Applied Linear Algebra
Universidad Antonio de Nebrija
Area of Study
Algebra, Calculus, Mathematics
Taught In English
Recommended U.S. Semester Credits3
Recommended U.S. Quarter Units4
Hours & Credits
Applied Linear Algebra
Prerequisites: basic calculus and algebra
Office hours: to be communicated the first day of class
1. Course Description
The course will focus on matrix and vector methods for studying systems of linear equations, with an emphasis on concrete calculations and applications. Specific topics to be covered include matrices, Gaussian elimination, vector spaces, LU decomposition, orthogonality, the Gram–Schmidt process, determinants, inner products, eigenvalue problems, and applications to differential equations and Markov processes.
2. Learning Objectives
Students who successfully complete this course will be able to:
• Use matrices to solve linear systems of equations;
• Verify whether a given set is a vector space;
• Find bases of subspaces;
• Find matrix representations of linear transformations and use them in applied problems;
• Determine eigenvalues and bases of eigenspaces;
• Determine and use matrix factorizations such as LU, QR and SVD;
• Enhance their understanding of the above concepts through occasional MATLAB-based homework problems.
The majority of the course syllabus follows the main methodological guidelines of the Communicative Approach, based on the core principles of procedure conception and constructive acquisition of knowledge. The methodology is based on the teaching-learning procedures, focused on the learner, which encourages active participation and results in the development of general and specific competencies that prove knowledge, capacities and attitudes for their future professional careers.
The form of assessment is based on the core principles of the educational assessment, i.e., an active and participative teaching-learning process focused on the learner. The instructor uses numerous and differentiated forms of assessment to calculate the final grade received for this course. For the record, these are listed below. The content, criteria and specific requirements for each assessment category will be explained in greater detail in class.
5.1. Grading system
In the Spanish educational system, it is required to quantitatively express the result of each student’s evaluation. In order to do so, Nebrija faculty uses different strategies and instruments such as: papers,
exams, tests, projects, self-evaluation activities, etc. In order to issue a final grade for the Spanish Plus programs the following scale is established:
- 30 % Attendance and active participation in class
- 30% Daily work/ Papers/ Essays
- 40% Exams/ Final papers or projects*
Therefore, the final grade is the average between attendance and participation, daily work and exams, presentations, projects and essays.
Active participation in class is evaluated by means of different activities such as:
- Activities and exercises correction;
- Reflection upon the different contents in the course;
- Oral activities (individual, in pairs or in groups). Fluency, correction, adequacy and relevance are taken into account.
Daily work makes reference to any activity or task that is done inside or outside of the classroom, whether during the class time or at any other time.
Exams/ Final papers or projects
The course includes a midterm and a final written exam on theoretical concepts and course facts. If a student, unjustifiably, does not do or submit an exam, paper or project, it will be graded with a ‘0’.
* A minimum grade of 5 must be obtained in a final exam/ final project in order to pass the course.
5.2. Attendance, participation and grading policies
5.2.1. Attendance policy
Attendance is mandatory. In case of missing 5 or more sessions in one course, the student will receive a zero in his/her participation and attendance grade. In addition, not attending classes will not excuse the student from handing in in any homework, papers or essays previously assigned.
The following situations must be considered:
- Each session of class will count as an absence.
- Two delays of more than 15 minutes will be considered an absence. The entrance to class will not be allowed after 30 minutes once it has started.
- There are no excused absences. E.g.: Not attending class because of sickness will count as an absence. The student is responsible for catching up with any homework done while absent.
- Exams dates have been officially approved by the University, therefore, they will not be changed.*
*Except for those courses where the professor will set up specific dates and inform the students at the beginning of the program.
Courses and course hours of instruction are subject to change.
Eligibility for courses may be subject to a placement exam and/or pre-requisites.
Availability of courses is based on enrollment numbers. All students should seek pre-approval for alternate courses in the event of last minute class cancellations