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.
Annotation: Within the schedule set by the centre or degree programme, 15 minutes of one class will be reserved for students to evaluate their lecturers and their courses or modules through questionnaires.
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 |
20% of the mark of the course corresponds to the delivery of problems to the seminars (S).
There will be a written test, in the middle of the semester, to evaluate the theoretical and practical abilities of the subject. The date of the test will be set by the degree coordinator. The mark on 10 (P) of this test will correspond to 30% of the total mark.
50% of the mark corresponds to that obtained in the final exam (F). In this exam
the theoretical and practical knowledge of the subject will be evaluated.
If in F a mark greater than or equal to 3.5 is obtained, then the student obtains the mark N = 0.20 · S + 0.30 · P + 0.50 · F. The subject will be passed, therefore, if the grade N is equal to or higher than 5 and if, at least, a 3.5 has been taken in the final exam.
Honor registrations will be awarded based on the value of the mark N.
There will be a recuperation exam corresponding to the final exam. Only students who have obtained a grade of less than 3.5 in the final exam or who have a grade of N <5 will be able to take this exam. In this case, we will calculate the value N '= MAX (N; 0.20 · S + 0.30 · P + 0.50 · R), where R denotes the mark of the recuperation exam and the final mark will be N' provided this value does not exceed 7, otherwise, the final mark will be 7.
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, Bellaterra, 2007.
[3] David S. Dummit and Richard M. Foote, Abstract Algebra, 3rd. Edition, Wiley, 2003.
[4] J.B. Fraleigh. A First course in abstract algebra. Pearson Education, 7th Edition, 2014. Review: https://www.maa.org/press/maa-reviews/abstract-algebra
[5] T. W. Hungerford, Abstract Algebra, Brooks/Cole, 2013. Review:
https://www.maa.org/press/maa-reviews/abstract-algebra-an-introduction
It is not planned to use any specific software in the subject. However, an algebraic manipulator (Maple, Sage, ....) can be useful when making calculations.
There are specific programs for manipulating groups such as GAP - Groups, Algorithms, Programming -
a System for Computational Discrete Algebra that is useful to know and that can solve most of the most computational problems of groups.