Algebra I

Code:

M241

Acronym:

M241

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2011/2012 - 1S

Active?	Yes
Web Page:	http://moodle.up.pt/course/view.php?id=1993
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	4	Plano de Estudos a partir de 2008	3	-	7,5	-
L:B	0	Plano de estudos a partir de 2008	3	-	7,5	-
L:CC	16	Plano de estudos de 2008 até 2013/14	2	-	7,5	-
			3
L:F	6	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	106	Plano de estudos a partir de 2009	2	-	7,5	-
L:Q	0	Plano de estudos Oficial	3	-	7,5	-
M:CC	2	PE do Mestrado em Ciência de Computadores	1	-	7,5	-
			2

Teaching language

Portuguese

Objectives

Introduction to basic algebra concepts.

Program

1- PRELIMINARiES
1.1. Binary relation
1.2. Order relation
1.3. Equivalence relation

2- Groups
2.1. Basic notions and examples.
2.2. Subgroups
2.3. The index of a subgroup
2.4. Normal subgroup and the quotient group
2.5. Homomorphisms and the Homomorphism Theorem
2.6. Direct products
2.7. Some special groups
2.7.1 Cyclic groups
2.7.2 The symmetric group
2.7.3 The group of symmetries
2.8. Abelian group finitely generated
2.8.1. The Fundamental Theorem of finitely generated Abelian groups

3- Rings
3.1. Definition and basic properties
3.1.1. Rings
3.1.2. Divison rings, integral domains and fields
3.1.3. Subrings
3.1.4. Direct product of rings
3.1.5. Homomorphisms and isomorphisms
3.1.6. Ideals and the factor ring
3.1.7. The Theorem of the Homomorphism
3.1.8. The fraction field of a domain
3.2. Some important examples of rings
3.2.1. The ring of integers
3.2.2. The ring of integers mod n
3.2.3. The field of rational numbers
3.2.4. O corpo dos números reais
3.2.5. The ring of polynomials
3.2.6. The field of complexes numbers

Mandatory literature

000053376. ISBN: 972-592-076-7
000044387
000013719

Complementary Bibliography

000075646. ISBN: 972-8469-27-6

keywords

Physical sciences > Mathematics > Number theory
Physical sciences > Mathematics > Algebra > Group theory
Physical sciences > Mathematics > Algebra

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Description	Type	Time (hours)	Weight (%)	End date
Attendance (estimated)	Participação presencial	75,00
	Total:	-	0,00

Eligibility for exams

All the students who does not attend more than 4 TP's will be excluded from the course..

Students are exempt from attending the TP if:
- they have attended the course before;
- they are part of a mobility program outside the country;
- students covered by a special status that allows it.
Students in this situation can apply to be exempt until October the 8th.

Calculation formula of final grade

Students will be assessed through two midterm quizzes and a final exam. These midterm quizzes can replace some parts of the first exam if the students wishes so. The first final exam will have three groups, the last group count 4 points (out of 20), the remaining two groups 8 points. The first two parts of the first exam can be replaced by a midterm quiz according to the following table:

First part– the first quiz on October the 28th (this quiz counts 8 points)

Second part - second quiz on December the 7th (counts 8 points)

Any student with a score higher than 9.5 can be asked to do an oral examination, in such a case the final grade will be the arithmetic mean of the scores obtained in the written and oral part.

Examinations or Special Assignments

Any special exam is a written exam. Any student applying for this exam can be asked to do short oral or written test to decide whether he/she is prepared to take the exam. In case the student fails this test he/she will not be allowed to take the special exam.