MB003 Linear Algebra and Geometry I

Faculty of Informatics
Spring 2010
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)
Mgr. David Kruml, Ph.D. (seminar tutor)
prof. Dr. rer. nat. RNDr. Mgr. Bc. Jan Křetínský, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Jan Paseka, CSc.
Faculty of Informatics
Timetable
Fri 12:00–13:50 A107
  • Timetable of Seminar Groups:
MB003/01: Fri 14:00–15:50 B007, J. Paseka
MB003/02: Tue 8:00–9:50 B007, D. Kruml
MB003/03: Tue 10:00–11:50 B007, D. Kruml
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
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
  • 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 http://www.math.muni.cz/~slovak.
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
The course is also listed under the following terms Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2011, Spring 2012.
  • Enrolment Statistics (Spring 2010, recent)
  • Permalink: https://is.muni.cz/course/fi/spring2010/MB003