T2_MB101 Linear models

Pan-university studies
Spring 2013
Extent and Intensity
0/6. 0 credit(s). Type of Completion: -.
Teacher(s)
Mgr. Martin Panák, Ph.D. (lecturer)
prof. RNDr. Jan Slovák, DrSc. (lecturer)
Mgr. Jitka Hořanská (seminar tutor)
Guaranteed by
prof. RNDr. Jan Slovák, DrSc.
Faculty of Informatics
Contact Person: Mgr. Lukáš Másilko
Supplier department: Support Centre for Students with Special Needs
Timetable of Seminar Groups
T2_MB101/T01: Mon 8:00–9:55 Učebna S4 (35a), Thu 10:00–11:55 Učebna S4 (35a), J. Hořanská
T2_MB101/T02: Tue 10:00–11:55 Učebna S4 (35a), Wed 8:00–9:55 Učebna S1 (36a), Fri 10:00–11:55 Učebna S4 (35a), J. Hořanská
Prerequisites
SOUHLAS
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.
The capacity limit for the course is 6 student(s).
Current registration and enrolment status: enrolled: 0/6, only registered: 0/6, only registered with preference (fields directly associated with the programme): 0/6
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 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. 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.
Syllabus
  • 1. Warm up (4 weeks) -- scalars, scalar functions, combinatorial examples and identities, finite probability, geometric probability, geometry of the plane, relations and mappings, eqivalences nad 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 processes (population models) and Markov chains.
  • $. Analytical geometry (2 weeks) -- geometrical applications: line, plane, parametric versus non-paramteric descriptions, positioning of planes and lines, projective space extension, angle, length, volume, elementary 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
This is a tutorial-based course.
Assessment methods
No completion. The subject is only offered to students with special needs. It is designed as a record of individual instruction.
Language of instruction
Czech
Further comments (probably available only in Czech)
Information on completion of the course: Předmět se neukončuje.
The course is taught each semester.
General note: Předmět je určen pouze studentům se specifickými nároky. Slouží k evidenci individuální výuky.
Information on course enrolment limitations: Předmět slouží k evidenci individuální výuky. Pro zápis předmětu je vždy nutný souhlas.
  • Enrolment Statistics (recent)
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