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73026 - Elements of Mathematics and Logic (A.Y. 2015/2016) Stampa

73026 - Elements of Mathematics and Logic (EML, 12 CFU), is composed by the following modules:

Elements of Mathematics and Logic (Mod. 1, Mat.)

Course syllabus

1. Basic Notions
(a) Sets, cartesian products
(b) Functions, infinite sets
(c) Natural numbers and induction
(d) Cardinality

2. Discrete Mathematics
(a) Integers
(b) Euclidean algorithm
(c) Modular arithmetic
(d) Monoids, lists
(e) Graphs, paths
(f) Rings of polynomials
(g) Complex numbers

3. Mathematical Logic
(a) Syntax: predicate calculus and formal theories
(b) Semantics: interpretations, models
(c) Soundness and completeness for first order logic
(d) Outline of the theorems of Gödel, Turing and Church

4. Linear Algebra
(a) Rings of matrices
(b) Outline of vector spaces
(c) Systems of linear equations

Language

Italian

Teacher

Maria Pia Cavaliere

Teaching style

In presence

Lesson timetable

Wednesday: 11:00 - 13:00, room 506
Friday: 11:00 - 13:00, room 506

Attendance

Not required

Course hour allocation

This course consists of 48 hours of lectures, including 12 hours of exercises.


Elements of Mathematics and Logic (Mod. 2, Logic)

Course syllabus

1. Basic Notions
(a) Sets, cartesian products
(b) Relations: orders, equivalences
(c) Functions, infinite sets
(d) Cardinality

2. Discrete Mathematics
(a) Natural numbers and induction
(b) Integers
(c) Complex numbers
(d) Matrices
(e) Polynomials
(f) Euclidean algorithm
(g) Modular arithmetic
(h) Structures: monoids, lists, graphs, paths

3. Linear Algebra
(b) Outline of vector spaces
(c) Systems of linear equations

4. Mathematical Logic
(a) Syntax: predicate calculus and formal theories
(b) Semantics: interpretations, models
(c) Soundness and completeness for first order logic
(d) Outline of the theorems of Gödel, Turing and Church

Language

Italian

Teacher

Giuseppe Rosolini

Teaching style

In presence

Lesson timetable

Tuesday: 9:00 - 11:00, room 506
Thursday: 11:00 - 13:00, room 506

Attendance

Not required

Course hour allocation

This course consists of 48 hours of lectures, including 8 hours of exercises.