Search    Print

Algebra e Logica
Algebra and Logic
Maria Chiara Brambilla

Seat Ingegneria
A.A. 2015/2016
Credits 6
Hours 48
Period II
Language ENG

Prerequisites
First year Mathematics courses, in particular Linear Algebra and Geometry

Learning outcomes
The course aims to provide familiarity with the most common algebraic structures and provide the students with basic notions of mathematical logic.

Program
Sets. Operations with sets. Functions. Order relations. Semigroups. Groups. Rings. Fields. Theorems of Lagrange, Bezout, Euler, Fermat. Permutation groups. determinants. Quotient group. Finitely generated Abelian groups. Order relations. Zorn lemma. Boolean algebras. Logical circuits. Elements of mathematical logic.

Development of the examination
LEARNING EVALUATION METHODS
The learning evaluation is carried out by two exams: - a practical examination, which consists of solving exercises and problems related to the topics explained in the course. - a theoretical examination, consisting in a discussion of the topics of the course. In particular the knowledge and the understanding of all definitions, theorems and proofs explained in the classes will be tested. The practical exam is preliminary to the theoretical one. It is necessary to pass the practical exam in order to do the theoretical one. The two exams must be passed in the same exam session. If the student fails the theoretical exam, he/she must repeat also the practical one

LEARNING EVALUATION CRITERIA
In order to pass the learning evaluation, the student must demonstrate that he/she has understood the basic concepts of algebra and logic explained in the course. In particular in the practical test the student must show that he/she is able to apply independently the learned techniques in solving exercises and problems. In the theoretical exam the student must be able to expose the theoretical contents with the correct language and accuracy

LEARNING MEASUREMENT CRITERIA
Each of the tests is graded on a scale from 0 to 30. The final grade will be decided starting from the two test grades.

FINAL MARK ALLOCATION CRITERIA
The final grade will be positive only if in both of the tests the students gets the passing grade (18/30). The maximal grade is reached if the student proves a knowledge and a thorough understanding of the course content. The maximal grade with honors is reserved to the students who passed both of the tests in a complet and correct way, showing special independence and excellence

Recommended reading
A.Facchini, Algebra e matematica discreta, Zanichelli

Courses

• Ingegneria Informatica e dell'Automazione (Corso di Laurea Triennale (DM 270/04))