Algebra I

Code:

M241

Acronym:

M241

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2014/2015 - 1S

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

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:AST	0	Plano de Estudos a partir de 2008	3	-	7,5	-
L:B	1	Plano de estudos a partir de 2008	3	-	7,5	-
L:F	0	Plano de estudos a partir de 2008	2	-	7,5	-
L:G	0	P.E - estudantes com 1ª matricula anterior a 09/10	3	-	7,5	-
		P.E - estudantes com 1ª matricula em 09/10	3	-	7,5	-
L:M	96	Plano de estudos a partir de 2009	2	-	7,5	-
L:Q	0	Plano de estudos Oficial	3	-	7,5	-
M:CC	0	PE do Mestrado em Ciência de Computadores	1	-	7,5	-	-

Teaching language

Portuguese

Objectives

The student should know the concepts and basic results of Group Theory and Ring Theory, both at the level of application in the classical examples of these structures and in an abstract level.

Learning outcomes and competences

The student should know the concepts and basic results of Group Theory and Ring Theory, both at the level of application in the classical examples of these structures and in an abstract level. It is intended that this unit contribute to the development of skills of abstract reasoning and domain of the mathematical method. 

Working method

Presencial

Program

Basic notions: binary, order and equivalence relations. 

 

Groups: elementary definitions and properties; important examples of groups (integers, reals and complexes; integers modulo n; permutations; linear groups; groups of symmetries); subgroups and generators; cyclic groups; Cayley graphs; cosets and Theorem of Lagrange; normal subgroups and quotient groups; conjugacy; homomorphisms e isomorphisms; Cayley’s Theorem; Fundamental Homomorphism Theorem; direct product of groups; Fundamental Theorem of Finitely Generated Abelian Groups.

 

Rings: elementary definitions and properties; rings, integral domains and fields; subrings; direct product of rings; homomorphisms and isomorphisms; ideals and quotient rings; prime and maximal ideals; Fundamental Homomorphism Theorem; Polynomial Rings. 

Mandatory literature

Fernandes, R.L., Ricou; Introdução à Álgebra, IST Press, 2004

Complementary Bibliography

Fraleigh, John B; A first course in abstract algebra, Addison-Wesley, 1967
Rotman, Joseph; A first course in abstract algebra, 3 edition, Pearson, 2005

Teaching methods and learning activities

Exposition of the theory by the teacher. Exercise sheets are provided to the students some of which to be solved in the practical lessons. The webpage of the course contains other materials, e.g.exams from previous years and resolution of the tests. Regular tutorial time to provide individual support to the students. The students have access to the evaluation tests and exams, and are entitled to receive all the explanations and corrections they require.

keywords

Physical sciences

Evaluation Type

Distributed 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	70,00
Frequência das aulas	70,00
Total:	140,00

Eligibility for exams

The students are not required to attend the classes.

Calculation formula of final grade

The students have the opportunity of doing three tests during the semestre. A student that has a positive evaluation on a test, is not required to do the correspondent part in the final exam. A student that has a positive evaluation on the sum of the three tests is not required to do the final exam.

A special complementary evaluation is required to obtain final grades greater than 17. Only in the second period of exams, a  complementary evaluation may be considered for students with grades greater than 8,5 but inferior to 9,5.

Special assessment (TE, DA, ...)

The exams required under the special cases previewed in the law will be written, but may be preceded by na oral exam to establish if the student should be admitted or not to the written exam. 

Classification improvement

The student has the right to make a (single) attempt to improve his final classification by doing the exam in one of the two exam periods following the one when he was approved. The final marking is the highest among the original marking and the marking of the new exam.

Observations

Article 13th of the General Regulation for Students’ Evaluation in the University of Porto, approved the 19th May 2010: ``Any student who commits fraud in an exam or test fails that exam and will face disciplinary charges by the University.'