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

Multiple Choice Questions

1. What is true about real numbers between 0 and 1?
(a) They are not denumerable.
(b) They are denumerable,
(c) No sum can be determined.
(d) There is no set for these numbers.

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

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

4. What did Cantor develop?
(a) A system to identify prime numbers of very large size.
(b) A method to factor very large composite numbers.
(c) A method to find the sum of a geometric series.
(d) A system to compare relative sizes of cardinal numbers.

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

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

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

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

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

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

11. Who encourages Newton during his studies at Cambridge?
(a) Henry Briggs.
(b) Isaac Barrow.
(c) Henry Stokes.
(d) John Napier.

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

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

14. Which of the following was NOT a field in which Isaac Newton made enormous advances?
(a) Biology.
(b) Physics.
(c) Mathematics.
(d) Optics.

15. What did Gauss do with his best work?
(a) He published it.
(b) He gave it to his students.
(c) He gave it to his son to publish.
(d) He did not publish it.

Short Answer Questions

1. What did mathematicians want to perfect in the mid-19th century?

2. What did George Cantor determine to be true of a set of rational numbers?

3. Where was Euler born?

4. What did most of 19th century mathematics focus on, as highlighted by Dunham?

5. What was aleph naught?

(see the answer keys)

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