Università degli Studi di Urbino Carlo Bo / Portale Web di Ateneo


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.

Bridging Courses

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.

« back Last update: 21/01/2013

Il tuo feedback è importante

Raccontaci la tua esperienza e aiutaci a migliorare questa pagina.

Il tuo 5x1000 per sostenere le attività di ricerca

L'Università di Urbino destina tutte le risorse che deriveranno da questa iniziativa alla ricerca scientifica ed al sostegno di giovani ricercatori.

15 22

Se sei vittima di violenza o stalking chiama il 1522, scarica l'app o chatta su www.1522.eu

Il numero, gratuito è attivo 24 h su 24, accoglie con operatrici specializzate le richieste di aiuto e sostegno delle vittime di violenza e stalking.

Posta elettronica certificata

amministrazione@uniurb.legalmail.it

Social

Università degli Studi di Urbino Carlo Bo
Via Aurelio Saffi, 2 – 61029 Urbino PU – IT
Partita IVA 00448830414 – Codice Fiscale 82002850418
2024 © Tutti i diritti sono riservati

Top