Ring Theory and Applications

Code:

M2012

Acronym:

M2012

Level:

200

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2019/2020 - 2S

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	1	Plano de estudos a partir de 2014	2	-	6	56	162
			3
L:F	1	Official Study Plan	2	-	6	56	162
			3
L:G	1	study plan from 2017/18	2	-	6	56	162
			3
L:M	10	Official Study Plan	2	-	6	56	162
L:Q	0	study plan from 2016/17	3	-	6	56	162

Teaching language

Portuguese

Objectives

Familiarization with basic ring, field, and Galois theory and some of its applications.

Learning outcomes and competences

Understand the basic concepts and results of ring and field theory, including homomorphisms, ideals, polynomial rings, field extensions, the structure of finite fields, and their applications, namely in cryptography and error correcting codes.

Working method

Presencial

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

It is recommended that students previously take courses introducing abstract algebraic concepts such as "Teoria de Grupos" and "Álgebra Linear e Geometria Analítica I".

Program

Mandatory literature

Carlos Menezes; Apontamentos de Teoria de Anéis e Aplicações-2019-2020

Complementary Bibliography

David S. Dummit; Abstract algebra. ISBN: 0-13-005562-X

Teaching methods and learning activities

Presentation of the course material by the teacher. Solution and discussion of exercises.

keywords

Physical sciences > Mathematics > Algebra

Evaluation Type

Evaluation with final exam

Assessment Components

designation	Weight (%)
Exame	100,00
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

No restrictions.

Calculation formula of final grade

Final exam only.

Special assessment (TE, DA, ...)

Any type or special examination can be from one the following types: exclusively by an oral examination,  only  a written exam, one oral examination and a written exam.

The decision of which of the above types is each special examination  is exclusively the responsability of the teacher  assigned to the curricular unit.

Observations

There was an agreement with students to have two homeworks during the semester,
each one with the overall mark of 6 valores, and a final exam with three parts, the first two parts corresponding
to the syllabus of the first and second homework,
each one with a overall mark of 6 valores,
and the third part with the overall mark of 8 valores. will be in a classroom of the Faculty. The student can choose between the mark obtained in each homework or the mark obtained in the corresponding part of the final exam.