M1110 Linear Algebra and Geometry I

Faculty of Science
autumn 2017
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. Jiří Janda, 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 18. 9. to Fri 15. 12. Mon 14:00–15:50 M1,01017
  • Timetable of Seminar Groups:
M1110/01: Mon 18. 9. to Fri 15. 12. Fri 12:00–13:50 M5,01013, J. Paseka
M1110/02: Mon 18. 9. to Fri 15. 12. Fri 10:00–11:50 M1,01017, J. Paseka
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 will master the basic notions concerning vector spaces and linear maps, *they will be able to use the notions from linear algebra in their further study, *they will gain good computational skills with matrices and systems of linear equations.
Learning outcomes
Passing the course, *the students will master the basic notions concerning vector spaces and linear maps, *they will be able to use the notions from linear algebra in their further study, *they will 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 2016, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (autumn 2017, recent)
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