MA0002 Discrete Mathematics

Faculty of Education
Autumn 2017
Extent and Intensity
2/0/0. 5 credit(s). Type of Completion: zk (examination).
Teacher(s)
Mgr. Helena Durnová, Ph.D. (lecturer)
Guaranteed by
Mgr. Helena Durnová, Ph.D.
Department of Mathematics – Faculty of Education
Supplier department: Department of Mathematics – Faculty of Education
Timetable
Wed 7:30–9:10 učebna 35
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course serves as propaedeutics for theoretical mathematical disciplines (algebra and mathematical analysis). The aim of the course is the preparation of the students for the study of theoretical mathematical disciplines, namely algebra and mathematical analysis. During the lectures, students will meet the symbolic representation in practical examples, in the homework assignment, they will learn these methods through a sample of tasks. Students will thus learn in discrete forms the methods they will later use in mathematical analysis.
Learning outcomes
Successful graduates of the course will be prepared for the study of theoretical mathematical disciplines, i. e. algebra and mathematical analysis.
Syllabus
  • 1. Divisibility. Signs of divisibility. Remainder classes. 2. Computation using congruence. Some interesting theorems from the theory of numbers. 3. Diophantine equations. Solvability of equations in integers. 4. Finite sums. 5. Defining sequences recurrently. 6. Partial sums. 7. Function factorial. Combination numbers. Basic rules of combinatorics. 8. Basic categories of combinatorics according to Jacob Bernoulli. Deriving formulas in combinatorics. 9.-10. Combintaorial tasks with numbers 11.-12. Combinatorial tasks with geometric shapes.
Literature
  • SMULLYAN, Raymond M. Jak se jmenuje tahle knížka? Translated by Antonín Vrba - Hanuš Karlach. Vydání druhé, upravené,. Praha: Portál, 2015, 198 stran. ISBN 9788026208228. info
  • HERMAN, Jiří, Radan KUČERA and Jaromír ŠIMŠA. Metody řešení matematických úloh I. 3. vyd. Brno: Masarykova univerzita, 2011, 278 pp. ISBN 978-80-210-5636-7. info
  • HERMAN, Jiří, Radan KUČERA and Jaromír ŠIMŠA. Seminář ze středoškolské matematiky. 1. dotisk 2., přeprac. vyd. Brno: Masarykova univerzita, 2007, 51 s. ISBN 978-80-210-3528-7. info
  • HERMAN, Jiří, Radan KUČERA and Jaromír ŠIMŠA. Counting and Configurations: Problems in Combinatorics, Arithmetic, and Geometry. 1st ed. New York: Springer-Verlag, 2003, 410 pp. Canadian Mathematical Society Books in Math., 12. ISBN 0-387-95552-6. info
  • HERMAN, Jiří, Jaromír ŠIMŠA and AT AL. Sbírka testových úloh k maturitě z matematiky (Testing problems for high-school leaving exams in mathematics). Praha: Prometheus, 2002, 279 pp. ISBN 80-7196-249-X. info
  • HERMAN, Jiří, Radan KUČERA and Jaromír ŠIMŠA. Equations and Inequalities: Elementary Problems and Theorems in Algebra and Number Theory. 1st ed. New York: Springer-Verlag, 2000, 355 pp. Canadian Mathematical Society Books in Math., 1. ISBN 0-387-98942-0. info
  • HERMAN, Jiří, Radan KUČERA and Jaromír ŠIMŠA. Metody řešení matematických úloh II (Methods how to solve mathematics exercises II). Brno: Masarykova univerzita Brno, 1997, 355 pp. ISBN 80-210-1630-2. info
  • HERMAN, Jiří, Radan KUČERA and Jaromír ŠIMŠA. Metody řešení matematických úloh I. 2., přeprac. vyd. Brno: Masarykova univerzita, 1996, 278 s. ISBN 80-210-1202-1. info
  • VRBA, Antonín. Grafy : pro III. ročník tříd gymnázií se zaměřením na matematiku, na matematiku a fyziku a pro seminář a cvičení z matematiky ve IV. ročníku gymnázií. 1. vyd. Praha: Státní pedagogické nakladatelství, 1989, 75 s. info
  • VRBA, Antonín. Kombinatorika. 1. vyd. Praha: Mladá fronta, 1980, 130 s. URL info
  • VILENKIN, Naum Jakovlevič. Kombinatorika. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1977, 298 s. URL info
  • VRBA, Antonín. Princip matematické indukce. 1. vyd. Praha: Mladá fronta, 1977, 138 s. URL info
Teaching methods
Theoretical lectures and homework assignments: students will turn in a set of solved tasks for each topic (including commentaries).
Assessment methods
Written and oral exam.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Autumn 2018, Autumn 2019, autumn 2020, Autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (Autumn 2017, recent)
  • Permalink: https://is.muni.cz/course/ped/autumn2017/MA0002