Degree | Type | Year | Semester |
---|---|---|---|
2500149 Mathematics | OB | 2 | 2 |
The previous academic requirements will be found in the subjects Fundamentals of Mathematics and Linear Algebra, first year.
The skill acquired in algebraic manipulations, and the familiarity with operations in arithmetic contexts or groups of permutations, will continue to be developed, moving to a higher level of abstraction, which is very common in Mathematics. References to vector spaces as a model of algebraic structure and to your knowledge of matrix manipulation will also be frequent. Matrices will be a particularly important source of examples.
The objectives of this subject are of two types: to achieve
training in basic algebra and gaining knowledge and skills
to manipulate abstract objects.
Among the training objectives we highlight the following:
correctly understand and use language and mathematical reasoning in general and algebraic reasoning in particular. Be able to make small demonstrations, develop meaning
critical of mathematical statements,
develop combative attitudes and creativity in the face of problems and, finally, learn to apply abstract concepts and results in concrete examples. Present reasoning or a problem in public and develop agility to answer mathematical questions in a conversation.
The subject is organized in four parts:
I. Group Theory.
II. Commutative rings
III. Factorization.
IV. Finite fields.
This subject has three ours per week of theory lasses, one hour per wek of problem classes, and, during the semester, eight seminar sessions, two ours each.
Students will have the lists of problems previously to be able to work before the problem classes. In classe, you can not solve all the problems but we recommend that students work on their own and asj the teachers their questions. In the seminar sessions the students will work under the supervison of the teacher. In some of these seminars, some exercises will be given that will count for the final mark of the subject.
Title | Hours | ECTS | Learning Outcomes |
---|---|---|---|
Type: Directed | |||
Directed | 16 | 0.64 | |
Theory classes | 43 | 1.72 | |
Type: Supervised | |||
Sminars | 14 | 0.56 | |
Type: Autonomous | |||
Seminar preparation | 145 | 5.8 |
- The student will obtain 10% of the mark of the subject with the delivery of exercises previously done. We denote by LP the mark on 10 calculated as the average of deliveries.
-A written examination will be carried out to evaluate the theoretical and practical knowledge of the subject in mid-semester. The mark on 10 (P1) of this examination will count 30% of the mark of the course.
-In some of the seminars, classroom exercises will be given. They will be short exercises to evaluate practical aspects of the newly completed seminar. The mark (S) on 10, calculated as the average of the seminar marks, will count 10% of the marks of the subject.
-50% of the mark of the mark of the subject will correspond to the mark P2 obtained in the final examination. This examination will eveluate the student's practical an theoretical knowledge.
The mark of the subject is obtained by the expression N = 0,10.LP + 0,10.S + 0,30.P! + 0,50.P2. The student will pass if N is greater or equal than 5.
The qualificacion of Excellent with honours will be awarded based on N
There will be a resit examination corresponding the final examination. Only students with the mark N less than 5 and who have been presented to the examination that give rise to the P1 and P2 marks may attend the resit examination. In this case, the final mark of the subject will be calculated as Max(N; 0,10.LP + 0,10.S + 0,30.P1 + 0,50.R) where R denotes the mark of examination resit
Title | Weighting | Hours | ECTS | Learning Outcomes |
---|---|---|---|---|
Autonomous | 145 hours , 5,8 ECTs | 4 | 0.16 | 2, 3, 1, 4, 8, 7, 6, 5 |
Supervised | 14 hours, 0,56 ECTS | 3 | 0.12 | 2, 3, 1, 4, 8, 7, 6, 5 |
[1] R. Antoine, R. Camps, J. Moncasi. Introducció a l'àlgebra abstracta. Manuals de la UAB, Servei de Publicacions de la UAB, nº 46, Bellaterra, 2007.
[2] F. Cedó, V. Gisin, Àlgebra bàsica, Manuals de la UAB, Servei de Publicacions de la UAB, nº 21, 2007.
[3] P. M. Cohn, Algebra, vols. 1 i 2, John Wiley and Sons, 1989.
[4] J. Dorronsoro, E. Henández, Números, Grupos y anillos, Addison-Wesley, 1996.
[5] F. Delgado, C. Fuertes, S. Xambó, Introducción al Álgebra: anillos, factorización y teoria de cuerpos, Universidad de Valladolid, 1998.
[6] J. B. Fraleight, A First course in Abstract algebra, Addison-Wesley, !982.
[7] T. W. Hungerford, Alñgebra, Springer-Verlag, 1974.