Algebra II

Code:

M341

Acronym:

M341

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2013/2014 - 1S

Active?	Yes
Web Page:	https://moodle.up.pt/course/view.php?id=547
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:AST	0	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	0	Plano de estudos de 2008 até 2013/14	3	-	7,5	-
L:F	0	Plano de estudos a partir de 2008	3	-	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	15	Plano de estudos a partir de 2009	3	-	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	-
			2

Teaching language

Suitable for English-speaking students

Objectives

The student should know and understand the concepts and basic results of Galois Theory, including basic familiarity with the classical examples, applications of these structures and also at an abstract level. It is intended that this unit contribute to the development of skills of abstract reasoning and familiarity with the mathematical method.

 

Learning outcomes and competences

One expects that the students learns the basic aspects of Galois theory.

Working method

Presencial

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

 M241 Álgebra I

M141 and M142 Álgebra Linear I and II

Program

 1. Introduction - classical formulas

2. Rings

3. Domains and Fields

4. Homomorphisms and ideals

5. Quotient rings

6. Polynomial rings over fields

7. Prime and Maxmial ideals

8. Irreducible polynomials

9. Splitting fields

10. Galois group

11. Roots of unity

12. Solvability by radicals

13. Independence of characters

14. Galois extensions

15. Galois' fundamental theorem

16. Applications

17. Galois Theorem

Mandatory literature

000049708. ISBN: 0-387-97305-2

Complementary Bibliography

000084951. ISBN: 1-85223-986-9
000044388. ISBN: 0-201-16847-2

Teaching methods and learning activities

The theoretical content will be lectured in two classes of 1,5 hours per week and will be worked out with the students in 1,5 hours of example classes. Furthermore the students shall write two testes.

keywords

Physical sciences > Mathematics > Algebra
Physical sciences > Mathematics > Algebra > Group theory
Physical sciences > Mathematics > Algebra > Field theory

Evaluation Type

Distributed evaluation without final exam

Assessment Components

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

Calculation formula of final grade

Two quizzes will be held during the semester.

 Each of the quizzes counts as follows:

1º quiz = 8 values

 2º quiz = 12 values

 The final grade is the sum of the grades  of the two tests.

Examinations or Special Assignments

1st test: 31.10.2013 (8 points)

2nd test: 19.12.2013 (12 points)

Classification improvement

The students that intent to improve their final grade can do an exam in the época de recursos.

There is no possibility to improve only part of the final grade.