MB201 Linear models B

Faculty of Informatics
Autumn 2012
Extent and Intensity
4/2. 6 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
Mgr. Martin Panák, Ph.D. (lecturer)
prof. RNDr. Jan Slovák, DrSc. (lecturer)
RNDr. David Klaška (seminar tutor)
doc. Mgr. Aleš Návrat, Dr. rer. nat. (seminar tutor)
RNDr. Jan Vondra, 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
Mon 16:00–17:50 D1, Mon 16:00–17:50 D3, Mon 16:00–17:50 D2, Wed 10:00–11:50 D3
  • Timetable of Seminar Groups:
MB201/01: Wed 14:00–15:50 G123, M. Panák
MB201/02: Thu 14:00–15:50 C511, A. Návrat
MB201/03: Fri 12:00–13:50 G125, D. Klaška
MB201/04: Fri 14:00–15:50 G125, D. Klaška
Prerequisites
! MB005 Foundations of mathematics && !NOW( MB101 Linear models ) && ! MB101 Linear models
High school mathematics.
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
The course is the first part of the four semester block of Mathematics in its exetended form. In the entire course, the fundamentals of general algebra and number theory, linear algebra and analysis, numerical methods, combinatorics as well as probability and statistics are presented. Passing this four semester course will allow the student to deal with basic mathematical concepts and problems and he/she will master the discrete and continuous intuition necessary for the mathematical formulation of real problems. The first part of the course, in particular, aims at the principles of mathematics, linear algebra, elementary geometry and some explicit applications. The extended version adds more demanding mathematical tools and relations to the content of MB101.
Syllabus
  • 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
  • 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
Four hours of lectures (two of them shared with MB101), two hours of tutorial. Final written test followed by oral examination. Results of tutorials/homeworks are partially reflected in the assessment.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Information on the extent and intensity of the course: 2.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, Autumn 2017, Autumn 2018.
  • Enrolment Statistics (Autumn 2012, recent)
  • Permalink: https://is.muni.cz/course/fi/autumn2012/MB201