MB003 Linear Algebra and Geometry I

Faculty of Informatics
Spring 2012
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. Jiří Janda, Ph.D. (seminar tutor)
Mgr. Radek Šlesinger, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Jan Paseka, CSc.
Faculty of Informatics
Supplier department: Faculty of Science
Timetable
Fri 12:00–13:50 G123
  • Timetable of Seminar Groups:
MB003/01: Fri 14:00–15:50 G123, J. Paseka
MB003/02: Mon 10:00–11:50 G125, J. Janda
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
  • 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.
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 2010, Spring 2011.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/fi/spring2012/MB003