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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. Approximately when did Johannes Kepler live?

2. What is the study of geometric properties that are invariant under projective transformations?

3. When did Sir Isaac Newton live?

4. According to the author in Chapter 6, “Infinity's Twin,” “i” appears whenever one takes the square root of what?

5. According to the author in Chapter 5, “Infinite Zeros and Infidel Mathematicians,” Jean le Rond d'Alembert had satisfied the mathematician's need for what?

Short Essay Questions

1. How old is the universe estimated to be by astronomers today? How did they calculate this age?

2. How are electrons described in Chapter 8, “Zero Hour at Ground Zero”?

3. Who was Carl Gauss? What discovery did he make regarding imaginary numbers?

4. Who devised the concept of a limit in calculus? What problems did the limit solve?

5. What discovery did Georg Cantor make regarding different types of infinities? How are these types defined?

6. How did l’Hopital address the problem of zero, according to the author in Chapter 5, “Infinite Zeros and Infidel Mathematicians”?

7. What problem do black holes present in physics, according to the author in Chapter 8, “Zero Hour at Ground Zero”?

8. What does the author say thermodynamics has taught us in Chapter 7, “Absolute Zeros”?

9. What problems were encountered in calculus with zero? How did zero apply to the physical world, according to the author in Chapter 5, “Infinite Zeros and Infidel Mathematicians”?

10. What discovery did Friedrich Riemann make in the field of projective geometry?

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

Describe and discuss the concept of the “limit” proposed by Jean Le Ron D'Alembert and its impact on calculus and mathematics. What impact did the discoveries of Jean Le Ron D'Alembert have on the concepts of zero and infinity?

Essay Topic 2

Discuss the biography and the mathematical and philosophical contributions of Archimedes of Syracuse. How did Archimedes first encounter the infinite? How did this discovery influence his work and the work of mathematicians after him?

Essay Topic 3

Describe and discuss the origins and history of mathematics within Islamic culture. When was the House of Wisdom built? Who first coined the term “algebra”? When was the term coined?

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