FI:MB003 Linear Algebra and Geometry I - Course Information
MB003 Linear Algebra and Geometry I
Faculty of InformaticsSpring 2011
- Extent and Intensity
- 2/2. 4 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
- Teacher(s)
- prof. RNDr. Jan Paseka, CSc. (lecturer)
doc. Lukáš Vokřínek, PhD. (seminar tutor) - Guaranteed by
- prof. RNDr. Jan Paseka, CSc.
Faculty of Informatics - Timetable
- Fri 12:00–13:50 A107
- Timetable of Seminar Groups:
MB003/02: Thu 16:00–17:50 G101, L. Vokřínek - Prerequisites (in Czech)
- ! MB102 Mathematics II &&!NOW( MB102 Mathematics II )
- 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 17 fields of study the course is directly associated with, display
- Course objectives
- Linear algebra belongs to the fundamentals of mathematical education. Passing the course, the students should - master the basic notions concerning vector spaces and linear maps and, furthermore, they should - gain good computational skills with matrices and systems of linear equations.
- Syllabus
- Scalars, vectors and matrices: Properties of real and complex numbers, vector spaces and their examples, $R^n$ and $C^n$, multiplication of matrices, systems of linear eguations, Gauss elimination, computation of inverse matrices.
- Vector spaces - basic notions: Linear combinations, linear independence, basis, dimension, vector subspaces, intersections and sums of subspaces, coordinates.
- Linear mappings: Definition, kernel and image, linear isomorphism, matrix of linear mapping in given bases, transformation of coordinates.
- Systems of linear equations: Properties of sets of solutions, rank a matrix, existence of solutions.
- Determinants: Permutations, definition and basic properties of determinants, computation of inverse matrices, application to systems of linear equations.
- Affine subspaces in $R^n$: Definition, parametric and implicit description, affine mapping.
- Scalar product in $R^n$: Definition and basic properties of scalar product
- Literature
- Slovák, Jan. Lineární algebra. Učební texty. Brno:~Masarykova univerzita, 1998. 138. elektronicky dostupné na
http://www.math.muni.cz/~slovak . - Zlatoš, Pavol. Lineárna algebra a geometria. Předběžná verze učebních skript MFF UK v Bratislavě.
- Slovák, Jan. Lineární algebra. Učební texty. Brno:~Masarykova univerzita, 1998. 138. elektronicky dostupné na
- Teaching methods
- Lectures: theoretical explanation with practical examples. Exercises: solving problems for understanding of basic concepts and theorems, contains also more complex problems, homeworks. Students will be asked to have an active participation at seminars and to obtain 40 % of possible points from two written tests.
- Assessment methods
- Form: lectures and exercises. Exam: written. Requirements: to manage the theory from the lecture, to be able to solve the problems similar to those from exercises
- Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- Study Materials
The course is taught annually. - Listed among pre-requisites of other courses
- Teacher's information
- http://www.math.muni.cz/~cadek
- Enrolment Statistics (Spring 2011, recent)
- Permalink: https://is.muni.cz/course/fi/spring2011/MB003