A course is the basic teaching unit, it's design as a medium for a student to acquire comprehensive knowledge and skills indispensable in the given field. A course guarantor is responsible for the factual content of the course.
For each course, there is a department responsible for the course organisation. A person responsible for timetabling for a given department sets a time schedule of teaching and for each class, s/he assigns an instructor and/or an examiner.
Expected time consumption of the course is expressed by a course attribute extent of teaching. For example, extent = 2 +2 indicates two teaching hours of lectures and two teaching hours of seminar (lab) per week.
At the end of each semester, the course instructor has to evaluate the extent to which a student has acquired the expected knowledge and skills. The type of this evaluation is indicated by the attribute completion. So, a course can be completed by just an assessment ('pouze zápočet'), by a graded assessment ('klasifikovaný zápočet'), or by just an examination ('pouze zkouška') or by an assessment and examination ('zápočet a zkouška') .
The difficulty of a given course is evaluated by the amount of ECTS credits.
The course is in session (cf. teaching is going on) during a semester. Each course is offered either in the winter ('zimní') or summer ('letní') semester of an academic year. Exceptionally, a course might be offered in both semesters.
The subject matter of a course is described in various texts.
BIE-LA2.21 Linear Algebra 2 Extent of teaching: 2P+2C Instructor: Forough M., Klouda K. Completion: Z,ZK Department: 18105 Credits: 5 Semester: L Annotation:
Students will broaden their knowledge gained in the BIE-LA1 introductory course, where only vectors in the form of n-tuples of numbers were considered. Here we will introduce vector spaces in a general abstract form. The notions of a scalar product and a linear map will enable to demonstrate the profound link between linear algebra, geometry, and computer graphics. The other main topic will be numerical linear algebra, in particular problems with solving systems of linear equations on computers. The issues of numerical linear algebra will be demonstrated mainly on the matrix factorization problem. Selected applications of linear algebra in various fields will be presented.
Lecture syllabus:
1. Abstract vector spaces, infinite-dimensional vector spaces. 2. Scalar products, vector norm, orthogonality. 3. Scalar products and analytical geometry. 4. [2] Linear maps and their matrices. 6. Affine transformations, homogeneous coordinates, projections and operations in 3D space as linear maps. 7. Introduction to numerical mathematics. 8. Solving systems of linear equations on computers. 9. [2] Matrix factorizations (LU, SVD, QR): computation and applications. 11. [3] Applications of linear algebra: the least-squares method, linear programming, recurrent equations. Seminar syllabus:
1. Abstract vector spaces. 2. Scalar products, vector norm, orthogonality. 3. Analytical geometry. 4. Linear maps. 5. Matrices of linear maps. 6. [2] Affine transformations, homogeneous coordinates, projections and operations in 3D space as linear maps. 8. Systems of linear equations. 9. [2] Matrix factorizations (LU, SVD, QR). 11. The least-squares method. 12. Linear programming. 13. Recurrent equations. Literature:
1. Lloyd N. T., David B. : Numerical Linear Algebra. SIAM, 1997. ISBN 978-0898713619. 2. Lyche T. : Numerical Linear Algebra and Matrix Factorizations. Springer, 2020. ISBN 978-3030364670. 3. Gentle J. E. : Matrix Algebra: Theory, Computations and Applications in Statistics (2nd Edition). Springer, 2017. ISBN 978-3319648668. 4. Lengyel E. : Mathematics for 3D Game Programming and Computer Graphics (3rd Edition). Cengage Learning PTR, 2011. ISBN 978-1435458864. Requirements:
We assume the students finished course BI-LA1.21.
http://courses.fit.cvut.cz/BI-LA2 The course is also part of the following Study plans:
Study Plan Study Branch/Specialization Role Recommended semester BIE-PI.21 Computer Engineering 2021 PS 2 BIE-SI.21 Software Engineering 2021 V 2 BIE-TI.21 Computer Science 2021 PS 2 BIE-IB.21 Information Security 2021 (Bachelor in English) V 2 BIE-PS.21 Computer Networks and Internet 2021 VO 2 BIE-PV.21 Computer Systems and Virtualization 2021 V 2
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