AoK: Mathematics Flashcards
What is mathematics?
The science of rigorous proof
What are abstract patterns, in mathematics?
Concepts in systematized relationship, expressed in a symbolic system, with no reference to the world
What is the main difference between pure mathematics and applied mathematics?
Pure: not concerned with practical applications
Applied: mathematical tools to enable research in another area
What is an axiom?
basic assumption of a system
What is a theorem?
conclusions found through deductive reasoning from axioms
In math, what is validity?
reasoning according to the rules
In math, what is truth?
content of the statements
What is collective knowledge?
Once something is proven, it remains that way
What is logic?
The study of valid forms of reasoning
Which mathematical systems transcend all cultures?
- Counting
- Locating
- Measuring
- Designing
- Playing
- Explaining
