## MB151 Linear models

Faculty of Informatics
Spring 2023
Extent and Intensity
2/2/0. 3 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Taught in person.
Teacher(s)
doc. Mgr. Ondřej Klíma, Ph.D. (lecturer)
Mgr. Pavel Francírek, Ph.D. (seminar tutor)
Mgr. Jan Jurka (seminar tutor)
doc. Mgr. Michal Kunc, Ph.D. (seminar tutor)
Mgr. Richard Smolka (seminar tutor)
Mgr. Miloslav Štěpán (seminar tutor)
Guaranteed by
doc. Mgr. Ondřej Klíma, Ph.D.
Department of Computer Science - Faculty of Informatics
Contact Person: doc. Mgr. Ondřej Klíma, Ph.D.
Supplier department: Department of Mathematics and Statistics - Departments - Faculty of Science
Prerequisites (in Czech)
! MB101 Mathematics I && ! MB201 Linear models B
Doporučujeme studentům mít absolvovaný předmět IB000, i když po obsahové stránce na něj bezprostředně nenavazujeme.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 53 fields of study the course is directly associated with, display
Course objectives
Introduction to linear algebra and analytical geometry.
Learning outcomes
At the end of this course, students should be able to: understand basic concepts of linear algebra; apply these concepts to iterated linear processes; solve basic problems in analytical geometry.
Syllabus
• The course is the first part of the four semester block of Mathematics. In the entire course, the fundamentals of general algebra and number theory, linear algebra, mathematical analysis, numerical methods, combinatorics, as well as probability and statistics are presented. Content of the course Linear models:
• 1. Introduction (3 weeks) -- motivating examples, real and complex numbers, roots of real polynomials, matrix multiplication, recurrence relations (incl. recurrence in combinatorics), geometry in two dimensions.
• 2. Vector spaces (4 weeks) -- systems of linear equalities, matrix calculus (determinant and inverse matrix), vector spaces (formal definition and examples), linear independence, basis, coordinates, scalar product, length of vector, orthogonality, explicit formulas for recurrence relations.
• 3. Linear mappings (2 weeks) -- representation of linear mappings, eigenvalues and eigenvectors; linear transformations in three dimensions, iterated linear processes (population models and discrete Markov chains).
• 4. Analytical geometry (4 weeks) -- affine and Euclidean spaces (line, plane descriptions, angle, length, volume); systems of linear (in)equalities - linear programming problem; elementary classification of quadrics.
Literature
not specified
• HORÁK, Pavel. Algebra a teoretická aritmetika. 2. vyd. Brno: Masarykova univerzita, 1993. 145 s. ISBN 8021008164. info
Teaching methods
Two hours of lectures, two hours of tutorial. Lecture covering the theory with illustrative solved problems. Tutorials devoted to solving numerical problems.
Assessment methods
During the semester, two obligatory mid-term on-line exams are evaluated (each for 20 points). The final exam has 2 parts (on-line part for 20 points and part in presence form for 40 points). The student needs in total 50 points or more (from 100 points accessible) for successful completion of the course. An activity during the semester (an attendance in seminars or supplementary tests) is a necessary condition for the access to the final examination.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
Listed among pre-requisites of other courses
The course is also listed under the following terms Spring 2020, Spring 2021, Spring 2022.
• Enrolment Statistics (Spring 2023, recent)