Semigroups

Code:

M570

Acronym:

M570

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2019/2020 - 2S

Active?	Yes
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Doctoral Program in Mathematics

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
IUD-M	3	PE do Prog Inter-Univ Dout Mat	1	-	9	60	243

Teaching language

English

Objectives

To acquire the necessary background in topics of semigroup theory and its applications to allow students to understand current research work in the area.

Learning outcomes and competences

Sufficient familiarity with topics of semigroup theory and its applications to be able to understand and attack research problems in the area.

Working method

Presencial

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

Basic knowledge of algebra and topology.

Program

Depending on the interests of the students and the lecturer, various topics of semigroup theory and its applications may be considered, among the following are examples:

• elements of algebraic semigroup theory;


• semigroups of transformations;


• finite semigroups and automata;


• topological semigroups and profinite semigroups;


• varieties and pseudovarieties of semigroups;


• Burnside problems for semigroups;


• connections with symbolic dynamics;


• representation theory for finite semigroups.

Mandatory literature

John M. Howie; Fundamentals of semigroup theory. ISBN: 0-19-851194-9
Jorge Almeida; Finite semigroups and universal algebra. ISBN: 981-02-1895-8
John Rhodes; The q-theory of finite semigroups. ISBN: 978-0-387-09780-0

Complementary Bibliography

Mark V. Sapir; Combinatorial algebra. ISBN: 978-3-319-08030-7
Benjamin Steinberg; Representation theory of finite groups. ISBN: 978-1-4614-0775-1
Douglas Lind; An introduction to symbolic dynamics and coding. ISBN: 0-521-55124-2
Ganyushkin, Olexandr; Mazorchuk, Volodymyr; Classical Finite Transformation Semigroups, Springer. ISBN: 978-1-84800-281-4

Teaching methods and learning activities

Presentation of the course mateiral by the teacher, with discussion with the students, when relevant. Possibility of presentation of some specific topics by the students.

keywords

Physical sciences > Mathematics > Algebra

Evaluation Type

Distributed evaluation without final exam

Assessment Components

designation	Weight (%)
Trabalho escrito	100,00
Total:	100,00

Amount of time allocated to each course unit

designation	Time (hours)
Estudo autónomo	112,00
Frequência das aulas	56,00
Total:	168,00

Eligibility for exams

Unconditional.

Calculation formula of final grade

The student evaluation consists in homework composed of lists of exercises to be solved individually by students without any help other than access to bibliographic references, that must be duly acknowledged. Each question proposed for homework is graded for a maximum of one point. THe final grade is the total of points divided by the number of assigned questions, times 20. At the end of the semester, an extra homework set may be proposed for grade improvement; the grades obtained in each individual question may then be used to replace lower grades for questions obtained during the semester.

Examinations or Special Assignments

In case some specific topic is presented by a student in class, the corresponding grade may be considered with the weight of 10% should in that way the final grade be improved.