Course details

Linear Algebra

SLA FME BUT SLA Acad. year 2019/2020 Winter semester 6 credits

The course deals with following topics: Sets: mappings of sets, relations on a set.
Algebraic operations: groups, vector spaces, matrices and operations on matrices.
Fundamentals of linear algebra: determinants, matrices in step form and rank of a matrix, systems of linear equations. Euclidean spaces: scalar product of vectors, eigenvalues and eigenvectors. Fundamentals of analytic geometry: linear concepts, conics, quadrics.

Guarantor

Deputy Guarantor

Language of instruction

Czech

Completion

Credit+Examination (written)

Time span

39 hrs lectures, 22 hrs exercises, 4 hrs pc labs

Assessment points

60 exam, 20 half-term test, 20 exercises

Department

Lecturer

Instructor

Subject specific learning outcomes and competences

Students will be made familiar with algebraic operations,linear algebra, vector and Euclidean spaces, and analytic geometry. They will be able to work with matrix operations, solve systems of linear equations and apply the methods of linear algebra to analytic geometry and engineering tasks. When completing the course, the students will be prepared for further study of mathematical and technical disciplines.

Learning objectives

The course aims to acquaint the students with the basics of algebraic operations, linear algebra, vector and Euclidean spaces, and analytic geometry. This will enable them to attend further mathematical and engineering courses and deal with engineering problems. Another goal of the course is to develop the students' logical thinking.

Prerequisite kwnowledge and skills

Students are expected to have basic knowledge of secondary school mathematics.

Study literature

• Thomas, G. B., Finney, R.L.: Calculus and Analytic Geometry, Addison Wesley 2003.
• Howard, A. A.: Elementary Linear Algebra, Wiley 2002.
• Rektorys, K. a spol.: Přehled užité matematiky I., II., Prometheus 1995. (in Czech)
• Nicholson, W. K.: Elementary Linear Algebra with Applications, PWS 1990.
• Searle, S. R.: Matrix Algebra Useful for Statistics, Wiley 1982.
• Karásek, J., Skula, L.: Algebra a geometrie, Cerm 2002. (in Czech)
• Nedoma, J.: Matematika I., Cerm 2001. (in Czech)
• Nedoma, J.: Matematika I., část první: Algebra a geometrie, PC-DIR 1998. (in Czech)
• Horák, P., Janyška, J.: Analytická geometrie, Masarykova univerzita 1997. (in Czech)
• Janyška, J., Sekaninová, A.: Analytická teorie kuželoseček a kvadrik, Masarykova univerzita 1996.(in Czech)
• Mezník, I., Karásek, J., Miklíček, J.: Matematika I. pro strojní fakulty, SNTL 1992. (in Czech)
• Horák, P.: Algebra a teoretická aritmetika, Masarykova univerzita 1991. (in Czech)
• Procházka, L. a spol.: Algebra, Academia 1990. (in Czech)
• Gilbert Strang: Introduction to Linear Algebra, Fifth Edition. Wellesley-Cambridge Press; Fifth Edition edition (June 10, 2016). ISBN-13: 978-0980232776.

Syllabus of lectures

1. week. Relations, equivalences, orders, mappings, operations, algebraic structures, fields.
2. week. Vector spaces, subspaces, homomorphisms. The linear dependence of vectors, the basis and dimension..
3. week. Matrices and determinants.
4. week. Systems of linear equations.
5. week. The characteristic polynomial, Eugen values, Eugen vectors. Jordan normal form.
6. week. Dual vector spaces. Linear forms.
7. week. Bilinear and quadratic forms.
8. week. Unitary spaces. Schwarz inequality. Orthogonality.
9. week. Inner, exterior, cross and triple products - relations and applications.
10. week. Symplectic spaces.
11. week. Affine and Euclidean spaces. Geometry of linear objects.
12. week. Projective spaces.
13. week. Geometry of conics and quadrics.

Syllabus of numerical exercises

Week 1: Basics of mathematical logic and operations on sets.
Following weeks: Seminar related to the topic of the lecture given in the previous week.

Syllabus of computer exercises

Seminars with computer support are organized according to current needs. They enable students to solve algorithmizable problems with computer algebra systems.

Progress assessment

Course-unit credit requirements: Active attendance at the seminars.
Form of examinations: The examination has a written and an oral part. In a 120-minute written test, students
solve the following 5 problems.
During the oral part of the examination, the examiner goes through the test with the student. The examiner should inform the students at the last lecture about the basic rules of the examination and the evaluation of its results.
Rules for classification: Student can achieve 4 points for each problem. Therefore, the students may achieve 20 points in total.
Final classification: A (excellent): 19 to 20 points
B (very good): 17 to 18 points
C (good): 15 to 16 points
D (satisfactory): 13 to 14 points
E (sufficient): 10 to 12 points
F (failed): 0 to 9 points

Controlled instruction

Attendance at lectures is recommended, attendance at seminars is required. The lessons are planned on the basis of a weekly schedule. The way of compensation for an absence is in the competence of the teacher.

The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.

Schedule

DayTypeWeeksRoomStartEndLect.grpGroupsInfo
Tuelecturelectures TA5/U5 13:0015:50 1MIT 2MIT xx Kureš
Thuexerciselectures TA5/U4 14:0015:50 1MIT 2MIT xx Kureš
Thuexerciselectures TA5/U4 16:0017:50 1MIT 2MIT xx Kureš

Course inclusion in study plans