MB201 Linear models B

Faculty of Informatics
Autumn 2017
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. (seminar tutor)
Guaranteed by
prof. RNDr. Jan Slovák, DrSc.
Faculty of Informatics
Contact Person: prof. RNDr. Jan Slovák, DrSc.
Supplier department: Faculty of Science
Timetable
Tue 14:00–15:50 A217, Fri 10:00–11:50 D1, Fri 10:00–11:50 D3
  • Timetable of Seminar Groups:
MB201/01: Mon 12:00–13:50 A320, J. Šilhan
MB201/02: Mon 16:00–17:50 A320, J. Šilhan
MB201/03: Tue 8:00–9:50 B204, J. Šilhan
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 / 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 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
    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
  • J. Slovák, M. Panák a kolektiv, Matematika drsně a svižně, učebnice v přípravě
    not specified
  • 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
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
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, Autumn 2018.
  • Enrolment Statistics (Autumn 2017, recent)
  • Permalink: https://is.muni.cz/course/fi/autumn2017/MB201