M1125 Fundamentals of Mathematics

Faculty of Science
Autumn 2010 - only for the accreditation
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. Pavel Horák (lecturer)
Mgr. Zbyněk Vrba (seminar tutor)
Guaranteed by
doc. RNDr. Eduard Fuchs, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
! M1120 Discrete Mathematics && !NOW( M1120 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
Course objectives
The aim of the course is to repeat and enlarge high school knowledge of mathematics and then to present further topics especially of algabraic character. After passing the course, the student will be able to understand and explain basic mathematical notions and techniques and their mutual context.
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
  • Horák, Pavel. Základy matematiky. Učební text. www.math.muni.cz/~horak/
  • HORÁK, Pavel. Cvičení z algebry a teoretické aritmetiky. 3. vyd. Brno: Masarykova univerzita, 2006, 221 s. ISBN 8021039701. info
  • 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. Current requirements: Written tests in exercises. Student's presence in exercises is obligatory.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
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 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 2017, Autumn 2018.