DISCRETE STRUCTURES

This course is one of the core activities of the three-year degree course in Computer Science and its aim is to present the fundamental ideas and concepts of discrete, as opposed to continuum, mathematics. The student will be gradually introduced to the main mathematical proof techniques and to the main discrete structures.

Knowledge and understanding:
- main definitions and results of discrete mathematics;
- discrete structures for computer science;
- rudiments of combinatorics.

Ability to apply knowledge and understanding:
- formalization of sentences expressed in natural language;
- use of the main mathematical proof techniques;
- abstraction and generalization.

There is no specific requirement.

- Propositional and first order logic
- Rudiments of number theory
- Induction principle
- Sets, functions and relations
- Principles of combinatorics

Elementi di matematica discreta. Interi. Calcolo Combinatorio e Grafi.
Giuseppe Lancia
Independently Published, 2018

The exam consists of a written test, with the possibility of an oral exam as an additional assessment if deemed necessary by the instructor or requested by the student. Attending students can take intermediate tests during the semester, which replace the written exam, and may be followed by an oral integration under the terms described above.

Description of the written test:
The written test aims to assess the student's problem-solving skills, knowledge of fundamental concepts in discrete mathematics, and the ability to solve exercises and prove theorems. It consists of open exercises covering the main topics of the course. The use of notes, books, or electronic devices is not allowed during the written test.
The written test may be followed by an oral exam, should the instructor deem it necessary or the student wish to improve the result. The oral exam includes a discussion of the written work, an evaluation of problem-solving abilities, and an assessment of theoretical knowledge and expressive skills. The oral exam is only conducted if the written test is deemed sufficient. In case of a negative outcome in the oral exam, the written test must be retaken.

Description of the intermediate tests:
The intermediate tests, held in class, allow students to be exempted from the final written exam if successfully passed. The content of these tests is equivalent to that of the final written exam. Each intermediate test is graded on a scale of thirty, and the final grade is the average of the intermediate test scores. Failure to submit an intermediate test results in a score of zero, which will be included in the average.

Exam evaluation:
The evaluation is based on open exercises. The grade for the written test is the sum of the points assigned to each problem, with a minimum score of 18 required to pass the exam and a maximum score of 30 e lode. Students who pass the written test may choose to take an oral exam (optional), which could modify the final grade, including the possibility of failure.

Frontal lesson on the blackboard.

Italian

written

This subject deals with topics related to the macro-area "Poverty and inequalities" and contributes to the achievement of one or more goals of U. N. Agenda for Sustainable Development