Discrete Mathematics
A.Y. 2023/2024
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 can be attended as a single course.
Course syllabus and organization
Single session
Responsible
Lesson period
First semester
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.
If time allows, we will also discuss some basic geometry: planes, lines, parallel, orthogonality and interserctions in dimensions 2 and 3.
- 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.
If time allows, we will also discuss some basic geometry: planes, lines, parallel, orthogonality and interserctions in dimensions 2 and 3.
Prerequisites for admission
Basic Logic and Mathematics skills, including properties and operations on numbers (integers, rationals, reals), powers, roots and their properties, polynomials (operations, factoring, divisions with remainder, principle of identity), equations and algebraic inequalities of first and second degree or reducible to them, literal calculus, ability to distinguish between hypotheses and theses.
Teaching methods
Frontal lessons.
Teaching Resources
We will make notes available on the Ariel platform.
Assessment methods and Criteria
The exam will consist of a written test divide in two parts: the first will consist of direct questions, the second will consist of more structured exercises to solve.
During the course, we will assign some optional homework, which will not be evaluated but used to test the level of understanding achieved by the class.
The structure of the exam might vary, would the sanitary situation force us to do so.
During the course, we will assign some optional homework, which will not be evaluated but used to test the level of understanding achieved by the class.
The structure of the exam might vary, would the sanitary situation force us to do so.
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:
Barbieri Viale Luca, Luperi Baglini Lorenzo
Educational website(s)
Professor(s)
Reception:
Tuesday h. 2-4 p.m. or email contact
Office - Math Department