Ring Theory and Applications

Code:

M2012

Acronym:

M2012

Level:

200

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2018/2019 - 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	0	Plano de estudos a partir de 2014	2	-	6	56	162
			3
L:F	0	Official Study Plan	2	-	6	56	162
			3
L:G	0	study plan from 2017/18	2	-	6	56	162
			3
L:M	6	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 and field theory and some of its applications.

Learning outcomes and competences

Understanding 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

Thomas W. Judson; Abstract Algebra Theory and Applications (open textbook made available by the author at http://abstract.ups.edu)

Complementary Bibliography

Fraleigh John B.; A first course in abstract algebra. ISBN: 9781292024967
Norman R. Reilly; Introduction to Applied Algebraic Systems, Oxford University Press, 2009. ISBN: 9780195367874

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.