Course content

Discrete Mathematics

Code:

143406

Abbreviation:

B36B05

Higher education institution:

Faculty of Geodesy

ECTS credits:

5.0

Load:

20(E) + 30(L) + 10(E)

Issuing teachers:

Assistant Professor Iva Kodrnja, PhD

Course contractors:

Assistant Professor Iva Kodrnja, PhD (E, L, E)

Course description:

Renew and expand the knowledge of basic mathematical concepts and methods used in computer engineering / informatics science. Develop a sense of different degrees of mathematical rigor and formalism and learn to use them in problem solving tasks. Distinguish parts of mathematics that studies finite systems, i.e. deals with objects that can assume only a specific value. Argue the reasons why the characteristics of the computer are described within the framework of finite mathematical systems. Become familiar with the language of computer science. Learning outcomes at the level of the programme to which the course contributes <ul><li>Understand mathematical methods and physical laws applied in geodesy and geoinformatics. <li>Apply knowledge of mathematics and physics for the purpose of recognizing, formulating and solving of problems in the field of geodesy and geoinformatics. <li>Use information technology in solving geodetic and geoinformation tasks <li>Exercise appropriate judgements on the basis of performed calculation processing and interpretation of data obtained by means of surveying and its results. <li>Take responsibility for continuing academic development in the field of geodesy and geoinformatics, or related disciplines, and for the development of interest in lifelong learning and further professional education.</ul> Learning outcomes expected at the level of the course <ul><li>recognize and apply basic types of mathematical reasoning; <li>define and classify binary relations on sets knowing their properties and typical examples; <li>pronounce and apply the properties of relations in systems for data processing and for the development of functional algorithms; <li>adopt basic combinatorial concepts and counting rules and recognize them when counting the elements of a finite set; <li>determine the generating function of the starting sequence and identify and solve simple recurrence relations; <li>apply the theory of Boolean algebra to design logic circuits and networks; <li>distinguish the basic concepts of graph theory; <li>Compare and model certain combinatorial problems using graph theory (shortest path algorithm, nearest neighbor algorithm,...).</ul> Course content broken down in detail by weekly class schedule (syllabus) <ul><li>Mathematical logic 2h <li>Sets and relations 2h <li>Ordered sets and mashes 2h <li>Applications in informatics 2h <li>Introduction to combinatorics (counting techniques) 4h <li>Recursive functions 1h <li>Applications in informatics 2h <li>1st preliminary exam 1h <li>Dirichlet principle; Generating functions; Ramsey's theorem 2h <li>Boolean algebra (definition and properties, Boolean functions) 2h <li>Graphs (paths and cycles) 2h <li>Directed graphs 2h <li>Graph colourings 2h <li>Applications in informatics 2h <li>Film: Mashes (mashes/graphs) 1h <li>2nd preliminary exam /The final exam. 1h</ul> Screening student work <ul><li>Class attendance - Requirement for the signature <li>independent assignments - 10% <li>Seminar essay - 20% <li>Tests - 70% <li>Oral exam - optional <li>Written exam - 70%</ul>

Enrollment prerequisites:

Basics of Geoinformatics (passed)

Programming (passed)

Course in study programme:

Code	Name of study	Level of study	Semester	Required/Elective
71	Geodesy and Geoinformatics	undergraduate	6	elective

* the course is not taught in that semester

Legend

E - Seminar

L - Lectures