MB101 Mathematics I

Faculty of Informatics
Spring 2018
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. Josef Šilhan, Ph.D. (lecturer)
Mgr. David Kruml, Ph.D. (seminar tutor)
doc. RNDr. Martin Čadek, CSc. (assistant)
RNDr. Jiří Glozar (assistant)
Guaranteed by
prof. RNDr. Jan Slovák, DrSc.
Faculty of Informatics
Supplier department: Faculty of Science
Timetable
Wed 8:00–9:50 D3, except Wed 16. 5.
  • Timetable of Seminar Groups:
MB101/01: Thu 8:00–9:50 A320, J. Šilhan
MB101/02: Thu 10:00–11:50 A320, J. Šilhan
MB101/03: Thu 12:00–13:50 A320, D. Kruml
MB101/04: Thu 16:00–17:50 A320, D. Kruml
Prerequisites (in Czech)
! MB005 Foundations of mathematics && ! MB201 Linear models B
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 16 fields of study the course is directly associated with, display
Course objectives
Introduction to linear algebra and analytical geometry.
Learning outcomes
At the end of this course, students should be able to: understand basic concepts of linear algebra and probability; apply these concepts to iterated linear processes; solve basic problems in analytical geometry.
Syllabus
  • The course is the first part of the four semester block of Mathematics. In the entire course, the fundamentals of general algebra and number theory, linear algebra, mathematical analysis, numerical methods, combinatorics, as well as probability and statistics are presented. Content of the course Linear models:
  • 1. Warm up (4 weeks) -- scalars, scalar functions, combinatorial examples and identities, finite probability, geometric probability, geometry of the plane, relations and mappings, equivalences and orderings.
  • 2. Vectors and matrices (3 weeks) -- vectors, vector space, linear independence, basis, linear mappings, matrices, matrix calculus and determinants, orthogonality, eigenvalues and eigenvectors.
  • 3. Linear models (3 weeks) -- systems of linear (in)equalities, linear programming problem, linear difference equations, iterated linear processes (population models) and Markov chains.
  • 4. Analytical geometry (2 weeks) -- geometrical applications: line, plane, parametric versus non-parametric descriptions, positioning of planes and lines, projective space extension, angle, length, volume, elementary classification of quadrics.
Literature
    recommended literature
  • MOTL, Luboš and Miloš ZAHRADNÍK. Pěstujeme lineární algebru. 3. vyd. Praha: Univerzita Karlova v Praze, nakladatelství Karolinum, 2002, 348 s. ISBN 8024604213. 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
  • J. Slovák, M. Panák a kolektiv, Matematika drsně a svižně, učebnice v přípravě
    not specified
  • FUCHS, Eduard. Logika a teorie množin (Úvod do oboru). 1. vyd. Brno: Rektorát UJEP, 1978, 175 s. 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
Two hours of lectures, two hours of tutorial. Lecture covering the theory with illustrative solved problems. Tutorials devoted to solving numerical problems.
Assessment methods
During the semester, two obligatory mid-term exams are evaluated (each for max 10 points). In the seminar groups there are 5 tests during the semester. The seminars are evaluated in total by max 5 points. Students, who collect during the semester (i.e., from tests and mid-term exams) less than 8 points, are graded as X and they do not proceed to the final examination. The final exam is two hours long and written for max 20 points. For successful examination (the grade at least E) the student needs in total 22 points or more.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Information on course enrolment limitations: Přednostně určen pro neúspěšné z podzimu 2006
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, 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, Autumn 2018, Spring 2019.
  • Enrolment Statistics (Spring 2018, recent)
  • Permalink: https://is.muni.cz/course/fi/spring2018/MB101