"Practical Foundations of Mathematics"

"Practical Foundations of Mathematics"

[Paul Taylor]

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		Practical Foundations of Mathematics

			    Paul Taylor
		    Department of Computer Science
		   Queen Mary and Westfield College
		           London E1 4NS

		  http://www.dcs.qmw.ac.uk/~pt/book/

	    Cambridge Studies in Advanced Mathematics #59
   (the series in which "Stone Spaces" by Johnstone and "Introduction
    to Higher Order Categorical Logic" by Lambek and Scott appeared.)

     ISBN: 0-521-63107-6    xii+576 pages    List price: £50 or $80

I understand that the text and cover have now been printed, and are due to
be bound on Monday 22 March in Cambridge, so I expect to see my own copy by
the end of next week; orders should be dispatched after the Easter holiday.

	PLEASE SEE BELOW FOR THE BEST WAY TO ORDER YOUR COPY.

The (not very informative) names of the chapters are:
   I   First Order Reasoning         VI   Structural Recursion
   II  Types and Induction           VII  Adjunctions
   III Posets and Lattices           VIII Algebra with Dependent Types
   IV  Cartesian Closed Categories   IX   The Quantifiers
   V   Limits and Colimits 

The back cover "blurb" reads:
   Practical Foundations collects the methods of construction of the
   objects of twentieth century mathematics. Although it is mainly
   concerned with a framework essentially equivalent to intuitionistic
   ZF, the book looks forward to more subtle bases in categorical type
   theory and the machine representation of mathematics. Each idea is
   illustrated by wide-ranging examples, and followed critically along
   its natural path, transcending disciplinary boundaries between
   universal algebra, type theory, category theory, set theory, sheaf
   theory, topology and programming.

   The first three chapters will be essential reading for the design
   of courses in discrete mathematics and reasoning, especially for the
   ``box method'' of proof taught successfully to first year informatics
   students. Chapters IV, V and VII are an introduction to categorical
   logic. Between the formal languages translations are provided which
   are fluent, showing how to write vernacular proofs which are sound in
   formal logics.  Chapter VI is a new approach to term algebras,
   induction and recursion, which have hitherto only been treated either
   naively or with set theory.

   The last two chapters prove in detail the equivalence of types and
   categories, in particular between generalised algebraic theories and
   categories with display maps.

   Students and teachers of computing, mathematics and philosophy will
   find this book both readable and of lasting value as a reference work.

The web page currently just gives just the list of contents (down to the
names of subsections), but when I have time to work on it I intend use it
to publish many of the specific comments that people have made about the
text (if those people are willing), and provide an interface for making
further comments, and, of course, corrections.  CUP has indicated that
they have no objection to my publishing the entire text on the web in any
form short of a printable DVI or PS file; when I have found a translator
that actually works on my text, I intend to make an HTML version, obviously
without most of the mathematical formulae, to feed to the web crawlers.

			HOW BEST TO ORDER YOUR COPY

This depends on whether you would like to make a large donation to

(a) your bookstore's profits:  just quote the ISBN to them;

(b) CUP's profits: fill in their web order form (no discount, by policy,
                   and you pay cost of postage);

(c) the UK Inland Revenue:  wait until April 6 before you do anything;

(d) the author, who has committed career suicide by writing this book at all.

The special deal that I have negotiated is this.  CUP is ADAMANT that it is
contrary to their policy to give discounts for direct orders, even though
the Web is now clearly the best way of ordering research-level books.
However, by personal arrangement with my editor and the marketing manager,
if you email, fax or phone the marketing manager,
	Richard Knott,   email:  rknott@cup.cam.ac.uk
	tel:  +44 1223 325 916   fax:  +44 1223 315 052,
with your address and credit card number, mentioning that you saw this message
from me, you get the book at list price INCLUSIVE of overland postage
(normally £2.50), and I get some commission.  If you want airmail delivery,
there is an extra £2.50 charge.

