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
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.
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
FUCHS, Eduard. Logika a teorie množin (Úvod do oboru). 1. vyd. Brno: Rektorát UJEP, 1978. 175 s. info
HORÁK, Pavel. Algebra a teoretická aritmetika. 2. vyd. Brno: Masarykova univerzita, 1993. 145 s. ISBN 8021008164. info
Two hours of lectures, two hours of tutorial. Lecture covering the theory with illustrative solved problems. Tutorials devoted to solving numerical problems.
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 F 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.