MB151 Linear models

Faculty of Informatics
Spring 2020
Extent and Intensity
2/2/0. 3 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
doc. Mgr. Ondřej Klíma, Ph.D. (lecturer)
Mgr. Milan Bačík (seminar tutor)
Mgr. Martin Doležal (seminar tutor)
doc. Mgr. Josef Šilhan, Ph.D. (seminar tutor)
doc. RNDr. Martin Čadek, CSc. (assistant)
Mgr. Pavel Francírek, Ph.D. (assistant)
Mgr. Jonatan Kolegar (assistant)
Mgr. Radka Penčevová (assistant)
prof. RNDr. Jan Slovák, DrSc. (assistant)
doc. Lukáš Vokřínek, PhD. (assistant)
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
Timetable
Mon 17. 2. to Fri 15. 5. Wed 10:00–11:50 D1, Wed 10:00–11:50 D3
  • Timetable of Seminar Groups:
MB151/T01: Wed 19. 2. to Sun 24. 5. Wed 14:00–16:40 115, M. Doležal, Nepřihlašuje se. Určeno pro studenty se zdravotním postižením.
MB151/01: Mon 17. 2. to Fri 15. 5. Wed 8:00–9:50 A320, O. Klíma
MB151/02: Mon 17. 2. to Fri 15. 5. Mon 14:00–15:50 A320, J. Šilhan
MB151/03: Mon 17. 2. to Fri 15. 5. Mon 16:00–17:50 A320, J. Šilhan
MB151/05: Mon 17. 2. to Fri 15. 5. Tue 8:00–9:50 A320, M. Doležal
MB151/06: Mon 17. 2. to Fri 15. 5. Tue 10:00–11:50 A320, M. Doležal
MB151/07: Mon 17. 2. to Fri 15. 5. Mon 8:00–9:50 B204, M. Bačík
MB151/08: Mon 17. 2. to Fri 15. 5. Mon 10:00–11:50 B204, M. Bačík
MB151/09: Mon 17. 2. to Fri 15. 5. Tue 8:00–9:50 B204, M. Bačík
MB151/10: Mon 17. 2. to Fri 15. 5. Tue 10:00–11:50 B204, M. Bačík
MB151/11: Mon 17. 2. to Fri 15. 5. Wed 8:00–9:50 B204, M. Bačík
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
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 (interest computation and 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 exams are evaluated (each for max 10 points). In the seminar groups there are 5 tests during the semester. The seminars are evaluated in total by max 5 points. Students, who collect during the semester (i.e., from tests and mid-term exams) less than 8 points, are graded as X and they do not proceed to the final examination. The final exam is written (max 20 points). For successful examination (the grade at least E) the student needs in total 22 points or more.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.
  • Enrolment Statistics (Spring 2020, recent)
  • Permalink: https://is.muni.cz/course/fi/spring2020/MB151