Course Details for A.Y. 2015/2016

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

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 second-degree 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

• A.Y. 2013/2014
• A.Y. 2014/2015
• A.Y. 2015/2016
• A.Y. 2016/2017
• A.Y. 2017/2018
• A.Y. 2018/2019