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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 Dunham describe about the following series 1 + 2 + 3 + 4. . .?
2. When was Euler born?
3. What series was Euler most famous for?
4. On who's work did Euler base his number theory?
5. Who else, besides Newton, independently discovered a calculus method?
Short Essay Questions
1. Describe some of Gauss's work.
2. Describe some of the characteristics of Leonhard Euler, and what made him successful.
3. Describe what the Bernoullis discovered about series, and give an example.
4. Explain why Eulers sum of Ï€Â²/6 was in some ways surprising.
5. Describe Cantor's difficult personal life.
6. What were the two transfinite cardinals discovered by Cantor, and what method did he use to determine them?
7. Give an example of a series who's sum is still unknown.
8. Describe who were Jakob and Johann Bernoulli.
9. Summarize in a few sentences, what types of number sets did Cantor prove to be denumerable and non-denumerable.
10. What was Euler able to prove about 2²ⁿ + 1? Why was this a great accomplishment?
Write an essay for ONE of the following topics:
Essay Topic 1
Write a three part essay on the lives and work of both Euler and Gauss.
Part 1) What was similar about Euler and Gauss from an early age? What characteristics did they have in common?
Part 2) Give some examples of great theorems proposed by Euler and by Gauss. Do you think their work had anything in common mathematically?
Part 3) What could be considered Euler's greatest work? What could be considered Gauss's greatest work? How did both mathematicians advance the study of mathematics?
Essay Topic 2
Write an essay to explain what is meant by "infinitude of primes." Use the following questions to guide your writing. What was Euclid's definition of a prime number? How were prime and composite numbers related according to Euclid?
Essay Topic 3
In all of the great theorems presented in Dunham's book, which theorem do you think made the most impact on the history of mathematics? Write an essay to defend your opinion with reference to Dunham's descriptions and conclusions.
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