## M1110 Linear Algebra and Geometry I

Faculty of Science
Autumn 2024
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Taught in person.
Teacher(s)
doc. RNDr. Martin Čadek, CSc. (lecturer)
Mgr. Petr Liczman (seminar tutor)
prof. RNDr. Jan Paseka, CSc. (seminar tutor)
doc. Mgr. Josef Šilhan, Ph.D. (seminar tutor)
Mgr. Mária Šimková (seminar tutor)
Guaranteed by
prof. RNDr. Jan Paseka, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
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
there are 6 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 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. Systems of linear equations. Determinants Affine subspaces
Literature
• PAVOL, Zlatoš. Lineárna algebra a geometria (Linear algebra and geometry). Bratislava: Albert Marenčin PT, s.r.o. 741 pp. ISBN 978-80-8114-111-9. 2011. info
• PASEKA, Jan and Pavol ZLATOŠ. Lineární algebra a geometrie I. Elportál. Brno: Masarykova univerzita. ISSN 1802-128X. 2010. URL info
• Anton H., Rorres.C.: Elementary Linear Agebra, 8th edition, Application Version, Wiley, 2000, ISBN 0471170526.
• ŠMARDA, Bohumil. Lineární algebra. Praha: Státní pedagogické nakladatelství. 159 s. 1985. info
• ŠIK, František. Lineární algebra zaměřená na numerickou analýzu. Vyd. 1. Brno: Masarykova univerzita v Brně. 177 s. ISBN 8021019962. 1998. 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. 196 s. ISBN 8021003200. 1991. info
• HORÁK, Pavel. Úvod do lineární algebry. 3. vyd. Brno: Rektorát UJEP Brno. 135 s. 1980. info
• Zlatoš P.: Lineárna algebra a geometria, připravovaná skripta MFF Univerzity Komenského v~Bratislavě, elektronicky dostupné na http://thales.doa.fmph.uniba.sk/katc/
Teaching methods
Lectures, exercises (tutorials) and homeworks.
Assessment methods
The exam consists of three parts: a semester-long component, a written exam during the exam period, and an oral exam. To pass the semester-long component, you need to score at least 50% of the points in 6 short written tests. The written exam during the exam period consists of a numerical and a theoretical part. You need to score at least 5 points out of 10 in the theoretical part and 7 points out of 12 in the numerical part. Students who pass both parts of the written exam proceed to the oral exam. During the oral exam, you will be required to demonstrate understanding of the topics covered and the ability to illustrate the concepts and theorems with examples. Exam requirements: Mastery of the material covered in lectures and tutorials. In the case of distance learning, the material is available on the course website throughout the semester. You will be asked about definitions, theorems, examples, and proofs. Emphasis is placed on understanding. It is not enough to know the definitions and theorems; you need to be able to provide examples of the defined concepts and the main theorems. You are also required to be able to perform simple proofs. Here is a list of topics that are absolutely required. If you do not know these topics, you will fail the exam: 1. The concept of a vector space, examples. 2. The concept of a vector subspace, examples, sum and intersection. 3. The concept of linear independence of vectors, examples. 4. The concept of a linear span, examples. 5. Explanation of an algorithm that selects linearly independent vectors with the same linear span from a list of vectors. 6. Basis of a vector space, coordinates of a vector in a given basis, dimension, examples. 7. Linear transformation, kernel, image, examples. 8. Rank of a matrix. 9. Solving systems of linear equations, theorems on the structure of solutions, examples of these theorems. 10. Definition of the determinant using its properties. Additional notes: You are encouraged to ask questions during lectures and tutorials if you do not understand something. There are many resources available to help you prepare for the exam, including the textbook, lecture notes, and online resources.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
Listed among pre-requisites of other courses
Teacher's information
Lectures will be held in person according to the schedule. The exercises will start in person, but if necessary, we will switch to online mode. Grading methods - see above. For up-to-date information, please see the introductory section of the interactive syllabus. They will also be sent by email.
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 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023.
• Enrolment Statistics (Autumn 2024, recent)