## DISCRETE STRUCTURES AND LINEAR ALGEBRA MATEMATICA DISCRETA

#### Discrete Structures and Linear Algebra Matematica Discreta

A.Y. Credits
2012/2013 6
Lecturer Email Office hours for students
Devis Abriani Tue-Wed from 4 pm to 5 pm.

### Assigned to the Degree Course

Date Time Classroom / Location

### Learning Objectives

The objective of this Course is to provide knowledge of the language and of the main structures of algebra and familiarity with some of the most common techinques of combinatorial mathematics and linear algebra.

### Program

01. Sets and their relations:
01.01 Sets, equivalences and partitions.
01.02 Applications.
01.03 Composition of applications and inverse.
01.04 Cardinality: countable and uncountable sets.
01.05 Elements of combinatorics.
01.06 Total and partial order.

02. Matrices:
02.01 Definitions.
02.02 Addition of matrices and properties.
02.03 Product of matrices and properties.
02.04 Transpose.
02.05 Square matrices.

03. Theory of groups:
03.01 Semigroups.
03.02 Monoids.
03.03 Groups.
03.04 Homomorphisms.
03.05 Subgroups.
03.06 The group of permutations.

04. Theory of rings:
04.01 Rings and commutative rings.
04.02 Rings with identity.
04.03 Zero divisors.
04.04 Integral domains and fields.
04.05 Polynomials rings.

05. Linear algebra:
05.01 Vector spaces.
05.02 Linear dependence and independence.
05.03 Basis and dimension.
05.04 Subspaces.
05.05 Linear applications.
05.06 Kernel and image.
05.07 Matrices and linear applications.
05.08 Changes of basis.
05.09 Rank.
05.10 Linear Systems and Rouche'-Capelli's Theorem.
05.11 How to solve a linear system in practice.
05.12 Determinant and Cramer's theorem.
05.13 Minors and Rank.
05.14 Eigenvalues and Eigenvectors.
05.15 Diagonalization.

None.

### Teaching, Attendance, Course Books and Assessment

Teaching

Theory lectures and exercises, both face to face and online.

Attendance

Although recommended, course attendance is not mandatory.

Course books

Facchini, "Algebra e Matematica Discreta", Decibel Editrice, 2000.
S. Lang, "Linear Algebra" (second edition), UTM Springer-Verlag, 1989.

Assessment

Written and oral exam.

Disability and Specific Learning Disorders (SLD)

Students who have registered their disability certification or SLD certification with the Inclusion and Right to Study Office can request to use conceptual maps (for keywords) during exams.

To this end, it is necessary to send the maps, two weeks before the exam date, to the course instructor, who will verify their compliance with the university guidelines and may request modifications.

### Notes

The course is offered both face to face and online within the Laurea Degree Program in Applied Computer Science.

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