MB151 Linear models

Faculty of Informatics
Spring 2025
Extent and Intensity
2/2/0. 3 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
In-person direct teaching
Teacher(s)
doc. Mgr. Ondřej Klíma, Ph.D. (lecturer)
Mgr. Martin Dzúrik (seminar tutor)
Mgr. Pavel Francírek, Ph.D. (seminar tutor)
doc. Mgr. Michal Kunc, Ph.D. (seminar tutor)
doc. Mgr. Jan Koláček, Ph.D. (assistant)
Guaranteed by
doc. Mgr. Ondřej Klíma, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. Mgr. Ondřej Klíma, Ph.D.
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
!NOW( MB141 Linear alg. and discrete math )
We recommend that students have completed the course IB000, even if we do not directly follow it in terms of content. MB141 is a lightweight version of courses MB151 and MB154.
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 38 fields of study the course is directly associated with, display
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; 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. Content of the course Linear models:
  • 1. Introduction (3 weeks) -- motivating examples, real and complex numbers, roots of real polynomials, matrix multiplication, recurrence relations (incl. recurrence in combinatorics), geometry in two dimensions.
  • 2. Vector spaces (4 weeks) -- systems of linear equalities, matrix calculus (determinant and inverse matrix), vector spaces (formal definition and examples), linear independence, basis, coordinates, scalar product, length of vector, orthogonality, explicit formulas for recurrence relations.
  • 3. Linear mappings (2 weeks) -- representation of linear mappings, eigenvalues and eigenvectors; linear transformations in three dimensions, iterated linear processes (population models and discrete Markov chains).
  • 4. Analytical geometry (4 weeks) -- affine and Euclidean spaces (line, plane descriptions, angle, length, volume); systems of linear (in)equalities - linear programming problem; elementary classification of quadrics.
Literature
    not specified
  • HORÁK, Pavel. Algebra a teoretická aritmetika. 2. vyd. Brno: Masarykova univerzita, 1993, 145 s. ISBN 8021008164. info
Teaching methods
Two hours of lectures, two hours of tutorial. Lecture covering the theory with illustrative solved problems. Tutorials devoted to solving numerical problems.
Assessment methods
During the semester, two obligatory mid-term exams are evaluated (each for 25 points). The final exam is for 50 points. The student needs 50 points or more (from 100 points accessible) to complete the course. An attendance in seminars is a necessary condition for the access to the final examination.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
Listed among pre-requisites of other courses
The course is also listed under the following terms Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024.
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