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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.** In quantum mechanics, the concept of de Broglie waves reflects what?

**2.** What refers to an indeterminate polynomial equation that allows the variables to take integer values only?

**3.** According to the author in Chapter 5, “Infinite Zeros and Infidel Mathematicians,” Leibniz wanted to use infinitesimals in calculus which were termed what?

**4.** Who coined the term “fermion” in particle physics?

**5.** Jean le Rond d'Alembert came up with what idea that solved the zero problem in calculus?

## Short Essay Questions

**1.** 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”?

**2.** Who discovered “absolute zero”? How is absolute zero defined in Chapter 7, “Absolute Zeros”?

**3.** How did the field of quantum mechanics address the problem of zero in thermodynamics?

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

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

**6.** The author states in Chapter 6, “Infinity’s Twin” that before imaginary numbers could be accepted, several developments had to occur. Which was the first?

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

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

**9.** How were Georg Cantor’s mathematical principles applied to his theology? Who disagreed with his vision and why?

**10.** How did the discovery of imaginary numbers affect the study of algebra?

## Essay Topics

Write an essay for ONE of the following topics:

### Essay Topic 1

Discuss the origins, history, and evolution of mathematics in ancient Egypt. How was geometry developed in Egypt? How did the Egyptians use mathematics in the creation of the pyramids? How did the Nile relate to their use of mathematics?

### 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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