FI:MB101 Linear models - Course Information
MB101 Linear modelsFaculty of Informatics
- Extent and Intensity
- 2/2/0. 4 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
- doc. Mgr. Ondřej Klíma, Ph.D. (lecturer)
Mgr. Jana Bartoňová (seminar tutor)
Mgr. Pavel Francírek, Ph.D. (seminar tutor)
RNDr. Veronika Hajnová, Ph.D. (seminar tutor)
Mgr. Jonatan Kolegar (seminar tutor)
Mgr. Jan Reiss (seminar tutor)
Mgr. Radek Suchánek (seminar tutor)
doc. Mgr. Josef Šilhan, Ph.D. (seminar tutor)
doc. RNDr. Martin Čadek, CSc. (assistant)
- Guaranteed by
- prof. RNDr. Jan Slovák, DrSc.
Faculty of Informatics
Contact Person: doc. Mgr. Ondřej Klíma, Ph.D.
Supplier department: Faculty of Science
- Fri 10:00–11:50 D1, Fri 10:00–11:50 D3
- Timetable of Seminar Groups:
MB101/02: Tue 10:00–11:50 A320, O. Klíma
MB101/03: Tue 10:00–11:50 B204, J. Šilhan
MB101/04: Tue 12:00–13:50 A320, J. Bartoňová
MB101/05: Tue 16:00–17:50 A320, J. Bartoňová
MB101/06: Mon 16:00–17:50 B204, V. Hajnová
MB101/07: Mon 18:00–19:50 B204, V. Hajnová
MB101/08: Tue 12:00–13:50 B204, J. Kolegar
MB101/09: Tue 14:00–15:50 B204, J. Kolegar
MB101/10: Mon 10:00–11:50 B204, J. Reiss
MB101/11: Mon 12:00–13:50 B204, J. Reiss
MB101/12: Tue 18:00–19:50 A320, P. Francírek
MB101/14: Mon 10:00–11:50 A320, R. Suchánek
MB101/15: Mon 18:00–19:50 B410, R. Suchánek
MB101/90: Tue 8:00–9:50 A320, J. Šilhan
- Prerequisites (in Czech)
- ! MB005 Foundations of mathematics && ! NOW ( MB201 Linear models B ) && ! MB201 Linear models B
- 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 15 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 and probability; apply these concepts to iterated linear processes; solve basic problems in analytical geometry.
- 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. Warm up (4 weeks) -- scalars, scalar functions, combinatorial examples and identities, finite probability, geometric probability, geometry of the plane, relations and mappings, equivalences and orderings.
- 2. Vectors and matrices (3 weeks) -- vectors, vector space, linear independence, basis, linear mappings, matrices, matrix calculus and determinants, orthogonality, eigenvalues and eigenvectors.
- 3. Linear models (3 weeks) -- systems of linear (in)equalities, linear programming problem, linear difference equations, iterated linear processes (population models) and Markov chains.
- 4. Analytical geometry (2 weeks) -- geometrical applications: line, plane, parametric versus non-parametric descriptions, positioning of planes and lines, projective space extension, angle, length, volume, elementary classification of quadrics.
- recommended literature
- 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
- J. Slovák, M. Panák a kolektiv, Matematika drsně a svižně, učebnice v přípravě
- 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 two hours long and written for max 20 points. For successful examination (the grade at least E) the student needs in total 22 points or more.
- Language of instruction
- Follow-Up Courses
- Further Comments
- Study Materials
The course is taught each semester.
- Listed among pre-requisites of other courses
- MA007 Mathematical Logic
MB005 || MB101|| MB201|| PřF:M1120 || PřF:M1125
- MA015 Graph Algorithms
- MB141 Linear algebra and discrete mathematics
!NOW(MB151) && ( !MB151 || !MB154 ) && ( !MB101 || !MB104 )
- MB143 Design and analysis of statistical experiments
MB141 || MB142 || MB101 || MB201 || MB102 || MB202
- MB151 Linear models
!MB101 && !MB201
- MB153 Statistics I
( MB151 || MB101 || MB201 || MB152 || MB102 || MB202 ) && ( !MB103 && !MB203 && !MV011 )
- MB154 Discrete mathematics
!MB104 && !MB204 && ( MB101 || MB201 || MB151 || MB102 || MB202 || MB152 )
- MV008 Algebra I
(MB005||MB101||MB201||MB151) && !MB008
- PV275 Introduction to Quantum Computer Programming
( MB141 || MB151 || MB101 || MB201 ) && IB111
- MA007 Mathematical Logic