M1120 Fundamentals of mathematics

Faculty of Science
Autumn 2008
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
Mgr. David Kruml, Ph.D. (lecturer)
Mgr. Michaela Vokřínková (seminar tutor)
Mgr. Radek Šlesinger, Ph.D. (assistant)
Guaranteed by
prof. RNDr. Jiří Rosický, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Fri 12:00–13:50 A,01026
  • Timetable of Seminar Groups:
M1120/01: Thu 10:00–11:50 M4,01024, D. Kruml
M1120/02: Wed 16:00–17:50 M2,01021, D. Kruml
M1120/03: Mon 11:00–12:50 M2,01021, D. Kruml
M1120/04: Tue 16:00–17:50 M2,01021, M. Vokřínková
Prerequisites
! M1125 Fundamentals of Mathematics
Knowledge of high-school mathematics is supposeed.
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 course links up high school knowledge with basic mathematical concepts and ideas which a student needs. It mainly deals with fundaments of mathematical logic, set theory, and algebra.
Syllabus
  • Basic logical concepts (formulae, notation for mathematical statements, proofs)
  • Basics of set theory (set operations, including the Cartesian product).
  • Mappings (types of mappings, composition).
  • Cardinality of a set (finite, countable and uncountable sets).
  • Relations (types and properties of relations, composition).
  • Equivalences and partitions.
  • Ordered sets (order relations, Hasse diagrams, lattices and complete lattices).
  • Basic algebraic structures (grupoid, semigroup, group, ring, integral domain, field).
  • Number domains (construction, basic properties).
Literature
  • Horák, Pavel. Základy matematiky. Učební text. Podzimní semestr 2008.
  • HORÁK, Pavel. Algebra a teoretická aritmetika. 1 [Horák]. Brno: Rektorát Masarykovy univerzity Brno, 1991, 196 s. ISBN 80-210-0320-0. info
  • ROSICKÝ, Jiří. Algebra. 2. vyd. Brno: Vydavatelství Masarykovy univerzity, 1994, 140 s. ISBN 802100990X. info
Assessment methods
The subject consists of talks and obligatory seminars. Students are examined in 2 tests during the term (10 pts per each), final written test (40 pts), and oral exam (40 pts). The mark is calculated as follows: A 90-100, B 80-89, C 70-79, D 60-69, E 50-59, F 0-49.
Language of instruction
Czech
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 Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (Autumn 2008, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2008/M1120