UIN1066 Chapters in Discrete Mathematics II

Faculty of Philosophy and Science in Opava
Summer 2013
Extent and Intensity
2/0/0. 3 credit(s). Type of Completion: z (credit).
Teacher(s)
doc. Ing. Petr Sosík, Dr. (lecturer)
Guaranteed by
doc. Ing. Petr Sosík, Dr.
Institute of Computer Science – Faculty of Philosophy and Science in Opava
Prerequisites (in Czech)
UIN1065 Chapters in Discrete Mathemati
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 offers an introduction to a sequence of elegant methods of discrete mathematics which are useful, among others, when: (a) evaluating time and space complexity of recursive algorithms (b) analysing the behavior of algorithms calculating with real numbers (c) analysing algorithms of artificial intelligence (d) examining reliability of algorithms.
Syllabus
  • 1. Integer functions. Removal of the round and ceiling operators in inequalities. Floor/ceiling sums and recurrences. The binary operation mod and its applications.
    2. Binomické koeficienty, základní vztahy a možnosti úprav. Zobecnění na celočíselný a reálný obor. Sumy a rekurence s binomickými koeficienty.
    3. Generating functions. An example - Fibonacci numbers. Composite generating functions - sums, products, summation, difference, integral, derivation, convolution.
    4. Manipulation with generating functions. Applications of generating functions in evaluation of sums and recurrences. Application examples.
Literature
    recommended literature
  • MATOUŠEK, J., NEŠETŘIL, J. Kapitoly z diskrétní matematiky. Karolinum, Praha, 2000. info
  • GRAHAM, R., KNUTH, D., PATASHNIK, O. Concrete Mathematics. Addison-Wesley, New York, 1992. info
Assessment methods
Written exam
Language of instruction
Czech
Further Comments
The course can also be completed outside the examination period.
The course is also listed under the following terms Summer 1994, Summer 1995, Summer 1996, Summer 1997, Summer 1998, Summer 1999, Summer 2000, Summer 2001, Summer 2002, Summer 2003, Summer 2004, Summer 2005, Summer 2006, Summer 2007, Summer 2008, Summer 2009, Summer 2010, Summer 2011, Summer 2012, Summer 2014, Summer 2015.
  • Enrolment Statistics (Summer 2013, recent)
  • Permalink: https://is.slu.cz/course/fpf/summer2013/UIN1066