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
Introduction to linear algebra and analytical geometry.
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.
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.
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
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
Lecture combining theory with problem solving. Seminar groups devoted to solving 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 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.