UIAI209 Mathematics II

Faculty of Philosophy and Science in Opava
Summer 2020
Extent and Intensity
6/0/0. 7 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Luděk Cienciala, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Luděk Cienciala, Ph.D.
Institute of Computer Science – Faculty of Philosophy and Science in Opava
Prerequisites
Mathematics in the range secondary school curriculum.
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.
Syllabus
  • - Set theory, relations between sets, operations with sets, commutative, associative and distributive law.
    - Sessions binary relation in the set, display sets, narrowing, expansion, surjection, injection, bijection, identity, equivalence and decomposition sets, ordered sets.
    - Operations and set their properties.
    - Algebras, subalgebras, homomorphisms, groupoids, semigroups and groups, half circles, rings and fields.
    - Vector spaces, linear independence, basis and dimension of vector spaces, isomorphism of vector spaces, coordinate system.
    - Matrices, determinants, rank matrices, systems of linear equations. Forms on vector spaces, linear forms, bilinear forms, quadratic forms.
    - Linear, Linear vector spaces and matrices, linear transformations of a vector space.
    - Introduction to graph theory.
Literature
    recommended literature
  • Cienciala, L., Ciencialová, L. Teorie grafů a grafové algoritmy. Slezská univerzita v Opavě, 2014. ISBN 978-80-7510-060-3. info
  • Artin, M. Algebra. Pearson; 2 edition, 2010. ISBN 9780132413770. info
  • Jukl, M. Lineární algebra. Univerzita Palackého Olomouc, 2006. info
  • Hort, D., Rachůnek, J. Algebra I. VUP Olomouc, 2003. info
  • B. L. van der Waerden; F. Blum; J. R. Schulenberg. Algebra Volume I. Springer-Verlag, 2003. ISBN 0-387-40624-7. info
  • L. Bican. Lineární algebra a geometrie. Academia Praha, 2000. ISBN 80-200-0843-8. info
  • Fronček, D. Úvod do teorie grafů. Opava, FPF SU, 2000. info
  • Horák, P. Cvičení z algebry a teoretické aritmetiky I. Brno: MU, 1991. info
  • Kolář, J., Štěpánková, O., Chyti, M. Logika, algebry a grafy. Praha, SNTL/ALFA, 1989. info
  • Firlová, R., Šimon, J. Cvičení z algebry I. Pedagogická fakulta Ostravské univerzity, 1988. info
  • Blažek, J., Koman, M., Vojtašová, B. Algebra a teorietická aritmetika. Praha, SPN, 1985. info
  • Burian, K., Lbicher J. Algerbra I. Pedagogická fakulta Ostravské univerzity, 1982. info
  • J. T. Moore. Elements of Linear Algebra and Matrix Theory. McGraw Hill, New York, 1968. info
Teaching methods
Interactive lecture
Lecture with a video analysis
Assessment methods
Exam
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course can also be completed outside the examination period.
Information on the extent and intensity of the course: Přednáška 6 HOD/SEM.
Teacher's information
Credit: full-time students wrote the exercises two credit tests scoring 30 points each. All five students solve homework. For each homework gets 8 points. To obtain the credit needed 50 points. Points earned during the semester is multiplied by 0.4 and rounded up. Normalized points are counted for the exam.
Exam: Students may receive a maximum of 60 points from the exam. The successful it is necessary to obtain 30 points. To determine the mark of the test points earned in a semester of credit tests and the exam added. Maximum points is 100.
The course is also listed under the following terms Summer 2013, Summer 2014, Summer 2015, Summer 2016, Summer 2017, Summer 2018, Summer 2019, Summer 2021, Summer 2022, Summer 2023.
  • Enrolment Statistics (Summer 2020, recent)
  • Permalink: https://is.slu.cz/course/fpf/summer2020/UIAI209