Proof and deduction methods for engineering (5cr)
Course unit code: C-01906-MATA2700
General information
- Credits
- 5 cr
- Institution
- University of Jyväskylä
Objective
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.
Content
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.
Qualifications
MATP1700 Introductory Course to Mathematics in Engineering