M1120 Fundamentals of mathematics

Faculty of Science
Autumn 2007
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)
doc. Mgr. Michal Kunc, Ph.D. (seminar tutor)
Mgr. Michaela Vokřínková (seminar tutor)
Guaranteed by
prof. RNDr. Jiří Rosický, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Wed 9:00–10:50 U-aula
  • Timetable of Seminar Groups:
M1120/01: Mon 14:00–15:50 UP2, D. Kruml
M1120/02: Mon 16:00–17:50 UP2, D. Kruml
M1120/03: Thu 8:00–9:50 U1, M. Vokřínková
M1120/04: Thu 16:00–17:50 U1, M. Vokřínková
M1120/05: Thu 8:00–9:50 UM, M. Kunc
Prerequisites
! M1125 Fundamentals of Mathematics
Knowledge of 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
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, algebra and combinatorics.
Syllabus
  • 1. Basic logical notions (propositions, quantification, mathematical theorems and their proofs). 2. Basic properties of integers (division theorem, divisibility, congruences). 3. Basic set-theoretical notions (set-theoretical operations including cartesian product). 4. Mappings (basic types of mappings, composition of mappings). 5. Elements of combinatorics (variations, combinations, inclusion-exclusion principle) 6. Cardinal numbers (finite, countable and uncountable sets). 7. Relations (relations between sets, composition of relations, relations on a set). 8. Ordered sets (order and linear order, special elements, Hasse's diagrams, supremum a infimum). 9. Equivalences and partitions (relation of equivalence, partition and their mutual relationship). 10. Basic algebraic structures (grupoids, semigroups, groups, rings, integral domains, fields). 11.Homomorfhisms of algebraic structures (basic properties of homomorphisms, kernel and image of a homomorphism).
Literature
  • Childs, Lindsay. A Concrete Introduction to Higher Algebra, Springer-Verlag, 1979, 338s. ISBN 0-387-90333-x.
  • BALCAR, Bohuslav and Petr ŠTĚPÁNEK. Teorie množin. Vyd. 1. Praha: Academia, 1986, 412 s. info
  • ROSICKÝ, Jiří. Algebra. 2. vyd. Brno: Vydavatelství Masarykovy univerzity, 1994, 140 s. ISBN 802100990X. info
  • HORÁK, Pavel. Algebra a teoretická aritmetika. 1 [Horák]. Brno: Rektorát Masarykovy univerzity Brno, 1991, 196 s. ISBN 80-210-0320-0. info
  • Bude napsán speciální učební text.
Assessment methods (in Czech)
Zkoušení sestává ze dvou testů během semestru (po 10 bodech), hlavní písemné zkoušky (60 bodů) a ústní zkoušky (20 bodů). Známka se určí z celkového součtu podle klíče: 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)
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 2008, 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 2007, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2007/M1120