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Hi,
Sam
----- Original Message -----
To:
Sent: Friday, August 25, 2006 2:22
PM
Subject: Re: Mathematical Logic
I took a module in mathematical logic and thoroughly enjoyed it - though
I haven't taken the exam yet due to the AUT action! I'd certainly
recommend it if you enjoy maths; some of the stuff covered was essentially an
exercise in doing trivial things in a complicated way, for instance proving
arithmetical statements. Other things were much less trivial; especially
Godel's incompleteness theorem. A particular favourite of mine being Rice's
theorem.
As for books I found Bell & Machover 'A Course in
Mathematical Logic' helpful. it might be worth brushing up on set
theory notation; but I picked up most of what I needed to
know more through necessity than supplementary study.
Andrew Turner
(Yes...another Andrew)
On 8/25/06, A.M.Goldfinch@lse.ac.uk <A.M.Goldfinch@lse.ac.uk> wrote:
To
reply to this message or start a new topic please email: BUPS-DIS@bups.org
Hi
Andrew,
Thanks for your detailed reply. I think mathematical logic is
important for one's intellectual development. I've been hearing about
Godel's incompleteness theorems for years; being able to prove his theorems
would be very satisfying.
I'll check out Hamilton and Boolos et
al.
Best,
Another
Andrew
________________________________
From: Andrew Bacon
[mailto:andrew.bacon@lmh.ox.ac.uk
]
Sent: Thu 24/08/2006 19:26
To: Goldfinch,AM (ug)
Cc: BUPS-DIS@bups.org
Subject: Re:
Mathematical Logic
Hi there Andrew,
I would
strongly recommend mathematical logic if you are sure its your kind of
thing! However, I am always wary of recommending it, because the
introductory
courses can be very dry. (Also, mathematical
logic can sometimes be used to
talk about model theory, set theory,
recursion theory all of which I would
highly
recommend).
Basically my background is a degree in maths and
philosophy. So in my first year
I did logic taught by philosophers:
propositional calculus, predicate calculus
and soundness, completeness
and compactness for both languages (with a little
bit of philosophy of
language). In the second year I basically did *exactly* the
same syllabus
again, but this time taught by the mathematics department. But
despite
this, it was *very* different. The mathematician way is much more
pendantic and most of all fiddly, and I did not enjoy this particular
course
very much (although its compliment, set theory, was probably my
favourite
subject). However, this course is very important, and it paves
the way for the
interesting stuff that comes after. For example there
are Gödel's Incompleteness
theorems, or if you move towards model theory
the Lowenheim-Skolem theorems.
Then of course it will be helpful if you
want to get into set theory or the
philosophy of maths.
In terms
of books, the Enderton is good, so is Hamilton 'Logic for
Mathematicians'
(I think that's the name). Also 'Logic and Computability' by
Boolos,
Jeffrey and Burgess is a nice read and it covers a lot.
Anyway, just
check the syllabus to see what it says. It may well look exactly
like the
course you've done with the philosophy department but I can assure you
it
will still be worth doing. If it starts talking about the incompleteness
theorems, Gödel's constructible universe and so on, the jump might be a
big one.
Hope that helps,
Andrew
> To reply to this
message or start a new topic please email: BUPS-DIS@bups.org
>
>
>
Has anyone on this list taken mathematical logic? If so, I'd be
>
interested to hear your experiences. In your experience, how much of
a
> conceptual leap was it from first-order predicate logic? Are there
any
> books you'd especially recommend (I have Enderton's classic
'A
> Mathematical Introduction to Logic')? Are there any areas of
mathematics
> you'd recommend brushing up on before starting a
mathematical logic
> course? Which areas did you find most
challenging? Would you recommend
> mathematical logic?
>
>
Cheers.
>
>
> Browse or search the BUPS-DIS archives, or
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>
--
Andrew
Bacon
Lady Margaret Hall
07830048336
http://users.ox.ac.uk/~lady1900
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