SM/0176 - MATHEMATICAL LOGIC
Academic Year 2019/2020
Free text for the University
HECTOR CARLOS FREYTES (Tit.)
JORGE NUNO DOS SANTOS VITORIA
- Teaching style
- Lingua Insegnamento
|[60/65] MATHEMATICS||[65/10 - Ord. 2012] Generale||9||72|
|[60/65] MATHEMATICS||[65/20 - Ord. 2012] Applicativo||9||72|
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 ...).
The student have to acquire an autonomous and critical reflection on the course’s issues.
At the end of the course, the student will be able to applied the arguments regarding to the basic mathematic of the course.
Finally, the student must be able to find sources to update and deepen autonomously and constantly knowledges and professional competencies
Only basic notions on algebra
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
Hilbert style calculus (deductive systems)
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
Boolean algebra expressions, normal forms
Logic gates (some integrated circuits 7408, 7432, 7404 )
Encoders and decoders (some integrated circuits DM7446)
4. introduction to Category Theory
Categories, objects an arrows, monics, epics, isomorphism. Functors, natural transformations, equivalence of categories. Product, co-product, pullbacks, pushouts. Limits and colimits. Adjunction, counit–unit adjunction.
Classroom lectures. Laboratory activities are planned
Verification of learning
Written and oral test
The exams are expressed in thirtieths. The tests aim to attest the aims set up in the section "knowledge and comprehension".
The written exam covers chapters 1, 2 and 3 of the course, while the oral exam covers chapter 4. In order to pass the course, the student needs to pass both exams, and the final mark will be a scaled average (67% written, 33% oral).
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.
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
6) Basic Category theory (Tom Leinster, Cambridge University Press, 2014 - freely available at arXiv:1612.09375)
7) Topoi: The Categorial Analysis of Logic (Robert Goldblatt) Dover Pubns; (2006)
8) Basic Category Theory for Computer Scientists (Benjamin C. Pierce) Mit Pr (1991)
For an appointment send an e-mail to firstname.lastname@example.org
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.