SM/0125 - MATHEMATICAL LOGIC

Academic Year 2019/2020

Free text for the University

Objectives

Knowledge and understanding
The main objective of the course is devoted to provide students with the key tools for dealing with different kind logical and mathematical problems of various types (algebraic, digital techniques etc ...).

Making judgements
The student have to acquire an autonomous and critical reflection on the course’s issues.
Communication skills
At the end of the course, the student will be able to applied the arguments regarding to the basic mathematic of the course.
Learning skills
Finally, the student must be able to find sources to update and deepen autonomously and constantly knowledges and professional competencies

Prerequisites

Only basic notions on algebra

Contents

The initial purpose of the course is to give the theoretical, conceptual and methodological fundamental issues in mathematical logic. Application of the theoretical concept are considered.

1) Propositional logic
Propositional logic, Syntax
Propositional logic, Semantics
Boolean valuations
Hilbert style calculus (deductive systems)
Boolean algebras
Lindenbaum algebra
Soundness and completeness studies.

2)First order logic
First order logic, Syntax
First order logic, Semantics
Hilbert style calculus (First order deductive systems)
Soundness and completeness studies.

3. Applications: Introduction to digital technics
Binary codes
Boolean algebra expressions, normal forms
Karnaugh map
Logic gates (some integrated circuits 7408, 7432, 7404 )
Encoders and decoders (some integrated circuits DM7446)

Teaching Methods

Classroom lectures. Laboratory activities are planned

Verification of learning

Written test

The exam is expressed in thirtieths. In order to pass the exam that is with a minimum score of 18/30 the student must show a sufficient knowledge of all the addressed topics, with a proper use of the language. In order to achieve the maximum score of 30/30 cum laude, the student must show an excellent knowledge of all the dealt topics.

Texts

1) First-Order Logic and Automated Theorem Proving, (Melvin Fitting), Springer-Verlag New York 2nd edition 2012.
2) Introduction to Mathematical Logic, (Elliott Mendelson), Chapman and Hall ed., Sixth Edition (2015)
3) Sistemas electronicos digitales (Enrique mandado)
Marcombo, 10ma Ed, 2015.
4) Lectures on Boolean Algebras (Paul Halmos), Martino Fine Books, (2013)
5) A Shorter Model Theory, (Wilfrid Hodges), Cambridge University Press, 1997

More Information

For an appointment send an e-mail to hfreytes@gmail.com
Students with special needs may benefit from a Disabled Office (http://people.unica.it/disabilita/) that certifies their difficulties in order to arrange individualized programs and exams.