FI:MB151 Linear models - Course Information
MB151 Linear models
Faculty of InformaticsSpring 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:
MB151/01: 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
- 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 (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
- recommended literature
- PANÁK, Martin, Jan SLOVÁK and Michal BULANT. Matematika drsně a svižně (Brisk quide to mathematics). 2013. ISBN 978-80-210-6307-5. Available from: https://dx.doi.org/10.5817/CZ.MUNI.O210-6380-2013. Základní učebnice matematiky pro vysokoškolské studium. Na MU využívána zejména jako podpora výuky matematiky na Fakultě informatiky. info
- MOTL, Luboš and Miloš ZAHRADNÍK. Pěstujeme lineární algebru. 3. vyd. Praha: Univerzita Karlova v Praze, nakladatelství Karolinum, 2002, 348 s. ISBN 8024604213. info
- RILEY, K.F., M.P. HOBSON and S.J. BENCE. Mathematical Methods for Physics and Engineering. second edition. Cambridge: Cambridge University Press, 2004, 1232 pp. ISBN 0 521 89067 5. info
- 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
- MB141 Linear algebra and discrete mathematics
!NOW(MB151) && ( !MB151 || !MB154 ) - MB143 Design and analysis of statistical experiments
(MB141 || MB142 || MB151 || MB152) && !MB153 && !NOW(MB153) - MB153 Statistics I
(MB151 || MB152 || PřF:M1110 || PřF:M1100) && !NOW(MB143) - MB154 Discrete mathematics
MB151 || MB152 || PřF:M1110 || PřF:M1100 - MV008 Algebra I
MB151 - PV275 Introduction to Quantum Computer Programming
( MB141 || MB151 || MB101 || MB201 ) && IB111 - PV291 Introduction to Digital Signal Processing
MB151&& MB152
- MB141 Linear algebra and discrete mathematics
- Enrolment Statistics (Spring 2020, recent)
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