Math 29 Homework #22 We do not listen with the best regard to the verses of a man who is only a poet, nor to his problems if he is only an algebraist; but if a man is at once acquainted with the geometric foundations of things and with their festal splendor, his poetry is exact and his arithmetic musical. Ralph Waldo Emerson

	Reading Read what we covered in today's class: 7.2 Read what we will cover in the next class: 7.3 When reading 7.2 pay special attention to the following concepts: The definition and basic examples of c.e. sets, Theorems 2.3,4,5,6 which utilize what we already know about partially decidable predicates to provide information about c.e. sets, the characterization of c.e. sets given by Theorem 2.7, the characterization of the set of indices of total computable functions given by Theorem 2.9 (you should find this particularly interesting), the connection between c.e. sets and diophantine predicates, and the algebraic facts about c.e. sets given by Theorem 2.13. When reading 7.3 pay special attention to the following concepts: definition of productive sets, why are we interested in these sets?, also, pay special attention to Theorems 3.2, 3.4 (these provide us with lots of examples of productive sets), definition and examples of creative sets, Theorem 3.11 is also very important.

	Problems The following problems are due by the beginning of class on Wednesday 5/19. Define and give an example of each of the following: productive set creative set p. 132, # 7.2.18.8 p. 132, # 7.2.18.10 p. 132, # 7.2.18.11 p. 132, # 7.2.18.12 From the handout, provide a justification for the position in the arithmetical hierarchy of each of the sets listed under Definition 4.14 (specify the level if none is given).

	Presentations Joran, Theorem 7.2.16 on Monday 5/17 David, Theorem 7.3.2 and 7.3.4 on Wednesday 5/19 Amanda, Theorem 7.4.2 and 7.4.3 on Monday 5/24