MATA2700 Proof and deduction methods for engineering (5 cr)

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Study level:
Intermediate studies
Grading scale:
0-5
Language:
English, Finnish
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2024-2025, 2025-2026, 2026-2027, 2027-2028

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Opintojakso on tarkoitettu tekniikan alan kandidaatti- ja DI-ohjelmien opiskelijoille ja ohjelmiin hakemista suunnitteleville.

Description

  • Basics of mathematical reasoning and logic.
  • Direct and indirect reasoning.
  • Forming negations.
  • Pigeonhole principle.
  • Recursion, proof by induction, and structural induction.
  • Concepts needed in proving computer programs.
  • Basics of set theory: finiteness, countability, and uncountability. 

Learning outcomes

After completing the course, the student:

  • Can handle basic operations of set theory using Venn diagrams.
  • Knows what a counterexample and proving mean in mathematics.
  • Can apply direct and indirect reasoning to proof tasks.
  • Can form negations of mathematical statements.
  • Can interpret and write recursive definitions.
  • Can utilize structural induction in proving.
  • Knows the most important concepts of program verification: loop invariant, bound function (or ranking function), and class invariant.
  • Can read, present, and evaluate proofs in mathematics and programming.
  • Distinguishes between finite, countably infinite, and uncountable sets.
  • Knows the significance of proving for the reliability of programs. 

Additional information

Opintojakso on tarkoitettu ensisijaisesti tekniikan alan kandidaattiohjelmien opiskelijoille. Opintojaksoista MATA132 Todistamisen perusteet sekä MATA2700 Todistamisen ja päättelyn perusteet tekniikan alalla molempia ei voi sisällyttää matematiikan opintokokonaisuuteen.

Description of prerequisites

MATP1700 Introductory Course to Mathematics in Engineering

Literature

  • Richard Hammack: Book of proof

Completion methods

Method 1

Evaluation criteria:
Harjoitukset ja kurssitentti. Tarkemmat arviointiperusteet ilmoitetaan opetusohjelmassa.
Time of teaching:
Period 3
Select all marked parts

Method 2

Evaluation criteria:
Lopputentin pistemäärä
Select all marked parts
Parts of the completion methods
x

Participation in teaching (5 cr)

Type:
Participation in teaching
Grading scale:
0-5
Language:
English, Finnish
No published teaching
x

Exam (5 cr)

Type:
Exam
Grading scale:
0-5
Language:
English, Finnish

Teaching