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

Multiple Choice Questions

1. Where was Euler born?
(a) Switzerland.
(b) Germany.
(c) Finland.
(d) Denmark.

2. How did Euler prove if the number 4,294,967,297 was prime or composite?
(a) He factored it.
(b) He divided it by 2.
(c) He used Newton's calulus methods.
(d) He used his own rule of squares.

3. What did Cantor's work do to mathematics?
(a) It caused much agreement among mathematicians on the use of calculus.
(b) It raised arguments on the origins of geometry.
(c) It forced the reexamination of set theory.
(d) It caused a reevaluation of basic algebra.

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

5. 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 non-denumerable.
(d) They are denumerable.

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

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

8. Where did George Cantor live in the 1860s and 1870s?
(a) Russia.
(b) Britian.
(c) Scotland.
(d) Germany.

9. What did British scholars accuse Leibniz of?
(a) Plagiarizing Newton's calculus method.
(b) Stealing Newton's Binomial theorem.
(c) Publishing Newton's work without his approval.
(d) Conspiring the death of Newton.

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

11. What did Euler prove about 2²ⁿ + 1?
(a) That the statement is neither prime nor composite.
(b) That the statment is sometimes prime and sometimes composite.
(c) That the statement is always a prime number.
(d) That the statement is always a composite number.

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

13. Which of the following was a major part of Gauss' work in mathematics?
(a) Simple proofs to demonstrate Bernoulli's series.
(b) Proofs on the area of a square.
(c) Proofs to show that Archimedes' number theory was wrong.
(d) Elemental proofs related to the foundations of algebra.

14. 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 divergent series with a sum of 2.
(c) It's a convergent series of cubic numbers.
(d) It's a divergent series squared numbers.

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

Short Answer Questions

1. Who was Euler's teacher?

2. What sum did Euler find for the series?

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

4. What did Dunham describe about the following series 1 + 2 + 3 + 4. . .?

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

(see the answer keys)

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