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 logic, to the main mathematical proof techniques and to the main discrete structures.

Students will achieve the following learning outcomes:

i) Knowledge and understanding: understanding of the basic concepts of the main topics covered by discrete mathematics, including: logic, set theory, functions, relations, induction, combinatorics and number theory.

ii) Ability to apply knowledge and understanding: ability to solve exercises related to the theoretical topics covered in the course.

iii) Judgment: ability to choose the correct problem solving approach for a specific exercise and to adapt known solutions to new problems.

iv) Communication skills: knowing how to clearly and correctly explain definitions and the reasoning carried out in a mathematical proof.

v) Learning ability: knowing how to independently study new theoretical concepts of discrete mathematics.

There is no specific requirement.

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

Kenneth Rosen - Discrete mathematics and its applications (eight edition)

Written test with exercises, questions and proofs related to the main topics of the course. During the written test, the use of notes, books and electronic instruments is not permitted. Students can choose to take an intermediate test on the first part of the program and a final test at the end of the course on the rest of the program. In this case the final grade will be calculated as the average of the two tests.

The evaluation will assess the student's ability to solve problems related to the main topics of the course and to prove their knowledge of the theoretical concepts explained in the classes, thus verifying learning objectives from i) to v). In particular, the student will be assessed based on the following criteria:

i) Knowledge and understanding: The student must demonstrate familiarity with the formal notation introduced during the course, the main definitions, and the specific terminology.

ii) Ability to apply knowledge and understanding: The student must demonstrate the ability to solve exercises on the topics covered in the course.

iii) Judgment skills: The student must demonstrate the ability to apply the main proof techniques and adapt existing proofs.

iv) Communication skills: The student must demonstrate familiarity with the specific language and strong command of logical reasoning.

v) Learning ability: The student must demonstrate the capacity to understand concepts and definitions presented during the exam.

Regarding the indicated criteria, scores in the range of 18-22 indicate sufficient but limited skills, scores in the range of 23-26 indicate fair to more than fair skills, and scores in the range of 27-30 indicate good to excellent skills.

Frontal lesson on the blackboard. Assignment of recommended exercises to solve.

English

written