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 did Newton's calculus involve?
(a) Determining the area under a curve.
(b) Proving the existance of pi.
(c) Determining the volume of a sphere.
(d) Proving the cubic equation.

2. Which of the following is not denumerable, proven by Cantor's theorem?
(a) A set of rational numbers.
(b) A set of transcendental numbers.
(c) A set of imaginary numbers.
(d) A set of a geometric series.

3. What did Euler's sum surprisingly connect?
(a) The circumference of a circle and right triangles.
(b) The area under a curve.
(c) The area of squares and the area of circles.
(d) The squares of area and square roots.

4. Which of the following is a series that the Bernoullis proposed did not converge on a finite sum?
(a) 1 + 1/2 + 3/4 + 4/5 . . .
(b) 1 + 1/2 + 1/6 + 1/10 + 1/15 . . .
(c) 1 + 1/2 + 1/3 + 1/4 + 1/5 . . . 1/1000 . . .
(d) 1 + 2 + 3 + 4 + 5. . .

5. Where does the center of mathematical thinking shift to after Italy?
(a) To Turkey and Russia.
(b) To Germany and Russia.
(c) To Britian and Scotland.
(d) To France and Britian.

Short Answer Questions

1. To how many decimal places did Newton determine the number for pi?

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

3. What was the same about the series proposed by Leibniz and the series proposed by Bernoulli?

4. What is true about real numbers between 0 and 1?

5. What is the sum of the series 1 + 1/2³ + 1/3³ + 1/4³ ... 1/k³ . . .?

Short Essay Questions

1. Describe Newton's days in Cambridge and what he eventually came to discover.

2. Explain why Eulers sum of π²/6 was in some ways surprising.

3. Who was Georg Cantor, and what was significant about his work in mathematics?

4. What was the great theorem of this chapter? Describe it briefly.

5. Describe who were Jakob and Johann Bernoulli.

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

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

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

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

10. Explain what was the definition of a series before the Bernoullis, and give examples of what was known.

(see the answer keys)

This section contains 931 words (approx. 4 pages at 300 words per page) View a FREE sample