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Old Man Yells At Cloud


On 18/09/17 16:29, Ben Bacarisse wrote:
> Steve D'Aprano <steve+python at pearwood.info> writes:
> <snip>
>> To answer your question, what do I mean by int/int being undefined, I'd have to
>> dig into areas of maths that either weren't taught in the undergrad courses I
>> did, or that I've long since forgotten about. Something
>> about... fields?
> <snip>
>> This is a pretty specialised area of maths. You won't learn anything
>> about it in high school. And possibly not undergrad maths degrees. I
>> seem to vaguely recall just barely touching on groups, but not rings
>> or fields.
> 
> When you said before that you thought that undefined division was rather
> obscure I was going to mention that it's the basic difference between a
> ring and a field; the intent being that you'd go "oh, yes, of course
> it's not obscure at all".  I'm glad I didn't now, because you would not
> have seen it as the simple notion I expected!
> 
> Teaching rings and fields is (or at least was 30 or so years ago) 1st
> year undergraduate maths here in the UK.  Maybe it's changed.

I think I achieved a nodding acquaintance with rings, fields and vector 
spaces in Further Maths (pre-university), and then got the real deal in 
my first term at university.  I think they now happen later in the first 
year; looking at the on-line syllabus, the first two terms of IA Maths 
are now full of things that used to be taught at A-level.

-- 
Rhodri James *-* Kynesim Ltd