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This test consists of 5 short answer questions, 10 short essay questions, and 1 (of 3) essay topics.

Short Answer Questions

1. What did Cantor's cardinal numbers represent?

2. What series was Euler most famous for?

3. When was Euler born?

4. What is one proof that Euler was able to prove?

5. What was most noticeable about Euler at a young age?

Short Essay Questions

1. What was Gauss's major unpublished achievement in geometry?

2. Describe Cantor's difficult personal life.

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

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

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

6. Describe what mathematical and artistic movements are focused on in the second half of the 19th century.

7. Give an example of a series who's sum is still unknown.

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

9. Describe some of Gauss's work.

10. Explain how Gottfried Leibniz was able to publish his method of calculus.

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

In Dunham's book, there were many descriptions of mathematicians and their personal lives. Write an essay to describe the common elements or characteristics that seem to be shared among these historically famous mathematicians. Also, explain what personal characteristics made them all excellent mathematicians.

Essay Topic 2

Describe Gauss's work on what was to be known as non-euclidean geometry. What was Gauss's system for triangles where angles added up to fewer than 180 degrees? What were some of his conclusions? Did he publish his work? Was their any controversy surrounding his work on this system? Explain.

Essay Topic 3

Debate in essay format one of the following controversies:

a) Newton versus Leibniz.

b) Cardano versus Tartaglia.

Explain a defense for each side of the controversy, then propose your opinion with your final conclusions.

(see the answer keys)

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