Math 29 Homework #3 ...education becomes what it should be far more often - a really cooperative venture of older and younger searchers for the truth, the older only a little more informed and expert in probing the problem and only a little more aware of its baffling and unfathomable depths. Theodore M. Greene

	Quiz Remember that we have a quiz on Monday 4/5 on Lectures 1 - 3.

	Reading Read what we covered in today's class: 1.5, 2.1, 2.2 Read what we will cover in the next class: 2.3 When reading 1.5 pay special attention to the following concepts: domain coding, computable function on a domain other than N, the specific coding for Z. When reading 2.1 pay special attention to the following concepts: what are the basic functions? When reading 2.2 pay special attention to the following concepts: Note that this section is fairly detailed and technical, but the details are important and the effort we expend here will pay back nice dividends in the next couple classes. subroutine, standard form for a program, Lemma 2.2 (what does it say? why is it important?), program join, p(P), P[l1,...,ln -> l] When reading 2.3 pay special attention to the following concepts: substitution (composition), Theorem 2.3.1 (what does it say? why is this interesting?), rearrangement, identification and adding dummy variables to functions, Theorem 2.3.2 (what does it say? why is this interesting?).

	Problems The following problems are due by the beginning of class on Monday 4/5. Define and give an example for each of the following: join of programs substitution (aka: composition) p. 23, # 1.4.3 a,c p. 24, # 1.5.2.1 p. 24, # 1.5.2.2 Let P denote the program on page 18, Q denote the program on page 19 and R denote the program on page 21. For each of P, Q, R, specify if the program is in standard form and if not, specify a program in standard form which computes the same function. Specify the program PQ (using the standard form from the first part if necessary). What function does this program compute? Specify the program QR (using the standard form from the first part if necessary). What function does this program compute?

	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...)