Algebra II

Code:

M341

Acronym:

M341

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2014/2015 - 1S

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:AST	1	Plano de Estudos a partir de 2008	3	-	7,5	-
L:B	0	Plano de estudos a partir de 2008	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	11	Plano de estudos a partir de 2009	3	-	7,5	-
L:Q	0	Plano de estudos Oficial	3	-	7,5	-

Teaching language

Suitable for English-speaking students

Objectives

To get acquainted with the basic concepts of Galois theory. To deepen knowledge of group theory. To understand the proof of the unsolvability by radicals of the quintic.

Learning outcomes and competences

Capability of solving problems in the area. Autonomy on solving exercises.

Working method

Presencial

Program

1. 
   

   Polynomial rings

   
   


2. 
   

   Polynomial equations: classical formulae

   
   


3. 
   

   Factorization of polynomials

   
   


4. 
   

   Field extensions

   
   


5. 
   

   Fileld extensions as vectorial spaces

   
   


6. 
   

   Splitting field of a polynomial

   
   


7. 
   

   Finite fields and perfect fields

   
   


8. 
   

   Constructions with ruler and compass

   
   


9. 
   

   Galois groups

   
   


10. 
    

    Galois correspondence

    
    


11. 
    

    Normal extensions

    
    


12. 
    

    Group actions and the Theorems of Sylow

    
    


13. 
    

    Solvable groups

    
    


14. 
    

    Solvability by radicals

    
    

 

 

Mandatory literature

Rotman Joseph; Galois theory. ISBN: 0-387-98541-7
Fraleigh John B.; A first course in abstract algebra. ISBN: 0-201-16847-2

Complementary Bibliography

Lang Serge; Algebra. ISBN: 0-201-55540-9
Howie John M.; Fields and Galois theory. ISBN: 1-85223-986-9

Teaching methods and learning activities

Presentation of results and examples by the lecturer. Exercises shall be proposed to the students in advance and discussed in the classroom.

Evaluation Type

Distributed evaluation with final exam

Assessment Components

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

Calculation formula of final grade

Two (optional) tests will be held during the semester. Any student obtaining an average marking equal or superior to 10 at the tests needs not do the final exam. If they choose to do the exam at the normal season and present it for evaluation, their final marking will be the one obtained in the exam (the tests' marking having become irrelevant). All students failing to get over the threshold of 10 at the tests must do the final exam. A minimal mark of 8.0 is required in the exam to apply for a complementary oral exam. On any route (tests or final exam), final markings superior to 18 will require a complementary written exam.

Observations