UIIABP0044 Mathematics II

Faculty of Philosophy and Science in Opava
Summer 2024
Extent and Intensity
2/3/0. 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
Timetable
Mon 8:05–9:40 B1
  • Timetable of Seminar Groups:
UIIABP0044/A: Thu 17:40–20:05 B1, R. Poláková
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.
Literature
    required literature
  • CIENCIALA Luděk. Matematika II. Skripta. 76 stran. Slezská univerzita v Opavě, 2017.
    recommended literature
  • V. Jarník. Diferenciální počet I-II. info
  • VOPĚNKA, Petr. Nová infinitní matematika II: Nová teorie množin a polomnožin. Praha: nakladatelství Karolinum, 2015. ISBN 978-80-246-2986-5. info
  • VOPĚNKA, Petr. Nová infinitní matematika IV: Staronový diferenciální počet. Praha: nakladatelství Karolinum, 2015. ISBN 978-80-246-2984-1. info
  • DVOŘÁKOVÁ, L. Lineární algebra 1. Praha: ČVUT Praha, 2014. ISBN 978-80-01-05346-1. info
  • Cienciala, L., Ciencialová, L. Teorie grafů a grafové algoritmy. Slezská univerzita v Opavě, 2014. ISBN 978-80-7510-060-3. info
  • WILLERS, Michael. Algebra bez (m)učení: od arabských matematiků k tajným šifrám: matematika v každodenním životě: fascinující čísla a rovnice. Praha: Grada, 2012. ISBN 978-80-247-4123-9. info
  • Došlá, Z., Kuben, J. Diferenciální počet funkcí jedné proměnné. Brno: MU, 2004. info
  • Míka, S., Drábek, P. Matematická analýza I. ZČU Plzeň, 2003. info
  • Děmidovič Boris Pavlovič. Sbírka úloh a cvičení z matematické analýzy. 2003. ISBN 80-7200-587-1. info
  • DEVLIN, K. Jazyk matematiky. Praha: Argo, 2002. ISBN 80-7203-470-7. info
  • Černý, I., Rokyta, M. Differential and integral calculus of one real variable. Praha, Karolinum, 1998. info
  • BROŽKOVÁ, A. Cvičení z matematické analýzy I, II. Pedagogická fakulta Ostravské univerzity, 1995. info
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
Study Materials
The course is also listed under the following terms Summer 2021, Summer 2022, Summer 2023, Summer 2025.
  • Enrolment Statistics (recent)
  • Permalink: https://is.slu.cz/course/fpf/summer2024/UIIABP0044