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.

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.

There are no mandatory prerequisites for this exam.
It is worth noticing that the topics covered by this course will be used  in Procedural and Logic Programming, Calculus, Digital Signal and Image Processing, Modeling and Verification of Software Systems.

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

The written exam is passed if the mark (which is valid for the exam calls of the same session) is at least 18/30. The oral exam, which must be taken if the written exam is passed, if passed determines a spread between -12/30 and 12/30 of the previous mark, thus yielding the final mark.

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.

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

Some previous written exams with solution can be found here.