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FI:MB201 Linear models B - Course Information

## MB201 Linear models B

**Faculty of Informatics**

Autumn 2018

**Extent and Intensity**- 4/2. 6 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
**Teacher(s)**- doc. Mgr. Ondřej Klíma, Ph.D. (lecturer)

doc. Mgr. Josef Šilhan, Ph.D. (lecturer)

doc. Ilya Kossovskiy, Ph.D. (seminar tutor)

RNDr. Jiří Pecl, Ph.D. (seminar tutor) **Supervisor**- prof. RNDr. Jan Slovák, DrSc.

Faculty of Informatics

Contact Person: prof. RNDr. Jan Slovák, DrSc.

Supplier department: Faculty of Science **Timetable**- Wed 16:00–17:50 D2, Fri 8:00–9:50 D1, Fri 8:00–9:50 D3, Fri 8:00–9:50 D2
- Timetable of Seminar Groups:

*J. Pecl*, Nepřihlašuje se. Určeno pro studenty se zdravotním postižením.

MB201/01: Wed 10:00–11:50 A320,*O. Klíma*

MB201/02: Wed 12:00–13:50 A320,*O. Klíma*

MB201/03: Wed 14:00–15:50 A320,*J. Šilhan*

MB201/04: Wed 14:00–15:50 B204,*I. Kossovskiy* **Prerequisites**(in Czech)- !
**MB005**Foundations of mathematics && ! NOW (**MB101**Linear models ) && !**MB101**Linear models **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 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.
**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. The extended version MB201 adds more demanding mathematical tools and relations to the content of MB101.
- Additionally to the content of MB101, we shall cover: 1. Warm up -- axiomatics of scalars, formal proofs, inclusion and exclusion principle, matrix calculus in the plane, formal constructions of numbers
- 2. Vectors and matrices -- Laplace development of determinants, abstract vector spaces, linear mappings, unitary and adjoint mappings
- 3. Linear models -- Perron (-Frobenius) theory of positive matrices, canonical matrix forms and decompositions, pseudoinverses
- 4. Analytical geometry -- projective extension, affine, Euclidean and projective classification of quadrics.

**Literature**- MOTL, Luboš and Miloš ZAHRADNÍK.
*Pěstujeme lineární algebru*. 3. vyd. Praha: Univerzita Karlova v Praze, nakladatelství Karolinum, 2002. 348 s. ISBN 8024604213. info - J. Slovák, M. Panák a kolektiv, Matematika drsně a svižně, učebnice v přípravě

*recommended literature*- FUCHS, Eduard.
*Logika a teorie množin (Úvod do oboru)*. 1. vyd. Brno: Rektorát UJEP, 1978. 175 s. 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 - HORÁK, Pavel.
*Algebra a teoretická aritmetika.*2. vyd. Brno: Masarykova univerzita, 1993. 145 s. ISBN 8021008164. info

*not specified*- MOTL, Luboš and Miloš ZAHRADNÍK.
**Teaching methods**- Lecture combining theory with problem solving. Seminar groups devoted to solving 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 written test for max 20 points is followed by the oral examination for max 10 points. For successful examination (the grade at least E) the student needs in total 27 points or more.
**Language of instruction**- Czech
**Follow-Up Courses****Further comments (probably available only in Czech)**- Study Materials

The course is taught annually. **Listed among pre-requisites of other courses**- PřF:
**M7190**Game Theory

M1110 || M1111 || FI:MB101 || FI:MB201 || FI:MB003 **MA007**Mathematical Logic

MB005 || MB101|| MB201|| PřF:M1120 || PřF:M1125**MA015**Graph Algorithms

MB005||(MB101&&MB102)||(MB201&&MB102)||(MB101&&MB202)||(MB201&&MB202)||(PřF:M1120)||PROGRAM(N-IN)||PROGRAM(N-AP)**MB101**Mathematics I

!MB005 && !MB201**MV008**Algebra I

(MB005||MB101||MB201) && !MB008

- PřF:

- Enrolment Statistics (recent)

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