Tuesday, October 17, 2006

Well, it's the first day, and I'm already a bit behind in my reading, so this entry will have to be short. Not an auspicious start, I know, but lots of things came up.



At present, I've read 12 of the 50 pages that I set out for myself today, but I'll be up for another two hours or so, so I should make it to 50 before I turn in.



I'm pleased to say that the book is quite readable. When you're given a giant 700-page hardcover with nothing but math in it, it can be a bit intimidating. Fortunately, Knuth has a really nice writing style. I wasn't wrong about him being thorough! He takes the time to explain every point in great detail, so this has the virtue of being one of the few books in the world that can honestly make the claim that it is suitable both for beginners and experts. I find it much less dense than Purdom's book, even though it actually manages to explain more.



I've done most of the exercises for the first section - but there are a few at the end that have me a little stumped. Knuth has a rating system for exercises - where each gets a two-digit number. The first digit - from 1 to 5 - gives the basic level. So a 00 would be something you should instantly know the answer for, a 10 is just a test to see that you were paying attention, a 20 might take 15-20 minutes to work, but should pose no serious difficulties. Anything in the 30 range is a serious problem requiring more than an hour of thinking (more than two if the TV is on, he says), things in the 40s are appropriate for term projects in a class, and anything starting with a 5 is a known but as yet unsolved problem in the field. He also notes when exercises are "recommended," when they involve "math," and when they involve "higher math."



There is one very interesting problem (rated M25 - for "mathematically oriented, medium to moderate difficulty - will require more than 15min.") that involves a set of very simple equations that are computationally complete (like a Turing machine, they can perform any calculations we might consider "computation," though maybe not efficiently), and the reader is asked to implement the Euclidean Algorithm (for finding the greatest common divisor) with them. I haven't given it much though, and I probably won't tonight (finishing the reading takes precedence), so I won't say much about it today, but it's likely to appear in this column tomorrow.



Anyway - enough of this. Reading comes first. I admit I'm off to a shaky start, but am still optimistic I'll have the first three volumes out of the way by the end of November.



 

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