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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. Carl Gauss referred to mathematics as what?

2. The absolute value of a number may be thought of as its distance from what?

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

4. What term in theoretical physics refers to an extension of string theory in which 11 dimensions of spacetime are identified?

5. In what year was Albert Einstein awarded the Nobel Prize in 1921 for his “discovery of the law of the photoelectric effect”?

Short Essay Questions

1. What is expressed through the Rayleigh-Jeans law? How does this law relate to zero?

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

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

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

5. How is string theory described by the author in Chapter 8, “Zero Hour at Ground Zero”?

6. What problem does zero present when calculating tangent lines? What is a tangent?

7. 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?

8. Who created calculus? How did calculus differ from the other mathematical fields, according to the author in Chapter 5, “Infinite Zeros and Infidel Mathematicians”?

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

10. How did Max Planck address the problem of the ultraviolet catastrophe?

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

Define and discuss imaginary numbers and their impact on algebra and mathematic philosophy. Who discovered imaginary numbers and when? How do imaginary numbers behave in comparison to real numbers?

Essay Topic 2

Describe and discuss the advancements made in mathematics, music, and philosophy by Pythagoras. What is the Pythagorean Theorem? When was it developed? What were the beliefs of the Pythagoreans?

Essay Topic 3

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?

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