Journey Through Genius: The Great Theorems of Mathematics Test | Final Test - Easy

William Dunham (mathematician)
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This test consists of 15 multiple choice questions and 5 short answer questions.

Multiple Choice Questions

1. To how many decimal places did Newton determine the number for pi?
(a) Three places.
(b) Twelve places.
(c) Nine places.
(d) Eight places.

2. What did Cantor find after extending the continuum between 0 and 1 into two dimensions?
(a) That the set is equal to 1.
(b) That the series is infinite.
(c) That the set is still equal to c.
(d) That the set is infinite.

3. What did Gauss do with his best work?
(a) He gave it to his students.
(b) He did not publish it.
(c) He gave it to his son to publish.
(d) He published it.

4. Which of the following did Dunham concentrate on as one of Newton's great advances?
(a) Quintic theorem.
(b) Quadratic equation.
(c) Binomial theorem.
(d) Area of a sphere.

5. What was described as true about the series 1 + 1/2 + 1/6 + 1/10 + 1/15 + 1/21?
(a) It's a divergent series with a sum of 2.
(b) It's a divergent series squared numbers.
(c) It's a convergent series of cubic numbers.
(d) It's a convergent series of triangular numbers.

6. What did George Cantor discover?
(a) A way to determine the accuracy of a calculation.
(b) A way to compare the relative sizes of infinite sets.
(c) A method to measure infinity.
(d) A method to measure a curved area.

7. What was Dunham central theorem for this chapter?
(a) That the area of a circle is fundamentally related to the square of its area.
(b) That the sum of an infintire series is always infinite.
(c) That the sum of a set of real numbers is finite.
(d) That there are other transfinite cardinals greater than c.

8. What was most noticeable about Euler at a young age?
(a) He had an aptitude for literature.
(b) He had a remarkable memory.
(c) He was very athletic.
(d) He was not very quick with arithmatic.

9. What didn't Euler attempt?
(a) A series where exponents are even.
(b) A series where exponents are odd.
(c) A series starting with the number 1.
(d) A series of sequencially smaller terms.

10. What did Cantor define as the continuum?
(a) Real numbers between 0 and 1.
(b) All imaginary and real numbers.
(c) The square root of any real number.
(d) All imaginary numbers.

11. Where did Euler study at the age of 20?
(a) University of Moscow.
(b) Cambrigde.
(c) The Academy in St. Petersburg.
(d) Oxford.

12. What did mathematicians want to perfect in the mid-19th century?
(a) The method of finding the area under a curve.
(b) The definition of infinite.
(c) The definition of pi.
(d) The method of finding the volume of spheres.

13. What did Cantor develop?
(a) A method to find the sum of a geometric series.
(b) A method to factor very large composite numbers.
(c) A system to identify prime numbers of very large size.
(d) A system to compare relative sizes of cardinal numbers.

14. Who else, besides Newton, independently discovered a calculus method?
(a) John Napier.
(b) Gottfried Leibniz.
(c) Isaac Barrow.
(d) Pierre de Fermat.

15. What was true when Euler used n = 5 in the statement 2²ⁿ + 1?
(a) The statement was a composite number.
(b) The statement was a perfect number.
(c) The statement was not a prime number.
(d) The statement was a prime number.

Short Answer Questions

1. Who were Johann and Jakob Bernoulli?

2. Where was Euler born?

3. What did British scholars accuse Leibniz of?

4. What great theorem is presented by Dunham in this chapter?

5. Who encourages Newton during his studies at Cambridge?

(see the answer keys)

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