Math 29 Homework #5 I canšt say that in five years I am going to invent something. But I am going to research something, and I am going to have something.... If I find the truth, then the truth eventually will be useful. Jeong Han Kim

	Reading Read what we covered in today's class: 2.4 Read what we will cover in the next class: 2.4, 2.5 When reading 2.4 pay special attention to the following concepts: recursion, Theorem 2.4.2, look carefully at the examples in 2.4.3, Theorem 2.4.4 (what does it say? why is this interesting?). The rest of this section provides many specific examples of functions that are computable via recursion and, also, demonstrates that many common approaches mathematicians use for building functions preserve computability. Some important connections to decidabilty are also discussed. Read through this carefully and think of yourself as filling up your 'computability' toolbox with lots of good stuff... When reading 2.5 pay special attention to the following concepts: minimalization, Theorem 5.2 (what does it say? why is this important?), Corollary 5.3 (how is this different from Thm 5.2?), the Ackermann function.

	Problems The following problems are due by the beginning of class on Friday 4/9. Define and give an example for each of the following: the algebra of decidability bounded minimalization unbounded minimalization Why are Pr(x) and px computable? Provide complete justifications... p. 41, # 2.4.16.1 a,b,c,e (Theorem 4.15 may be helpful) p. 41, # 2.4.16.2

	Presentations David, Theorem 2.3.1 on Monday 4/5 Joran, Theorem 2.4.4 on Wednesday 4/7 Amanda, Theorem 2.5.2 on Friday 4/9 (maybe Monday...)