Teachings

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Professor
ANDREA LOI (Tit.)
Period
First Semester 
Teaching style
Convenzionale 
Lingua Insegnamento
 



Informazioni aggiuntive

Course Curriculum CFU Length(h)
[60/64]  MATHEMATICS [64/00 - Ord. 2012]  PERCORSO COMUNE 8 64

Objectives

KNOWLEDGE AND SKILLS 'UNDERSTANDING: learning the basic concepts of abstract algebra and algebraic structures such assemigroups, monoids, groups and rings.
CAPACITY OF APPLICATION: the student must be able to apply all the general knowledge necessary for the understanding of algebra
to recognize and analyzing the main algebraic structures.
JUDGEMENT: The course aims to stimulate objective teaching evaluation constantly offering students a comparison between the theoretical contents proposed while they were lessons
front and obtain them through self-study using the recommended texts and course material provided.
IN COMMUNICATION SKILLS: ability to express with the appropriate mathematical terminology the basic concepts of algebra with particular reference to theorems and proofs, while promoting and differentiating theses and hypotheses, showing a good grasp of the various demonstration techniques.
TO LEARN SKILLS: The student will develop a methodology of study and analysis that allows him to interpret and investigate the issues that will arise in the continuation of the study and the university career.
SKILLS EXPECTED: development of professional communication skills in mathematics, through the use of correct terminology and a description of organized and understandable manner useful not only to pass the exam, but also in view of a preliminary preparation subsequent examinations (in particular of geometry and algebrai).

Prerequisites

Injective and surjective maps; partially and totally ordered sets; Zorn Lemma; Equivalence and partition; prime numbers and the fundamental theorem of the algebra; Euler functions; linear and affine transformations; matrix calculation.

Contents

Algebraic structures; semigroups, monoids, groups, rings and fileds. Groups and subgroups: permutation groups, subgroups; cosets classes; normal subgroups, linear groups.
Homomorphisms and direct products: direct products of groups; quotient of grous, homomorphismi of groups; the theorems of homomorphisms for groups; the groups of automorphiisms of a group direct product of groups.

Abelian groups: cyclic groups; finite abelian groups, some infinite abelian groups.
Rings and ideals: definitions and examples; rules in a ring; the field of quatwernions; subrings; idelas; quotient rings; prime and maximal idelas in commutative rings.
Homomorphisms and direct product of rings: homomorphiisms and kernels; homomorphiisms theorem for rings; unitary rings and field of quotient of a domain, direct product of rings.

Teaching Methods

Blackboard and slides during the lectures, personal computer.

Verification of learning

The written test lasts 120 minutes and consists of two exercises
(the first on the theory of groups and the second on the theory of rings). A positive outcome of the written test (at least the complete solution of one of the exercise) is required to gain access to the oral exam .
The oral part of the examination is about 45 minutes with questions on main parts of the course program. A negative outcome of the oral test requires the repetition of the entire procedure (written and oral in series ) . The final vote , out of thirty, is a weighted average between the result of the written and oral exam .

Texts

I.N.Herstein, Topics in Algebra, Second Edition.

More Information

In http://people.unica.it/andrealoi/didattica/materiale-didattico/ students can find the detailed program and the exercises during class.

There is no student reception time. The student can apply for an appointment with the teacher via e-mail.

Our University provides support for students with specific learning disability (SLD). Those interested can find more informations at this link:
http://corsi.unica.it/matematica/info-dsa/

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