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
Abstract
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.
Key topics
  • 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).
Study resources and 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
Method of verifying learning outcomes and course completion requirements
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
Teacher's information
Tento kurz představuje nezbytnou průpravu pro navazující základní disciplíny studijního programu matematika, resp. aplikovaná matematika.
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, Autumn 2025, Autumn 2026.
  • Enrolment Statistics (Autumn 2008, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2008/M1120