Discrete Mathematics
A.Y. 2020/2021
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.
Lesson period: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
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.
- 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.
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.
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
MAT/02 - ALGEBRA
MAT/03 - GEOMETRY
MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS
MAT/05 - MATHEMATICAL ANALYSIS
MAT/06 - PROBABILITY AND STATISTICS
MAT/07 - MATHEMATICAL PHYSICS
MAT/08 - NUMERICAL ANALYSIS
MAT/09 - OPERATIONS RESEARCH
MAT/02 - ALGEBRA
MAT/03 - GEOMETRY
MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS
MAT/05 - MATHEMATICAL ANALYSIS
MAT/06 - PROBABILITY AND STATISTICS
MAT/07 - MATHEMATICAL PHYSICS
MAT/08 - NUMERICAL ANALYSIS
MAT/09 - OPERATIONS RESEARCH
Practicals: 24 hours
Lessons: 32 hours
Lessons: 32 hours
Professors:
Bianchi Mariagrazia, Luperi Baglini Lorenzo
Professor(s)