Practice Final (2018)-answers.docx - Math 338 History and...

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Math 338: History and Philosophy of Mathematics Practice final exam 1. Fill in the blanks a) The _ Indian (Hindu)_ mathematicians were responsible for introducing place values and the number zero. b) The Babylonians used base _ : _ was the first to emphasize the importance of proof
d) Euclid wrote five axioms for _
e) Apollonius wrote the classic book “_ _” in 200 BC
f) A conic section with eccentricity 1.0001 is _a hyperbola _ g) Fermat thought the formula _ 2 2 n + 1 _always gave a prime number. h) Descartes unified geometry and algebra by inventing _ graphs _ i) An integral is a _ sum _of infinitely many infinitesimals, while a derivative is a _ quotient _ of two infinitesimals. j) Gauss, Lobachevsky, and Bolyai discovered _ non-Euclidean geometry _. k) A set with א 0 elements is called _ countably _ infinite. l) Frege and Russell tried to base all of mathematics on _ logic _. m) G. H. Hardy’s wrote “There is no permanent place in the world for _ ugly _ mathematics.” n) The Continuum Hypothesis is _ independent _of the Z-F axioms of set theory.

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