Key words discrete mathematics, P170, P175, T120
Objectives While 'classical' mathematics makes use of real numbers and notions like continuity to provide a basis for Newtonian physics, the emergence of the computer with its digital store and data processing made clear the need for 'another kind' of mathematical logic.
Goal of the course is to make the student familiar with this other approach of mathematics, and give feelinng to the logic and elegance of binary (read: discrete) patterns -- with the link to applications in computer engineering.
Topics The broad term 'discrete mathematics' encompasses between others combinatorics (or the art of counting), graph theory (useful for data structuring and optimalisations in data handling), study of finite algebraic structures (good for coding, enumeration methods. ...) and discrete methods of solution (applicable everywhere where it goes about problems or structure with a finite twist).
We treat:
counting principles (recursive definitions, principle of induction), combinatorics, generating functions and recurrent relations (Fibonacci rows, rows of differences)
number theory (divisibility, counting modulo a number), groups, fields and field extensions.
logic (truth tables)
Graphs (properties and practical applications; introduction to Algoritmen I)
Prerequisites Competences obtained in Wiskunde II
Final Objectives General technical competences [ATC3,ATC4]
Being able to use research methods and techniques adequately for the solution of engineering problems.
Specific competences [SC8, SC9]
The students know basic algorithms and data structures. Implementation and application follows in the course Algoritmen I.
The students can apply the basic theory of combinatorics, finite fields and graphs in specific domains.
If necessary thay can obtain more insight in the domains quoted autonomously.
Materials used Handouts
Study costs Estimated total price: 8.0 EUR
Study guidance Explanations after theory lessons or on appointment, or by mail.
Teaching Methods Hearing college, interleaved with active participation by students.
Aided by an electronic learning platform, so that feedback goes smoothly.
Assessment Oral examination
Lecturer(s) Vakgroep Informatica
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