Group Theory

Code:

M2025

Acronym:

M2025

Level:

200

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2016/2017 - 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	10	Official Study Plan	3	-	6	56	162
L:CC	13	Plano de estudos a partir de 2014	2	-	6	56	162
L:M	96	Official Study Plan	2	-	6	56	162
L:Q	1	study plan from 2016/17	3	-	6	56	162
MI:ERS	8	Plano Oficial desde ano letivo 2014	2	-	6	56	162

Teaching language

Portuguese

Objectives

To introduce the basic concepts and results of Group Theory, both throught
the classical examples of these structure and in an abstract level.

Learning outcomes and competences

A student is expected to know the concepts and basic results of Group Theory and to develop skills of abstract reasoning.

Working method

Presencial

Program

1. Permutations; the set Sn; product of permutations in Sn; properties; even and odd permutations.
2. Groups; examples and elementary properties.
3. Subgroups; subgroups and generators.
4. Homomorphisms and isomorphisms; Cayley’s theorem.
5. Cyclic groups.
6. Direct product of groups; fundamental theorem of finitely generated abelian groups. 
7. Cosets and Lagrange's theorem; normal subgroups and quotient groups; fundamental homomorphism theorem.

 

Mandatory literature

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

Teaching methods and learning activities

The content of the syllabus is presented at the lectures, and proposed exercises are solved by the students at the practical classes.

keywords

Physical sciences > Mathematics > Algebra > Group theory

Evaluation Type

Distributed evaluation without final exam

Assessment Components

designation	Weight (%)
Teste	100,00
Total:	100,00

Eligibility for exams

Students are not required to attend classes.

Calculation formula of final grade

During the semester there will be two tests whose quotation sums 20. The second test will take place at the first exam season.

Course approval can be obtained 

1) by getting 9,5 or more in the sum of the grading of the three tests.

2) in the final exam, to be held at the second exam season.

The final exam consists of 2 parts, each corresponding to a test.

In the final exam, students who have not yet obtained approval (and only these) may choose not to solve one part of the exam, that would then get the grade of the corresponding test.