M1125 Fundamentals of Mathematics

Faculty of Science
autumn 2017
Extent and Intensity
2/2/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
RNDr. Jan Vondra, Ph.D. (lecturer)
Guaranteed by
RNDr. Jan Vondra, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 18. 9. to Fri 15. 12. Wed 14:00–15:50 M1,01017
  • Timetable of Seminar Groups:
M1125/01: Mon 18. 9. to Fri 15. 12. Tue 10:00–11:50 M5,01013, J. Vondra
M1125/02: Mon 18. 9. to Fri 15. 12. Wed 8:00–9:50 M5,01013, J. Vondra
Prerequisites
! M1120 Discrete Mathematics && !NOW( M1120 Discrete Mathematics ) && ! M1121 Discrete Mathematics && !NOW( M1121 Discrete 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
there are 7 fields of study the course is directly associated with, display
Course objectives
The aim of this cource is to lay the foundations of mathematics. The course deals with basic concepts and their good understanding and use.
Learning outcomes
Upon successful completion of this course the student should be able to: understand and explain the selected basic mathematical concepts; understand and explain the selected basic mathematical techniques; understand and explain the connection between the basic mathematical concepts.
Syllabus
  • 1. Basic logical notions
  • 2. Basic set-theoretical notions
  • 3. Basic number sets
  • 4. Basic properties of integers
  • 5. Mappings
  • 6. Relations
  • 7. Ordered sets
  • 8. Equivalences and partitions
  • 9. Basic algebraic structures with one operation
  • 10. Basic algebraic structures with two operations
  • 11.Homomorfhisms of algebraic structures.
Literature
    required literature
  • Horák, Pavel. Základy matematiky. Učební text. https://www.math.muni.cz/~vondra/vyuka/p2015/zm/zm_skripta_2013.pdf
  • Horák, Pavel. Základy matematiky. Učební text ke cvičení. https://www.math.muni.cz/~vondra/vyuka/p2015/zm/zm_sbirka_2013.pdf
    not specified
  • ROSICKÝ, Jiří. Algebra. 2. vyd. Brno: Vydavatelství Masarykovy univerzity, 1994, 140 s. ISBN 802100990X. info
  • CHILDS, Lindsay. A concrete introduction to higher algebra. 2nd ed. New York: Springer, 1995, xv, 522. ISBN 0387989994. info
Teaching methods
Lectures: theoretical explanations with practical applications. Exercises: solving problems focused on basic concepts and theorems, individual problem solving by students.
Assessment methods
Teaching: lectures, consultative exercises. Exam: written and oral.
Language of instruction
Czech
Further Comments
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 2010 - only for the accreditation, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, Autumn 2018.
  • Enrolment Statistics (autumn 2017, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2017/M1125