If you are not sure whether you actually want to buy the book yet, but you
think you might (or might be teaching a course based on it) please email
Richard Knott and say so, as soon as possible.  If I get evidence of
respectable sales prospects then I might persuade them to pay me an advance
on royalties THIS MONTH - in the tax year during which I was unemployed
for five months - instead of having a lump sum in May 2000 taxed at 40%.

Please, this is important if you think that academic authors deserve some
reward for the labour and demoralisation of eight years writing a book.

£50 is pretty good value for a research book of this size.  A recently
announced book on similar material, published by the Dutch company
Elsevier (North-Holland) costs TWICE the price (for 1/3 more pages).
CUP, being part of Cambridge University, has no shareholders and
counts as a charity for tax purposes, and there is no VAT on books in
Britain.  Even so, other recent books of same size in the same series
as mine retail at £65. I kept the price of mine down by doing the
whole of the typographical work myself (of course), and by NOT claiming
the £2350 that I could have got for providing lower quality
camera-ready hard copy instead of PostScript.

Paul

PS Unfortunately, despite my best efforts, I was not able to negotiate
a reduction in the Bank of England's interest rates, and therefore in
the present absurdly high Sterling exchange rate. Sorry. I will try to
do better next time.


CUP's postal address is
Cambridge University Press, The Edinburgh Building,
Shaftesbury Road, Cambridge, CB2 2RU, UK.

"Practical Foundations of Mathematics"

[Paul Taylor]

Practical Foundations of Mathematics,   ISBN 0-521-63107-6 

To be published by Cambridge University Press, as number 59 in their series
Cambridge Studies in Advanced Mathematics (which includes books by Peter
Johnstone and by Jim Lambek and Phil Scott). 

Please see http://www.dcs.qmw.ac.uk/~pt/book/index.html for details.

This is the LAST CALL FOR COMMENTS.

The text is already in the hands of the copy editor for the second time.
CUP hopes to have it published in time for the International Congress
of Mathematicians in Berlin in August, which means I have to finish it
by the end of May.

I am aware that my policy of only giving away single chapters has annoyed
people a bit, but it has been successful in its objective of getting
attention for the whole book.  (The most assiduous reader of "Proofs
and Types" got to chapter 12 out of 15).  I don't intend to distribute
any more chapters now, though if I owe you a copy of the whole draft
because you sent me comments on a chapter, please ask (tearing apart
sections 1.1 and 1.2 does not count).

If you have a copy of part of the book and have noticed a mis-conception,
please SPEAK NOW OR FOREVER HOLD YOUR PEACE.   There is really no point
in telling me about missing commas in any but the most recent versions
(ie 1998) as other readers, the copy editor and I have been through
the text several times since I last distributed copies (in July 1997).

When I am rid of the book itself, I intend to set up a web site as a
repository for citations, discussion, answers to exercises  and,
inevitably, corrections.  With the permission of the people concerned,
I intend to publish some of the correspondence I have had about the book
in this way, and there will be automatic facilities for readers to add
further comments. Therefore any comments you have about the book which
are too late for publication or which are not suitable for inclusion
will not be wasted.

I would like thank Pierre Ageron, Lars Birkedal, Luca Cattani,
Michel Chaudron, Thierry Coquand, Robert Dawson, Luis Dominguez,
Peter Dybjer, Susan Eisenbach, Fabio Gadducci, Gillian Hill, Martin Hyland,
Samin Ishtiaq, Achim Jung, Stefan Kahrs, J\"urgen Koslowski, Steve Lack,
Jim Lambek, Charles Matthews, Paddy Mccrudden, James Molony,
Edmund Robinson, Pino Rosolini, Martin Sadler, Alan Sexton,
Thomas Streicher, Charles Wells, Graham White, Andrew Wilson and Todd Wilson
for taking the trouble to read parts of the draft and giving their
detailed comments on it.
(Please tell me if you think you should be on this list but aren't.)

Paul Taylor