UIMOIBK037 Mathematics II

Faculty of Philosophy and Science in Opava
Summer 2025
Extent and Intensity
0/0/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Luděk Cienciala, Ph.D. (lecturer)
RNDr. Radka Poláková, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Luděk Cienciala, Ph.D.
Institute of Computer Science – Faculty of Philosophy and Science in Opava
Prerequisites
Mathematics I
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
The aim of the course is to acquaint students with the basic concepts of algebra.
Learning outcomes
After completing the course, the student will be able to:
- analyze and solve basic problems within the scope of the course.
Syllabus
  • 1. Set theory, relations between sets, operations on sets, commutative, associative and distributive laws.
  • 2.-3. Sets, binary relations in a set, representations of sets, contraction, extension, surjection, injection, bijection, identity, equivalence and decomposition of sets, ordering of sets.
  • 4. Operations in a set and their properties.
  • 5.-6. Algebras, subalgebras, homomorphisms, groupoids, semigroups and groups, semicircles, rings and solids.
  • 7.-8. Vector spaces, linear dependence, independence, bases and dimensions of vector spaces, isomorphism of vector spaces, coordinate system.
  • 9.-10. Matrices, determinants, rank of matrices, systems of linear equations. Forms on vector spaces, linear forms, bilinear forms, quadratic forms.
  • 11.-12. Linear mappings, linear mappings of vector spaces and matrices, linear transformations of a vector space.
  • 13. Introduction to graph theory.
Teaching methods
Interactive lecture
Lecture with a video analysis
Assessment methods
Credit:
The student writes within the exercises two credit tests scored a maximum of 30 points for each. He also submits solutions to five homework assignments. He gets a maximum of 8 points for each homework. 50 points are required to obtain the credit. The points obtained during the semester are multiplied by a coefficient of 0.4 and rounded up. Points recalculated in this way are included in the test.
Exam:
The student can get a maximum of 60 points from the exam test. You need to get 30 points to succeed. To determine the mark from the exam, the points obtained in the semester from the credit tests and the exam test are added up. The maximum number of points is 100.
Language of instruction
Czech
Further comments (probably available only in Czech)
Information on the extent and intensity of the course: 14 hod/sem.
The course is also listed under the following terms Summer 2021, Summer 2022, Summer 2023, Summer 2024.
  • Enrolment Statistics (Summer 2025, recent)
  • Permalink: https://is.slu.cz/course/fpf/summer2025/UIMOIBK037