View a FREE sample

This test consists of 15 multiple choice questions and 5 short answer questions.

Multiple Choice Questions

1. What hindered Euler's work as he grew older?
(a) He had very bad arthritis.
(b) His increasing blindness.
(c) He had a stroke.
(d) His hearing was getting worse.

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

3. What did Dunham describe about the following series 1 + 2 + 3 + 4. . .?
(a) The sum converges to infinity.
(b) The sum diverges to infinity.
(c) The sum grows ever smaller.
(d) The sum converges to a finite term.

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

5. What were the main technique(s) that Euler used to find the sum of the series?
(a) Calculus methods.
(b) Cubic equations.
(c) Trigonometry and basic algebra.
(d) Quadratic sums,

6. What did Dunham describe as the same between artistic movements and mathematical studies in the 19th century?
(a) They are both becoming less abstract.
(b) They are both less concern with reality.
(c) They are both fascinated on artificial images, such as photography.
(d) They are both focused on realism.

7. Which word best describes Newton's childhood?
(a) Simple.
(b) Cold.
(c) Troubled.
(d) Hard.

8. Who eventually solved the sum of the successive squared denominator series?
(a) Jakob Bernoulli.
(b) Leonhard Euler.
(c) John Napier.
(d) Johann Bernoulli.

9. When was Euler born?
(a) 1903.
(b) 1658.
(c) 1796.
(d) 1707.

10. What was aleph naught?
(a) A method to numerate terms.
(b) A method to determine the sum of a series.
(c) A symbol to state the sum of a series.
(d) A symbol to represent the number of items in a set.

11. In the Bernoulli's time, what was the current definition of a series?
(a) The sum of a finite series of terms.
(b) The infinite sum of a convergent series.
(c) The finite sum of a divergent series.
(d) The sum of a never-ending series of terms.

12. Which name does NOT belong?
(a) Blaise Pascal.
(b) John Napier.
(c) Francois Viete
(d) Renee Descartes.

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

14. What did George Cantor determine to be true of a set of rational numbers?
(a) They are all composite numbers.
(b) They are all prime numbers.
(c) They are denumerable.
(d) They are non-denumerable.

15. What great theorem is presented by Dunham in this chapter?
(a) A theorem on series developed by Jakob and published by Johann Bernoulli.
(b) A theorem on infinite series published by Jakob Bernoulli.
(c) A theorem on finite series developed by Johann Bernoulli.
(d) An improvement on Leibniz's caluclus as presented by Jakob Bernoulli.

Short Answer Questions

1. Where does the center of mathematical thinking shift to after Italy?

2. Which phrase best describes Newton as a student at Cambridge?

3. Which of the following is a quote from Bertrand Russell included by Dunham?

4. What was described as true about the series 1 + 1/2 + 1/6 + 1/10 + 1/15 + 1/21?

5. How did Gauss feel about his best work?

(see the answer keys)

This section contains 596 words (approx. 2 pages at 300 words per page) View a FREE sample