Degree | Type | Year | Semester |
---|---|---|---|
2500097 Physics | FB | 1 | 2 |
It is advisable to understand the main notions of the course Algebra I, specially those of Linear Algebra.
1. Diagonalization of matrices and endomorphisms
2. Bilinear forms
2.1 Symmetric bilinear forms over real vector spaces. Euclidian inner podruct.
2.2 Hermitian forms.
2.3 Minkowski product.
2.4 Orthogonal diagonalization of symmetric matrices: the Spectral Theorem. el Teorema espectral.
3. Lineal Geometry.
4. Multilinear Algebra
4.1 Dual space.
4.2 Tensors.
The objectives will be achieved indirectly in the following way:
1. Learning the techniques of diagonalization of matrices and endomorphisms.
2. Learning the algebraic foundations of Euclidean geometry and, more generally, the symmetrical bilinear forms on the real ones.
3. Learning the algebraic foundations of Minkowski's geometry
4. Learning the techniques of multilinear algebra and, in particular, working with tensors.
And all this accompanied by the development of logical reasoning, which is encouraged by teaching the demonstrations of many of the theorems of the course.
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 | |||
Lectures | 29 | 1.16 | 1, 2, 3, 4, 6, 7 |
Problem sessions | 21 | 0.84 | 1, 2, 3, 4, 6, 5, 7 |
Type: Autonomous | |||
Solving problems | 45 | 1.8 | 1, 2, 3, 4, 6, 5, 7 |
Studying theoretical concepts | 38 | 1.52 | 1, 2, 3, 4, 6, 5, 7 |
40% of the final score will be obtained after the completion of a partial test. Passing this test does not eliminate matter from the final exam.
45% of the final score will be obtained from the final exam
The remaining 15% will be calculated based on the submission of exercice sets.
Students who do not pass the subject after the final exam may submit to a resit exam, which will be worth 85% of the grade. Grade from submissions of exercices has no resit.
Only those students that have been submitted to the partial and final exams can do the resit exam.
After the final exam Honors may be already awarded.
Title | Weighting | Hours | ECTS | Learning Outcomes |
---|---|---|---|---|
A mid-term exam. | 40% | 2 | 0.08 | 1, 3, 4, 6, 5, 7 |
Final exam | 45% | 2.5 | 0.1 | 1, 2, 3, 4, 6, 5, 7 |
Resit exam | 85% | 2.5 | 0.1 | 1, 2, 3, 4, 6, 5, 7 |
Submission of exercise sets | 15% | 10 | 0.4 | 1, 2, 3, 4, 6, 5, 7 |
R. Camps, E. Nart, G. Solanes, X. Xarles, Àlgebra lineal i multilineal.
Complementary bibliography
Lectures
1. F. Cedó i A. Reventós, Geometria plana i àlgebra lineal, Manuals de la UAB, 39, 2004
2. A. Kostrikin and Y. Manin, Linear Algebra and Geometry, Gordon and Breach Science Publishers, Amsterdam, 1989.
Problemes
1. F. Cedó i V. Gisin, Àlgebra Bàsica, Manuals de la UAB, 1997.
2. J. García Lapresta, M. Panero, J. Martínez, J. Rincón y C. Palmero, Tests de Álgebra lineal, Editorial AC, Madrid, 1992.
3. J. Rojo y I. Martín, Ejercicios y Problemas de Álgebra Lineal, Mc. Graw-Hill, Madrid 1994.
4. A. de la Villa, Problemas de Algebra, CLAGSA, Madrid, 1994