Course Details for A.Y. 2016/2017
Name:
Matematica Discreta I / Discrete Mathematics I
Basic information
Credits:
: Bachelor Degree in Computer Science 6 CFU (a)
Degree(s):
Bachelor Degree in Computer Science 1^{st} anno curriculum General Compulsory
Language:
Italian
Course Objectives
The goal of this course is to expose the main concrete techniques in linear algebra (matrices, systems, determinants, vector spaces and linear maps) and to show the first strategies in abstract algebra.
Course Content
 Sets: functions, equivalence relations, products, elementary combinatorics.
 Permutations.
 Groups: subgroups, quotients, isomporphism theorems, factor groups, permutation groups, cyclic groups.
 Arithmetic: divisibility theory in the ring of integers and of polinomials over a field.
 Congruences. Chinese remainder theorem.
 Rings: subrings, ideals, quotients, isomorphism theorem, ring of polynomials, domains, euclidean rings, PID, UFD.
 Fields: simple field extensions, finite fields.
 Matrices and systems of linear equations: Gauss reduction, determinants.
 Vectors, vector spaces, independence, bases.
 inner product, cross product.
 Eigenvalues, eigenvectors. Diagonalization and canonical forms of matrices.
 Application: systems of differential equations.
Learning Outcomes (Dublin Descriptors)
On successful completion of this course, the student should

being aware of the main structures in Linear Algebra and Abstract Algebra.

demonstrate skill in mathematical reasoning, manipulation and calculation, demonstrate capacity for finding rigorous proofs of small problems; demonstrate skill in mathematical reasoning, manipulation and calculation by synthesizing geometric concepts into algebraic, functional, and problemsolving activities; demonstrate capacity to deduce properties of, and relationships between, figures from given assumptions and from using transformations.
Prerequisites and Learning Activities
Set Theory (language of set theory, the notion of function, graphs of fundamental functions, concept of sufficient and necessary condition), Numerical Structures (natural numbers, prime numbers, numerical fractions, rational numbers, basics of real numbers, inequalities, absolute value, powers and roots);
Elementary algebra ( polynomials and operations on polynomials, identity, first and seconddegree equations).
Assessment Methods and Criteria
Written exam and oral discussion of the written exam.
Textbooks
 W.K. Nicholson, Algebra lineare , McGraw Hill.
 B. Scimemi, Algebretta
Course page updates
This course page is available (with possible updates) also for the following academic years:
Course information last updated on: 09 aprile 2017, 12:27