M1110 Linear Algebra and Geometry I

Faculty of Science
Autumn 2016
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Jan Paseka, CSc. (lecturer)
Mgr. Jana Volaříková, Ph.D. (assistant)
Guaranteed by
doc. RNDr. Martin Čadek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 19. 9. to Sun 18. 12. Fri 10:00–11:50 M1,01017
  • Timetable of Seminar Groups:
M1110/01: Mon 19. 9. to Sun 18. 12. Fri 12:00–13:50 M2,01021, J. Paseka
M1110/02: Mon 19. 9. to Sun 18. 12. Mon 18:00–19:50 M5,01013, J. Volaříková
Prerequisites
!OBOR(AMV) && !OBOR(FINPOJ) && !OBOR(BIMAT) && !OBOR(UM)
High School Mathematics
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
  • Vector spaces.
  • Operations with matrices.
  • Gauss elimination.
  • Vector subspaces.
  • Linear independence.
  • Basis and dimension.
  • Coordinates.
  • Linear maps.
  • Matrices of linear maps.
  • Affine subspaces.
  • Systems of linear equations.
  • Determinants
  • Vector spaces with scalar product.
Literature
  • Zlatoš P.: Lineárna algebra a geometria, připravovaná skripta MFF Univerzity Komenského v~Bratislavě, elektronicky dostupné na http://thales.doa.fmph.uniba.sk/katc/
  • HORÁK, Pavel. Úvod do lineární algebry. 3. vyd. Brno: Rektorát UJEP Brno, 1980, 135 s. info
  • Anton H., Rorres.C.: Elementary Linear Agebra, 8th edition, Application Version, Wiley, 2000, ISBN 0471170526.
  • ŠMARDA, Bohumil. Lineární algebra. Praha: Státní pedagogické nakladatelství, 1985, 159 s. info
  • ŠIK, František. Lineární algebra zaměřená na numerickou analýzu. Vyd. 1. Brno: Masarykova univerzita v Brně, 1998, 177 s. ISBN 8021019662. info
  • Slovák, Jan. Lineární algebra. Učební texty. Brno:~Masarykova univerzita, 1998. 138. elektronicky dostupné na http://www.math.muni.cz/~slovak.
  • HORÁK, Pavel. Algebra a teoretická aritmetika. 2. vyd. Brno: Rektorát Masarykovy univerzity, 1991, 196 s. ISBN 8021003200. info
Teaching methods
Lectures: theoretical explanation with practical examples. Exercises: solving problems for understanding basic concepts and theorems, contains also more complex problems, homework. Students will be asked to have an active participation at seminars or to obtain 40 % of possible points from two written tests (8 from 20).
Assessment methods
Lecture 2 hours a week, seminar 2 hours a week. Examination written and oral. To access the examination one has to pass exercises. The examination has 3 parts. 1. part: During the semester, two obligatory mid-term exams are evaluated (each for max 10 points, 50 minutes long). Student may collect during the semester maximally 20 points. 2. part: If the student is able to pass exercises he may proceed to the final examination. This examination starts with a written exam that consists of 2 parts - theoretical (20 points) and practical (30 points). 3. part: Oral examination (30 points). Requirements: to manage the theory from the lecture, to be able to solve the problems similar to those from exercises. Evaluation (points <= 49 - F, 49 < points <= 59 - E, 59 < points <= 69 - D, 69 < points <= 79 - C, 79 < points <= 89 - B, 89 < points <= 100 - A).
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
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (Autumn 2016, recent)
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