Discrete Mathematics (5 cr)
Code: TX00CD83-3023
General information
Enrollment
02.05.2023 - 22.10.2023
Timing
23.10.2023 - 17.03.2024
Number of ECTS credits allocated
5 op
Mode of delivery
Contact teaching
Unit
School of ICT
Campus
Karaportti 2
Teaching languages
- Finnish
Degree programmes
- Industrial Management
Teachers
- Rakel Peltola
Groups
-
TXQ20SCMIndustrial Management, Supply Chain Management
-
TXQ20ICTIndustrial Management, ICT Business
-
TXQ22SCMIndustrial Management, Supply Chain Management
-
TXQ21ICTIndustrial Management, ICT Business
-
TXQ22ICTIndustrial Management, ICT Business
-
TXQ21SCMIndustrial Management, Supply Chain Management
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.