View a FREE sample

This test consists of 5 multiple choice questions, 5 short answer questions, and 10 short essay questions.

Multiple Choice Questions

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

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

3. What were the two types of transfinite cardinals defined by Cantor?
(a) c and pi.
(b) אₒ and c.
(c) pi and אₒ.
(d) 1 and pi.

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

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

Short Answer Questions

1. What did British scholars accuse Leibniz of?

2. Who else, besides Newton, independently discovered a calculus method?

3. What sum did Euler find for the series?

4. What was true when Euler used n = 5 in the statement 2²ⁿ + 1?

5. What was most noticeable about Euler at a young age?

Short Essay Questions

1. Describe the connection between Fermat and Euler's work.

2. Why did Euler start working on the sum of series?

3. Give an example of a series who's sum is still unknown.

4. What was Euler able to prove about 2²ⁿ + 1? Why was this a great accomplishment?

5. Describe the controversy that Newton was caught in with his publication of his calculus methods.

6. What was Gauss's major unpublished achievement in geometry?

7. What great theorems and work of Newton did Dunham highlight?

8. Describe the great theorem explained by Dunham in this chapter.

9. Explain any methods used by Cantor that were unsuccessful.

10. Describe what the Bernoullis discovered about series, and give an example.

(see the answer keys)

This section contains 757 words (approx. 3 pages at 300 words per page) View a FREE sample