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This test consists of 5 multiple choice questions, 5 short answer questions, and 10 short essay questions.

Multiple Choice Questions

1. Riemannian geometry describes the following objects: _____.
(a) Curved spaces.
(b) Finite, unbounded spaces.
(c) N-dimensional spheres.
(d) Six-dimensional manifolds.

2. Which of the following best describes the fate of Kaluza-Klein theory?
(a) It was quickly discarded as meaningless, but rediscovered by string theory.
(b) It became widespread for a short time, but receives almost no attention now.
(c) It became the mathematical basis of general relativity.
(d) It was updated through the 1970s, and eventually incorporated into string theory.

3. By what factor is the minimum mass of a wrapped string in determined?
(a) The vacuum energy of the dimension it is wrapped around.
(b) The string's Planck tension.
(c) The size of the circular dimension it is wrapped around.
(d) The string's winding number.

4. What is strong-weak duality?
(a) The relationship between bosonic-strong string theories and bosonic-weak theories.
(b) A relationship between the strong and weak coupling constants in two different string theories.
(c) The union of the strong and weak forces at high energies.
(d) The coupling of strong and weak forces in M-theory.

5. How many dimensions are necessitated by M-theory?
(a) Eight.
(b) Ten.
(c) Nine.
(d) Eleven.

Short Answer Questions

1. Which of the following methods has been used to determine the shape of the Calabi-Yau space?

2. How are black holes are widely believed to have originated?

3. Which of the following best describes a wormhole?

4. At what scale of length is quantum geometry necessitated?

5. What does the second law of thermodynamics state about entropy for a closed system?

Short Essay Questions

1. Describe the state of the universe's expansion, including what its ultimate fate might be.

2. Describe the difficulties in studying the entropy of a black hole.

3. What is mirror symmetry, and what is its relevance to string theory?

4. What is the strong-weak duality?

5. Describe the history of space-time tears in physics.

6. Describe Kaluza-Klein theory.

7. What is the relative composition of matter in the universe?

8. Describe the phenomenon of winding in string theory.

9. How are strings affected by extra dimensions?

10. How is the shape of the Calabi-Yau space is determined?

(see the answer keys)

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