MATH 338 Practice final.pdf - MATH 338 History and...

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1 MATH 338: History and Philosophy of Mathematics Practice final exam Fill in the blanks 1. The Hindu mathematicians were responsible for introducing place values and the number zero . 2. The Babylonians used base 60 arithmetic. 3. Thales was the first to emphasize the importance of proof . 4. Euclid wrote five axioms for geometry . 5. Apollonius wrote the classic book Conic Sections in 200 BC. 6. A conic section with eccentricity 1.0001 is a hyperbola . 7. A conic section with eccentricity less than 1 is an ellipse . 8. Fermat thought the formula 2 2 𝑛 + 1 always gave a prime number. 9. Descartes unified geometry and algebra by inventing graphs . 10. An integral is a sum of infinitely many infinitesimals , while a derivative is a quotient of two infinitesimals. 11. Gauss, Lobachevsky, and Bolyai discovered non-Euclidean geometries . 12. A set with 0 elements is called countably infinite. 13. Frege and Russell tried to base all of mathematics on logic . 14. G. H. Hardy’s wrote “There is no permanent place in the world for ugly mathematics.” 15. The Continuum Hypothesis is independent of the Z-F axioms of set theory. 16. Umar Al-Khayyami studied cubic equations, but his work was completed by Cardano. 17. Modern algebra was driven by two problems: The solution of the quintic equation and Fermat’s Last Theorem . 18. Andrew Wiles proved Fermat’s Last Theorem . 19. Peano wrote five axioms for natural numbers . 20. Euler proved that the sum of the reciprocals of the squares is 𝜋 2 6 . 21. Newton and Leibniz discovered Calculus independently. 22. Although we can prove there are infinitely many of them, there is no formula for prime numbers . 23. The Egyptians only (almost) used fractions with numerator 1 .

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