MB102 Mathematics II

Faculty of Informatics
Spring 2005
Extent and Intensity
2/2. 4 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
doc. Mgr. Ondřej Klíma, Ph.D. (lecturer)
doc. Mgr. Jaroslav Hrdina, Ph.D. (seminar tutor)
Mgr. David Kruml, Ph.D. (seminar tutor)
Mgr. Tomáš Lipenský (seminar tutor)
Mgr. Jan Pavlík, Ph.D. (seminar tutor)
Mgr. Eva Pellarová (seminar tutor)
RNDr. Veronika Svobodová, Ph.D. (seminar tutor)
RNDr. Lenka Viskotová, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Faculty of Informatics
Contact Person: doc. Mgr. Ondřej Klíma, Ph.D.
Timetable
Mon 9:00–10:50 D2, Mon 9:00–10:50 D1
  • Timetable of Seminar Groups:
MB102/01: Mon 11:00–12:50 B003, O. Klíma
MB102/02: Wed 14:00–15:50 B007, D. Kruml
MB102/03: Wed 16:00–17:50 B007, D. Kruml
MB102/04: Mon 15:00–16:50 B007, J. Pavlík
MB102/05: Mon 13:00–14:50 B007, J. Pavlík
MB102/06: Tue 14:00–15:50 B003, V. Svobodová
MB102/07: Tue 16:00–17:50 B003, V. Svobodová
MB102/08: Tue 10:00–11:50 B003, E. Pellarová
MB102/09: Tue 12:00–13:50 B003, E. Pellarová
MB102/10: Thu 16:00–17:50 B011, L. Viskotová
Prerequisites
! M003 Linear Algebra and Geometry I &&! M503 Linear Algebra and Geometry I && ! MB003 Linear Algebra and Geometry I &&!NOW( MB003 Linear Algebra and Geometry I )
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 11 fields of study the course is directly associated with, display
Course objectives
The second part of the block Mathematics I - IV. In the whole block the fundamentals of general algebra, linear algebra and analysis, including their application in probability, and graph theory are presented. The course Mathematics II, in particular, is concerned with the basic concepts from ring and field theory, with polynomials and rational functions, and mainly with the fundamentals of linear algebra.
Syllabus
  • Rings and fields.
  • Rings of polynomials.
  • Divisibility of polynomials, Euclidean algorithm, irreducible polynomials.
  • Roots of polynomials.
  • Rational functions, decomposition to partial fractions.
  • Matrices, algebra of matrices, rings of matrices.
  • Determinants, Laplace theorem.
  • Vector spaces, subspaces of vector spaces.
  • Linear dependence of vectors, basis and dimension of vector spaces.
  • Rank of matrices.
  • Regular matrices and inverse matrices.
  • Systems of linear equations, Frobenius theorem, Cramer rule, Gauss elimination method.
  • Linear mappings and linear transforms of vector spaces.
Literature
  • ROSICKÝ, Jiří. Algebra. I. 1. vyd. Brno: Rektorát UJEP, 1982, 140 . info
  • ŠIK, František. Algebra. Praha: Státní pedagogické nakladatelství, 1965, 94 s. info
  • HORÁK, Pavel. Úvod do lineární algebry. 3. vyd. Brno: Rektorát UJEP Brno, 1980, 135 s. info
  • HORÁK, Pavel. Algebra a teoretická aritmetika. 2. vyd. Brno: Rektorát Masarykovy univerzity, 1991, 196 s. ISBN 8021003200. info
  • HORÁK, Pavel. Algebra a teoretická aritmetika. 2. vyd. Brno: Masarykova univerzita, 1993, 145 s. ISBN 8021008164. info
Bookmarks
https://is.muni.cz/ln/tag/FI:MB102!
Assessment methods (in Czech)
Dvouhodinová přednáška a cvičení. Zkouška je písemná a má tři části- dva testy během semestru (2krát 10%) a závěrečná písemka(80%) ve zkouškovém období. Budou právě 4 termíny ve zkouškovém - 2 řádné, první opravný a druhý opravný. K připuštění ke zkoušce je třeba získat zápočet ze cvičení. Ten je podmíněn účastí, jsou dovoleny tři neomluvené neúčasti (a tři omluvené).
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Spring 2003, Spring 2004, Spring 2006, Spring 2007, Autumn 2007, Spring 2008, Autumn 2008, Spring 2009, Autumn 2009, Spring 2010, Autumn 2010, Spring 2011, Autumn 2011, Spring 2012, Autumn 2012, Spring 2013, Autumn 2013, Spring 2014, Autumn 2014, Spring 2015, Autumn 2015, Spring 2016, Autumn 2016, Spring 2017, Autumn 2017, Spring 2018, Autumn 2018, Spring 2019, Autumn 2019.
  • Enrolment Statistics (Spring 2005, recent)
  • Permalink: https://is.muni.cz/course/fi/spring2005/MB102