MB101 Mathematics I

Faculty of Informatics
Autumn 2011
Extent and Intensity
2/2. 4 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Roman Šimon Hilscher, DSc. (lecturer)
doc. RNDr. Michal Veselý, Ph.D. (lecturer)
Mgr. Libor Báňa (seminar tutor)
Mgr. Veronika Bernhauerová, Ph.D. (seminar tutor)
Mgr. Ondřej Černý (seminar tutor)
Mgr. Hana Julínková (seminar tutor)
Mgr. Dagmar Lajdová (seminar tutor)
Mgr. Jan Meitner (seminar tutor)
Mgr. Bc. Kamil Rajdl, Ph.D. (seminar tutor)
Mgr. Kateřina Štekovičová (seminar tutor)
Mgr. Jana Švédová (seminar tutor)
Ing. Mgr. Petr Valenta (seminar tutor)
Mgr. Silvie Zlatošová, Ph.D. (seminar tutor)
RNDr. Jan Vondra, Ph.D. (assistant)
Guaranteed by
prof. RNDr. Jan Slovák, DrSc.
Faculty of Informatics
Timetable
Thu 10:00–11:50 D1, Thu 10:00–11:50 D3, Fri 10:00–11:50 D1, Fri 12:00–13:50 D1
  • Timetable of Seminar Groups:
MB101/01: Thu 14:00–15:50 G124, P. Valenta
MB101/02: Wed 16:00–17:50 G124, L. Báňa
MB101/03: Tue 12:00–13:50 G125, P. Valenta
MB101/04: Wed 18:00–19:50 G124, V. Bernhauerová
MB101/05: Wed 14:00–15:50 G124, L. Báňa
MB101/06: Thu 8:00–9:50 G125, O. Černý
MB101/07: Fri 12:00–13:50 G124, H. Julínková
MB101/08: Fri 14:00–15:50 G124, H. Julínková
MB101/09: Mon 12:00–13:50 G124, S. Zlatošová
MB101/10: Tue 8:00–9:50 G125, S. Zlatošová
MB101/11: Tue 10:00–11:50 G125, D. Lajdová
MB101/12: Tue 18:00–19:50 G124, D. Lajdová
MB101/13: Fri 8:00–9:50 G124, J. Meitner
MB101/14: Fri 10:00–11:50 G124, J. Meitner
MB101/15: Mon 16:00–17:50 G124, J. Švédová
MB101/16: Tue 8:00–9:50 G124, J. Švédová
MB101/17: Thu 16:00–17:50 G124, K. Rajdl
MB101/18: Thu 18:00–19:50 G124, K. Rajdl
MB101/19: Tue 14:00–15:50 G125, K. Štekovičová
MB101/20: Tue 16:00–17:50 G125, K. Štekovičová
Prerequisites
! MB005 Foundations of mathematics &&! NOW ( MB005 Foundations of mathematics )
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 the course is directly associated with
there are 19 fields of study the course is directly associated with, display
Course objectives
The course is the first part of the four semester block Mathematics I - IV. In the entire block, the fundamentals of general algebra, linear algebra and analysis, numerical methods, combinatorics and graph theory, including some applications in probability theory and statistics are presented. Passing Mathematics I-IV will allow the student to deal with basic mathematical concepts and problems and he/she will master the discrete and continuous intuition necessary for the mathematical formulation of real problems. The course Mathematics I, in particular, aims at the principles of mathematics, linear algebra, elementary geometry and some explicit applications.
Syllabus
  • Scalars, scalar functions, combinatorial examples and identities, finite probability, geometric probability, difference equations.
  • Motivation geometric problems in space and plane, systems of linear equations, elimination of variables.
  • Relations and mappings, injectiv and surjectiv mappings, set cardinality, equivalences and decompositions.
  • Vector, vector space, linear independence, basis, linear mappings, matrices, matrix calculus and determinants.
  • Algebraical applications: systems of linear equations, linear difference equations, Markov chains
  • Geometrical applications: line, plane, parametric versus non-paramteric descriptions, positioning of planes and lines, projective space extension, angle, length, volume.
Literature
  • MOTL, Luboš and Miloš ZAHRADNÍK. Pěstujeme lineární algebru. 3. vyd. Praha: Univerzita Karlova v Praze, nakladatelství Karolinum, 2002. 348 s. ISBN 8024604213. info
  • FUCHS, Eduard. Logika a teorie množin (Úvod do oboru). 1. vyd. Brno: Rektorát UJEP, 1978. 175 s. info
  • FUCHS, Eduard. Kombinatorika a teorie grafů. 1. vyd. Praha: Státní pedagogické nakladatelství, 1986. 138 s. info
  • RILEY, K.F., M.P. HOBSON and S.J. BENCE. Mathematical Methods for Physics and Engineering. second edition. Cambridge: Cambridge University Press, 2004. 1232 pp. ISBN 0 521 89067 5. 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:MB101!
Teaching methods
Lecture about the theory with illustrative solved problems. Special illustrative solved problems given in a separate lecture. Seminar groups devoted to solving numerical problems.
Assessment methods
Two hours of lectures, two hours of presentations of typical problem solutions and tutorial. Final written test as examination. Results of tutorials/homeworks are partially reflected in the assessment.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
The course is taught each semester.
Information on the extent and intensity of the course: 2.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Spring 2006, Autumn 2006, Spring 2007, Autumn 2007, Spring 2008, Autumn 2008, Spring 2009, Autumn 2009, Spring 2010, Autumn 2010, Spring 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.
  • Enrolment Statistics (Autumn 2011, recent)
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