Math 29 Detailed Schedule

Note: x refers to chapter and x.y to chapter.section in Cutland.

Introduction: Notation and Historical BackgroundMar 281.1
Module 1: Turing MachinesMar 30, Apr 2   3.4, handout
Homework (due Monday, April 9)
Interlude: CodingApr 21.5, 3.6
Module 2: Partial Recursive FunctionsApr 4, 6, 92, 3.2-3
Interlude: The Church-Turing ThesisApr 6, 93.7
Homework: 2.5.4 #1, 3.7.2 #1 (ignore URM-computable; you're not giving a
machine/recursion definition anyway) (due Friday, Apr 13)
Module 3: Listing Programs and Universal MachinesApr 11-164, 5
Homework: 4.2.3, 4.3.2 #1,4, 4.4.1 #1 (due Monday, Apr 23)

New Schedule, picking up where we left off the old one
(still subject to change)
Computing and enumerating
Noncomputable sets (simple sets)
Turing reduction and Post's problem (oracle Turing machines)
(Aside: finite injury priority arguments)
Turing degrees (equivalence relations, partial orders)
Relativization and the Turing jump (the arithmetic hierarchy)
Lattice-theoretic questions
Homework: Look at this LaTeX example and then typeset this document (due Monday, May 14).
Favorable-looking ways to get TeX: TeX for Macs, TeX for Windows.
A second LaTeX example.
A LaTeX template file.
Overview of randomness
Kolmogorov complexity
Relative randomness
Some open questions
If time: reverse math

Relevant Web Links:

Module 1: Turing Machine Simulators Online

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