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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. When did René Descartes live?

2. René Descartes was a French philosopher and mathematician who spent most of his adult life where?

3. Approximately when did Muhammad ibn Ahmad al-Khwarizmi live?

4. The author states in Chapter 3, “Nothing Ventured” that the Indians borrowed Greek geometry but never worried about what?

5. What refers to the mean obtained by taking the reciprocal of the arithmetic mean of the reciprocals of a set of nonzero numbers?

Short Essay Questions

1. How did zero enter into Indian mathematics, according to the author in Chapter 3, “Nothing Ventured”?

2. How did Aristotle approach the concept of zero, according to the author in Chapter 2, “Nothing Comes of Nothing”?

3. What is the focus of the book, as established by the author in Chapter 0, “Null and Void”?

4. What paradox of Zeno of Elea’s is presented by the author in Chapter 2, “Nothing Comes of Nothing”?

5. How are ancient Babylonian mathematics described in Chapter 1, “Nothing Doing”?

6. What reason does the author give for why the Greeks and Romans resisted using zero in their mathematical systems in Chapter 1, “Nothing Doing”?

7. How does the author describe the early counting systems of prehistoric mathematics in Chapter 1, “Nothing Doing”?

8. How did mathematics and the concept of zero evolve in India through the 5th Century AD?

9. What inventions is Blaise Pascal credited with, according to the author in Chapter 4, “The Infinite God of Nothing”?

10. What caused the USS Yorktown to have a computer meltdown in 1997, according to the author in Chapter 0, “Null and Void”? How is the ship described?

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

Discuss the biography, works, and mathematical developments of Mohammed ibn-Musa al-Khowarizmi. When was his work, Compendious Book on Calculation by Completion and Balancing completed? What did this work entail?

Essay Topic 2

Discuss Guillaume de l'Hôpital, Bishop Berkeley, and l'Hôpital's rule. How are derivatives used to evaluate limits involving indeterminate forms under l'Hôpital's rule? How did these advancements deal with the problem of zero?

Essay Topic 3

Discuss the origins, development, and contributions of Babylonian mathematics. How did the Babylonian numeral system differ from that of the ancient Egyptians? Where has most of our information of Babylonian mathematics been derived?

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