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

Multiple Choice Questions

1. What did Dunham describe as lacking from calculus previous to the mid-19th century?
(a) Definitions of infinately large and small quantities.
(b) An explanation of non-Eulidean mathematics.
(c) Description of the word "area."
(d) Foundations that link it to the principles of geometry.

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

3. 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.

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

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

6. What did Cantor's beliefs lead him to think?
(a) That he was God.
(b) That he was learning about the origins of God.
(c) That he was tapping into the nature of God by delving into the infinite.
(d) That he was seeing God when he worked on equations.

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

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

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

10. Who was Euler's teacher?
(a) Gottfried Leibniz.
(b) Jakob Bernoulli.
(c) Isaac Newton.
(d) Johann Bernoulli.

11. Who were Johann and Jakob Bernoulli?
(a) Cousins and students with Leibniz in Paris.
(b) Cousins and students with Newton at Cambridge.
(c) Brothers and students of Leibniz.
(d) Twin brothers and students of Newton.

12. In what area was Gauss especially interested?
(a) The elements of number theory.
(b) The circumference of Earth.
(c) The elements of geometry.
(d) The proof of the infinite series.

13. Which of the following demonstrates the successive squared denominator series?
(a) 1 + 1/4 + 1/9 + 1/16 . . .
(b) 1 + 1/2 + 1/6 + 1/10 + 1/15 . . .
(c) 1 + 1/2 + 1/3 + 1/4 + 1/5 . . . 1/1000 . . .
(d) 1 + 1/2 + 3/4 + 4/5 . . .

14. 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 a prime number.
(d) The statement was not a prime number.

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

Short Answer Questions

1. Which of the following was a major part of Gauss' work in mathematics?

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

3. What is true about the successive squared denominator series proposed by the Bernoullis?

4. On who's work did Euler base his number theory?

5. Which of the following did Dunham concentrate on as one of Newton's great advances?

(see the answer keys)

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