Math 29 Homework #2

Mature scholars will testify that any volume in their library
which they have marked up
is worth infinitely more to them than
a new unmarked copy of the same book.
Theodore M. Greene

Reading

Read what we covered in today's class: 1.3, 1.4
Read what we will cover in the next class: 1.5, 2.1, 2.2

When reading 1.3 pay special attention to the following concepts:

  • URM-computable function, computable function, flow diagrams, make sure that you understand the process one goes through in writing programs for URMs.
When reading 1.4 pay special attention to the following concepts:
  • predicate, characteristic function of a predicate, decidable predicate, examples of decidable predicates.
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]

Problems

The following problems are due by the beginning of class on Thursday 4/1.
  • Define and give an example for each of the following:
    • characteristic function
    • the basic functions
    • URM-program in standard form
  • p. 21, # 1.3.3.1 b,c,d,e (include a flow diagram)
  • p. 22, # 1.3.3.2 (example 2.1 on pages 12 - 14)
  • p. 22, # 1.3.3.4
  • p. 23, # 1.4.3b

Presentations

The following are the choices available for the first presentations. More options will be provided if necessary:
  • Theorem 2.3.1 on Monday 4/5
  • Theorem 2.4.4 on Wednesday 4/7
  • Theorem 2.5.2 on Friday 4/9