View a FREE sample

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

Short Answer Questions

1. Which of the following was one of Gauss' early discoveries?

2. What did Newton's calculus involve?

3. What did Cantor develop?

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

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

Short Essay Questions

1. Describe who were Jakob and Johann Bernoulli.

2. What were the two transfinite cardinals discovered by Cantor, and what method did he use to determine them?

3. Summarize in a few sentences, what types of number sets did Cantor prove to be denumerable and non-denumerable.

4. Describe some of the characteristics of Leonhard Euler, and what made him successful.

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

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

7. Describe the connection between Fermat and Euler's work.

8. What was Euler able to prove about 2²ⁿ + 1? Why was this a great accomplishment?

9. Describe some of Gauss's work.

10. Describe the controversy that Newton was caught in with his publication of his calculus methods.

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

Write a three part essay to compare the work of Euclid to the work of Gauss.

Part 1) Explain what concepts both Euclid and Gauss worked with, and how they approached a similar problem.

Part 2) Compare what Euclid believed about triangles to what Gauss believed about triangles.

Part 3) How did both Gauss and Euclid advance mathematical understanding in their own time?

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

Write a three part essay to explain Archimedes determination of circular area.

Part 1) According to Archimedes what was pi, and why is this value needed to determine circular area?

Part 2) Explain how Archimedes used a right triangle to determine the area of a circle.

Part 3) Why was the determination of circular area useful at the time of Archimedes, and how did it advance the future of mathematics?

(see the answer keys)

This section contains 857 words (approx. 3 pages at 300 words per page) View a FREE sample