Algebra
Module: FUNDAMENTALS
Matter: MATHEMATICS I
Main language of instruction: Spanish
Other languages of instruction: Catalan, English
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Head instructor
Dra. Àurea CARTANYÀ - acartanya@uic.es
Office hours
The office hours are on Monday from 9:00 am to 10:pm.
Linear algebra is a fundamental subject for technical and scientific studies. Algebra involves the study of concepts such as vector spaces, matrices and systems of linear equations. It provides the student with the necessary means to solve a wide range of problems that govern physical phenomena. Likewise, it constitutes the solid and necessary mathematical base for multiple subjects of the following courses.
None
After passing the subject, students will have acquired the following skills:
Topic 0.
Preliminaries. Sets and applications. Rings and bodies.
Topic 1. Linear systems and matrices
1.1 Systems of linear equations
1.2 Matrices. Elementary transformations
1.3 Operations with matrices.
1.4 Regular matrices.
1.5 Determinants
Topic 2. Vector spaces.
2.1 Definition, properties.
2.2 Linear dependence
2.3 Generator systems. Bases.
2.4 Vector subspaces. Dimension of subspaces.
2.5 Sum and intersection of vector subspaces. Direct sum.
Topic 3. Linear applications.
3.1 Definition and examples.
3.2 Nucleus and image
3.3 Injective and exhaustive applications
3.4 Operations with linear applications
3.5 Matrix associated with the linear application
3.6 Base change.
Topic 4. Diagonalization
4.1 Preliminaries (polynomials, factoring)
4.2 Definition of the problem of diagonalization
4.3 Eigenvalues and autovectors
4.4 Characteristic polynomial
4.5 Endomorphism and diagonalizable matrices
Methodology
The subject will be taught face-to-face through theoretical classes and problem solving sessions.
The theory of the subject will be exposed in a rigorous way avoiding, however, an excess of formalization, which could mask the true purpose of the subject: teach the fundamentals of linear algebra to future bioengineers. For this reason, conceptual clarity will be emphasized. In addition, students will learn to deal with linear algebra problems using advanced computer programs.
The concepts must be consolidated by solving the exercises that are proposed to the student throughout each topic. These exercises will be resolved or discussed in class. It is also convenient for the student to solve more exercises in the books recommended in the bibliography.
Formation activities
First sitting
The evaluation of the subject consists of 4 blocks with the corresponding weights:
An essential requirement to pass the subject is to obtain a grade greater than or equal to 4 in the final exam. Otherwise the final grade of the subject will be the final exam grade and the rest of the blocks will not be taken into account.
If the weighted average of these four blocks is greater than or equal to 5 or the final exam grade is greater than or equal to 5, the student has passed the subject. The final grade of the subject will be the maximum between the weighted average of the 4 blocks and the final grade of the final exam.
Second sitting
Students who have not passed the subject in the first sitting will have the opportunity to return to take a final exam. The midterm exam, deliveries and multiple choice exam marks will remain unchanged. The evaluation criteria will be the same as in the first sitting.
Therefore, an essential requirement to pass the subject is to obtain a grade greater than or equal to 4 in the final exam of the second sitting. Otherwise the final grade of the subject will be the final exam grade of the second sitting and the other blocks will not be taken into account.
Then, if the weighted average between E, T, P and the final exam of the second sitting is greater than or equal to 5 or the mark of the final exam of the second sitting is greater than or equal to 5, the student has passed the subject in the second sitting.
Important considerations:
-Luis Miguel Merino y Evangelina Santos: Álgebra lineal con métodos elementales, Ediciones Paraninfo, 2015.
Further reading
-Ferran Puerta Sales: Álgebra lineal. Edicions UPC
-Manuel Castellet y Irene Llerena: Àlgebra lineal y geometria. Universitat Autonoma de Barcelona, Servei de Publicacions.
E: exam date | R: revision date | 1: first session | 2: second session: