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This test consists of 15 multiple choice questions and 5 short answer questions.

## Multiple Choice Questions

**1. What was Euler's contribution to understanding partitions?**
**(a)** A functional approximation. **(b)** A theorem about series. **(c)** Notes on the performance of nested square roots. **(d)** An algorithm, but without values.

**2. Who met Ramanujan in England?**
**(a)** Hardy. **(b)** Euler. **(c)** John Littlewood. **(d)** Neville.

**3. When did Ramanujan write to Hardy?**
**(a)** 1909. **(b)** 1920. **(c)** 1913. **(d)** 1916.

**4. What were Ramanujan and Hardy looking for in their work on partitions?**
**(a)** A point at which partitions broke down for prime numbers. **(b)** A way to define the number of partitions precisely. **(c)** A way to bridge partitions. **(d)** A theorem that demonstrated how partitions operate in series.

**5. How does Kanigel describe Ramanujan when he returned to India?**
**(a)** Spirited. **(b)** Sullen. **(c)** Devout. **(d)** Friendly.

**6. In his letter to Hardy, what was the importance of the thing Ramanujan claimed to have discovered?**
**(a)** It was just being discovered simultaneously at other math departments. **(b)** It had been a mystery for years. **(c)** No one under thirty had even tried it. **(d)** It was already common knowledge.

**7. What did Ramanujan and Hardy develop for working with partitions?**
**(a)** The circle method. **(b)** A refinement of Euler's suggestion. **(c)** A precise method for determining partitions for prime numbers. **(d)** Nested square roots.

**8. Based on his letter, what was Hardy trying to determine about Ramanujan?**
**(a)** How he had devised his theories. **(b)** Who his teachers had been. **(c)** Where he was from. **(d)** Whether he was a crank.

**9. How did Ramanujan respond to Hardy's request for proofs?**
**(a)** He sent them immediately. **(b)** He said he could not produce them. **(c)** He would send them if Hardy would help him financially. **(d)** He dragged his feet about sending them.

**10. What did Ramanujan discover when his friend Mahalanobis read a puzzle from the paper?**
**(a)** A proof to all problems like that puzzle. **(b)** The constant that resolves series to prime numbers. **(c)** The mystical nature of numbers. **(d)** The value of pi.

**11. What aspect of the English does Kanigel say affected Ramanujan?**
**(a)** Nationalism. **(b)** Affected coldness. **(c)** Intellectual rigor. **(d)** Chauvinism.

**12. What did Ramanujan petition Cambridge for?**
**(a)** The right to return. **(b)** Publication. **(c)** An assistant. **(d)** A stipend.

**13. Who was Leonard Euler?**
**(a)** Hardy's protégé. **(b)** A brilliant mathematician to whom Hardy compared Ramanujan. **(c)** Ramanujan's tutor. **(d)** A teacher at Cambridge.

**14. When do mathematicians believe Ramanujan did his best work?**
**(a)** Before he left for England. **(b)** During his illness. **(c)** On the ship back to India. **(d)** At Cambridge.

**15. How do people account for Ramanujan's self-assessment?**
**(a)** Ramanujan's arrogance. **(b)** Ramanujan's naïveté. **(c)** Overwork. **(d)** Hardy's coldness.

## Short Answer Questions

**1.** What was the doctor's prescription for Ramanujan's condition?

**2.** Who was Neville?

**3.** How does Kanigel describe John Littlewood?

**4.** How much of Ramanujan's work did Hardy believe was sound and original?

**5.** How does Kanigel characterize Ramanujan's theorems and formulas?

This section contains 478 words(approx. 2 pages at 300 words per page) |