Group Theory

Code:

M2025

Acronym:

M2025

Level:

200

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2019/2020 - 1S

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

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:B	0	Official Study Plan	3	-	6	56	162
L:CC	12	Plano de estudos a partir de 2014	2	-	6	56	162
			3
L:F	36	Official Study Plan	2	-	6	56	162
			3
L:G	4	study plan from 2017/18	2	-	6	56	162
			3
L:M	94	Official Study Plan	2	-	6	56	162
L:Q	0	study plan from 2016/17	3	-	6	56	162
MI:ERS	14	Plano Oficial desde ano letivo 2014	2	-	6	56	162
			3

Teaching language

Suitable for English-speaking students

Objectives

To introduce the concepts, methods and basic results of Group Theory, showing the origins of this discipline, presenting some of its applications, as well as how it subsumes results from other areas.

Learning outcomes and competences

Upon completing this curricular unit, the student should:

(1) master the basic concepts, methods, and results of group theory;

(2) to be able to analyze and solve problems within group theory, using the methods and results that best apply to the problems under study;

(3) to appreciate the connections of group theory to other areas of mathematics, such as geometry and number theory;

(4) be able to efficiently and clearly communicate their resolutions of problems, and their understanding of the subject.

Working method

Presencial

Program

• Notion of group and various examples (groups of permutations, symmetry groups, linear groups).


• Subgroups and cyclic groups.


• The direct product of groups.


• Cosets modulo a subgroup, normal subgroups and quotient groups.


• Homomorphisms and isomorphisms.


• Centralizers and normalizers.


• Group actions and the theorems of Sylow.


• Classification of groups with order up to 15.

Mandatory literature

J.S. Milne; Group Theory, 2017

Complementary Bibliography

Rotman Joseph; A first course in abstract algebra. ISBN: 0-13-011584-3
Fernandes Rui Loja; Introdução à álgebra. ISBN: 972-8469-27-6
Fraleigh John B.; A first course in abstract algebra. ISBN: 0-201-16847-2

Teaching methods and learning activities

The contact hours are distributed in theoretical and theoretical-practical classes. In the first ones, the contents of the program are studied, often using examples to illustrate the concepts treated and to guide the students in the resolution of exercises and problems. In the theoretical-practical classes, exercises and problems are solved, which are indicated in advance for each week. List of exercises and other course materials are available on the course page at Sigarra. In addition to the classes, there are weekly attendance periods where students have the opportunity to clarify their doubts.

keywords

Physical sciences > Mathematics > Algebra > Group theory

Evaluation Type

Distributed evaluation with final exam

Assessment Components

designation	Weight (%)
Exame	40,00
Teste	60,00
Total:	100,00

Amount of time allocated to each course unit

designation	Time (hours)
Estudo autónomo	106,00
Frequência das aulas	56,00
Total:	162,00

Eligibility for exams

There are no rules concerning attendance frequency.

Calculation formula of final grade

Approval of the course unit is obtained in the final exam.

There will be two tests of one hour each (on dates to be determined). Each test will have a weight of 30% of the final mark. The exam will consist of:

1) a one-hour test weighing 40% of the final grade for students wishing to use the sum of the scores obtained in the two tests,

or (disjunctive):

2) a 3 hour test with a weight of 100%.

The examination of the "appeal" period will be made in the same way as the one of "normal" period.

Special assessment (TE, DA, ...)

Examinations required under special statutes shall consist of a written test that may be preceded by an oral test, to assess if the student satisfies minimum conditions to attempt to obtain approval at the discipline in the written test.