Discrete Mathematics (5 ECTS)

Objective

After completing this course the student will be familiar with the basic concepts and facts in logic, set theory, relations, graphs and combinatorics. The student will have a vision of possible applications. In order to model technological systems and structures the student is able to utilize discrete models.

Content

1) Logic, theory of sets, relations and functions.
2) Combinatorics.
3) Graphs.

Content scheduling

Kurssilla on 1-2 viikon välein uusi aihe:

Joukko-oppi
- joukkojen algebra, potenssijoukko, Venn-diagrammit, dualismi

Relaatiot
-järjestetty pari, karteesinen tulo
-relaation määrittely
-refleksiivinen, symmetrinen, antisymmetrinen ja transitiivinen relaatio
- ekvivalenssirelaatio
- relaatioiden erilaiset esitystavat

Kombinatoriikka
- permutaatio, variaatio, kombinaatio
- takaisinpanolla ja ilman
- multijoukot
-laatikkoperiaate

Logiikka
-peruskäsitteet
-totuustaulut
-tautologiat ja lausekkeiden sievennykset niillä
-esimerkit valehtelijoiden saarilta ja klassikkokysymyksiä, paradokseja
-päättelyketjut, induktio, deduktio, modus ponens, modus tollens

Matemaattinen induktio

Lukujärjestelmät:
-binääri, oktaali, desimaali, heksadesimaali ja muitakin
-muunnokset suuntaan ja toiseen

Boolenalgebra
-algebran idea
-Boolne laskuja
-loogiset piirit ja portit
-Karnaugh-kartta

Vekkomallit
-erityisesti binäärisiin hakupuihin liittyviä
käsitteitä ja laskuja

Further information

Vapaasti valittava opinto Tutan 2-4 vuosikurssien opiskelijoille.

Evaluation scale

0-5

Assessment criteria, satisfactory (1)

1) Logic, theory of sets, relations and functions
The student is familiar with the concepts, notation and principles associated with proposition and predicate logic, set theory, relations and functions. The student is able to solve simple problems.
2) Combinatorics
The student is familiar with combinatorial concepts, notation and principles. The student is able to solve simple problems.
3) Graphs
The student is familiar with graph theoretic concepts, notation and principles. The student is able to solve simple problems.

Assessment criteria, good (3)

1) Logic, theory of sets, relations and functions
The student has a good command of the concepts, notation and principles associated with proposition and predicate logic, set theory, relations and functions. The student is able to solve fundamental problems.
2) Combinatorics
The student has a good command of combinatorial concepts, notation and principles. The student is able to solve fundamental problems.
3) Graphs
The student has a good command of graph theoretic concepts, notation and principles. The student is able to solve fundamental problems.

Assessment criteria, excellent (5)

1) Logic, theory of sets, relations and functions
The student has a deep understanding of the concepts, notation and principles associated with proposition and predicate logic, set theory, relations and functions. The student is able to solve challenging problems.
2) Combinatorics
The student has a deep understanding of combinatorial concepts, notation and principles. The student is able to solve challenging problems.
3) Graphs
The student has a deep understanding of graph theoretic concepts, notation and principles. The student is able to solve challenging problems.

Assessment criteria, approved/failed

1) Logic, theory of sets, relations and functions
The student is familiar with the concepts, notation and principles associated with proposition and predicate logic, set theory, relations and functions. The student is able to solve simple problems.
2) Combinatorics
The student is familiar with combinatorial concepts, notation and principles. The student is able to solve simple problems.
3) Graphs
The student is familiar with graph theoretic concepts, notation and principles. The student is able to solve simple problems.

Further information

Computer exercises will be included.

Further information

Computer exercises will be included.