the understanding of the teaching.
Lecture notes will be shared, whenever possible, through the Ariel platform.
Teaching Resources
The course we will be based on a textbook. However, there are many textbooks that cover the topics of the course. For example, we point out "Matematica discreta", authors Delizia, Longobardi, Maj, Nicotera, Editrice McGraw-Hill.
Assessment methods and Criteria
During the lessons Menti (https://www.menti.com/) will be used to test (but not to evaluate) the understanding of the teaching.
The understanding of the subject will be evaluated through written exams with exercises to be carried out on the whole course program. During the course, we will also carry out two intermediate tests (if the emergency situation will permit so). Students who obtain a positive assessment in both intermediate tests are exempted from the exam.
MAT/01 - MATHEMATICAL LOGIC - University credits: 0
MAT/02 - ALGEBRA - University credits: 0
MAT/03 - GEOMETRY - University credits: 0
MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS - University credits: 0
MAT/05 - MATHEMATICAL ANALYSIS - University credits: 0
MAT/06 - PROBABILITY AND STATISTICS - University credits: 0
MAT/07 - MATHEMATICAL PHYSICS - University credits: 0
MAT/08 - NUMERICAL ANALYSIS - University credits: 0
MAT/09 - OPERATIONS RESEARCH - University credits: 0
Practicals: 24 hours
Lessons: 32 hours