[M381-Logic] - #1: Objectives unit 1.

( Kick-off study M381-Logic )

After working through Logic Unit-1 ( Computability ) you should be able to:
(a) recall the definitions of the basic URM instructions and of a URM program;
(b) write down a trace table for the computation of a given URM program with a given input and state what is the output;
(c) draw a flow diagram for a given URM program;
(d) determine, in simple cases, which function of a given number of variables is computed by a given URM program;
(e) construct a URM program to compute a given function;
(f) write down the concatenation of given URM programs;
(g) calculate the values of a function defined by primitive recursion;
(h) write down a URM program to compute a function obtained by substitution or primitive recursion from given URM-computable functions.

(... From the Student Hat. - Probably the most valuable LRH ever said was: "When reading a book, be very certain that you never go past a word you do not fully understand. The only reason a person gives up a study or becomes confused or unable to learn is because he or she has gone past a word that was not understood." Studying then becomes 'handling misunderstoods', of which finding a definition is only the first step. With the definition one should be able to give the concept sufficient 'mass'. But mass is not sufficient either, studying the topic must have purpose. - Take URM for example. Where do these letters stand for in the context of M381-L? Can I describe the topic so that someone else would understand it? ( I.e. what does it look like, and so forth. ) Where and when will I need this topic? How does it relate to my long and short-term goals? ...)

URM stands for Unlimited Register Machine its a development of the TURING Machine and is used to investigate the theoretical limitations of computers. Whereas the Turing machine uses an infinite paper tape. The URM machine is based on infinite shift registers. It's meant to model the process of computing in a manner closer to current digital computers.

The whole theory of computability or rather its limitations plays a crucial part in developing Godel's theorem probably one of the most significant theorems showing the limits of formal systems. Essentially it showed that the hope of reducing all of mathematics to logic as Russell, Frege and Hilbert hoped was no longer tenable.

As to how it relates to your long and short term goals only you can decide. I would have thought some understanding of Godel's theorem was an essential part of any one who aspires to be a mathematician.

( By Chris from Chris's Maths Physics Philosophy and Music Blog )