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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) Finland.
(b) Denmark.
(c) Switzerland.
(d) Germany.

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

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

4. Who else, besides Newton, independently discovered a calculus method?
(a) Isaac Barrow.
(b) Gottfried Leibniz.
(c) John Napier.
(d) Pierre de Fermat.

5. What concept did Dunham end his book with?
(a) Heron's triangulated area.
(b) Newton's method of calculus.
(c) Archimedes and the infinite series.
(d) Cantor and his voyage into the infinite.

6. 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 still equal to c.
(c) That the series is infinite.
(d) That the set is equal to 1.

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

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

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

10. What did Gauss construct?
(a) A proof that demonstrates Newtonian physics.
(b) A system where the angles of a triangle add up to fewer than 180 degrees.
(c) A proof that demonstrated the circumference of Earth.
(d) A system where the angles of a triangle add up to more than 180 degrees.

11. In his later life, what position did Isaac Newton hold?
(a) Professor of philosophy in Paris.
(b) Angelican father.
(c) Warden of the Mint.
(d) Principle science advisor to Charles II.

12. What was the same about the series proposed by Leibniz and the series proposed by Bernoulli?
(a) Both series were composed of successively smaller terms.
(b) Both series were divergent.
(c) Both series were composed of successively larger terms.
(d) Both series were convergent.

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

14. Which of the following did Dunham concentrate on as one of Newton's great advances?
(a) Area of a sphere.
(b) Quintic theorem.
(c) Quadratic equation.
(d) Binomial theorem.

15. Where was George Cantor born?
(a) Britian.
(b) Russia.
(c) Germany.
(d) Switzerland.

Short Answer Questions

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

2. Which of the following was NOT a field in which Isaac Newton made enormous advances?

3. What did Dunham describe as lacking from calculus previous to the mid-19th century?

4. Where did Euler study at the age of 20?

5. What did Cantor develop?

(see the answer keys)

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