Group Theory

Code:

M2025

Acronym:

M2025

Level:

200

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2015/2016 - 1S

Active?	Yes
Web Page:	https://moodle.up.pt/course/view.php?id=883
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:CC	12	Plano de estudos a partir de 2014	2	-	6	56	162
MI:ERS	22	Plano Oficial desde ano letivo 2014	2	-	6	56	162

Teaching language

Portuguese

Objectives

Master the basic concepts and results of Group Theory studied, both in terms of its implementation in the classic examples of these structures, and in a general and abstract perspective.

Learning outcomes and competences

Working method

Presencial

Program

">Basics: binary relations, order and equivalence.

Groups: definitions and basic properties; important examples of groups (integers, real and complex; integers modulo n, permutations, linear groups, symmetry groups); subgroups and generators; cyclic groups; cosets and Lagrange theorem; normal subgroups and quotient groups; conjugation; homomorphisms and isomorphisms; Cayley theorem; Fundamental Theorem of Homomorphism; direct product groups;
">Fundamental Theorem of finitely generated Abelian groups.

Mandatory literature

Fraleigh John B.; A first course in abstract algebra. ISBN: 0-201-16847-2
Jacobson Nathan; Basic algebra. ISBN: 0-7167-0453-6 (Vol. I)

Teaching methods and learning activities

Lectures. Problem solving in practical classes. Other support contents providded on the course page.

Evaluation Type

Evaluation with final exam

Assessment Components

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

Eligibility for exams

Calculation formula of final grade

">- There will be carried two tests, both worth 10 points.

The tests are not mandatory.
">However, to be admitted to the second test it is necessary to obtain at least 2 points on the first test.


">- The final exam will consist of two corresponding parts, worth the same number of points.

- A student whoser grade is at least half of the maximum grade in a test (rounded to one decimal place) shall not be required to answer the corresponding part in the examination (at any time, except for improvement). ">In case you decide not to perform the corresponding part of the exam, the marks obtained in the test will be used to calculate the final grading.

">- In any case, if the student chooses to answer a part of the examination, that will be the grade used for the final classification.

- A student who obtains a sum of 9.5 in both tests is exempted from taking the exam. The final grade in the case of not performing the examination will then be the sum of the test scores, except possibly if you get ranked higher than 16 (see below).
">If you choose to take the exam the mark obtained then will be the final classification.

- To obtain ratings above 16 a further test is required.