A Companion to Analysis
I am very grateful to the splendid folks at the AMS for publishing A COMPANION TO ANALYSIS which may be ordered from the AMS bookstore or, we hope, your local bookshop for a mere $87 (even less if you are an AMS member). There is a collection of sketched answers to some of the exercises in Appendix K of the book at PS, DVI and PDF. A first list of corrections is given in PS, DVI and PDF. Eurospan distribute the book in the UK and Europe.
The Pleasures of Counting
Next let me remind you that The Pleasures of Counting is still available from all good bookshops. Longer than `With Rod and Line Through the Gobi Desert', funnier than `The Wit and Wisdom of the German General Staff' and with more formulae than `A Brief History of Time' it was voted Book of the Year by a panel consisting of Mrs E. Körner, Mrs W. Körner, Miss K. Körner and Dr A. Altman (née Körner). The paperback has ISBN 0 521 56823 4 and costs £46. The hardback (ISBN 0 521 56078 X) is still available at £70. If your local bookseller has failed to lay in sufficient stocks or you wish to participate in the information revolution you may order directly from CUP via CUP's gleaming modern web site.
If you wish to read it in German then Michael Basler has produced a splendid translation under the title "Mathematisches Denken. Vom Vergnügen am Umgang mit Zahlen" (ISBN 3-7643-5833-5). (There is a list of corrections contributed by Stephan Stiller here.)
Those who feel that the book would make just about the same sense if written in Chinese now have the oportunity to verify their conjecture. PDF.
Corrections and additions for first reprint of `PLEASURES OF COUNTING': DVI PS PDF LATEX and ordinary html.)
Corrections and additions not in first reprint of `PLEASURES OF COUNTING':
DVI
PS
PDF
LATEX.
Mathematika says `A cracking good tale; buy it for
your children and read it yourself.'
Zentralblatt says `politisch überkorrekt'.
Mathematics Magazine says `None of "introvert", "extrovert",
nor "anchor" appears [in the index.]'
Computer Shopper says `a real gem of a book'
The Australian's Review of Books says `[a] generous bouquet
.... [but] don't think ikebana here'
Notices of the AMS says `Make sure to recommend it to your
local high school library. If they are slow to purchase it,
then donate a copy.'
The last quotation is from one
of two long reviews accessible via
AMS Book (and other) Reviews.
On 23rd Nov 1998 `The Pleasures of Counting' was ranked
number two on the Amazon list
of most popular books on counting
and numeration beating
`The M&M's Brand Chocolate Candies Counting Book'
into third place.
I have produced a rather simple
Pleasures of Counting home page.
However, the main purpose of this home page
is to give access to the most
recent version of various collections of
well meant advice that I have produced.
The documents are available in dvi, ps, pdf and latex form.
(pdf documents can be read using
acrobat.)
Notes for the Part II course on Codes and Cryptography
in
DVI
PS
PDF
LATEX.
(There is a log of corrections in
DVI
PS
PDF
LATEX.)
Notes for the Part II course Linear Analysis in
DVI
PS
PDF
LATEX.
Notes for the Part II course Topics in Analysis. (Note that
the lecturer has more flexibility in this course than in most,
so topics may vary from year to year.)
This year's note are available in two documents.
The first contains the statements of the results
(together with the suggested exercises for supervisions)
as
PDF
LATEX,
and the second containing proofs of the results
(intended for home use as the lecturer may not keep
exactly to these proofs in the lectures) as
PDF
LATEX.
There is log of corrections (starting 12th August 2022) at
PDF
Notes for the 1B 'Topology and Metric Spaces' course.
DVI
PS
PDF
LATEX.
My Part 1A Analysis notes
in
DVI
PS
PDF
LATEX.
My Part 1A second half of the old course
Algebra and Geometry (fairly close to the new course 1A Groups) in
DVI
PS
PDF
PS
PDF
LATEX.
My Part 1B Complex Methods (P3) notes
in
DVI
PS
PDF
LATEX.
(There are now new complex variable courses with different
selections of material.)
My Part 1B Analysis (C9) notes
in
DVI
PS
PDF
LATEX.
These notes have been extended by Richard Johnson to include proofs
in
LATEX
PDF.
(Note that the analysis syllabuses have been rewritten since these
C9 notes were written).
My rather old Linear Mathematics notes
(WARNING the new syllabus contains substantially more.)
DVI
PS
PDF
LATEX
Next various Part III courses.
Notes for my Part III Topics in Fourier Analysis and
Complex Variable course (2009/10) in
DVI
PS
PDF
LATEX,
Notes for my Part III Functional Analysis
course.
in
DVI
PS
PDF
LATEX,
Notes for my Part III Topological Groups
course (note that the last part follows Rudin's book very closely)
in
DVI
PS
PDF
LATEX,
Notes for my 2012/13 Part III Fourier Analysis
course
in
DVI
PS
PDF
LATEX.
Notes for my Part III Complex Variable course in
DVI
PS
PDF
LATEX,
Please note that my Part III notes are particularly error prone.
My IIB course on Partial Differential Equations
(based very closely on notes by Joshi and Wassermann)
in
DVI
PS
PDF
LATEX.
(The course has now been completely rewritten.)
Notes on a course on a no longer existent
Rings and Modules in
DVI
PS
PDF
LATEX.
Notes on a no longer existent Calculus and Methods course in
DVI
PS
PDF
LATEX.
Skeleton notes
for an introductory course in Fourier Analysis
given at the 2003 PCMI conference in
DVI
PS
PDF
LATEX.
Solutions for some of the exercises for this course
kindly contributed by Mihai Stoiciu
DVI
PS
PDF
LATEX.
Caveat emptor, these notes come without guarantees of any kind.
All contain misprints and some (particularly the Part III notes)
much worse things.
Corrections are gratefully received.
If you have any problems obtaining these documents
write to me at
DPMMS, Wilberforce Road, Cambridge CB3 0WB
and I will send whichever one you want by classical means.
(Because of the interaction between my computer illiteracy
and the constant modernisation of our computer facilities
weird things occasionally happen. Please e-mail me
if they do.)
I would be happy to receive comments and suggestions for improvements.
I am particularly anxious for suggestions of possible sources of funding
for Part III students.
You can e-mail me by pressing
SCHAZAM! or if that does not
work by using the address twk@dpmms.cam.ac.uk. My favourite
e-mail ends with the words `this message needs no reply'.
You may wish to go to the
Faculty of Mathematics home page.
The guide to the University issued by the Administration
begins by saying that the heart of the University
`is a central administration team'. Later the guide
informs us
that the title of emeritus is a title applied
`to a .... Professor ... who has retired after the age of sixty.
... the term is not conferred as a ... mark of distinction.'
I am an emeritus professor.
I am also an emeritus fellow of
Trinity Hall, but
this position carries real advantages (to wit, access to good food
and good company). During my time there I was fortunate to work
with Tadashi Tokieda.
Those of a romantic disposition are directed to
A Valentine from Möbius.
If you would like a statement of the college's admission policy
for mathematics undergraduates, press
here. (Of course colleges are always fiddling with their web pages
so, if this does not work, google Trinity Hall and start from there.)
`There is no limit to what people will believe if they see it on the
internet' Alan Turing 1936.
Friends of the counterexample will be delighted to hear that
the OED has at last yielded to popular demand and accepted
it into the English language.
Fourier Analysis
and Exercises in Fourier Analysis
These ever popular works are still available from CUP.
First read Fourier Analysis (ISBN-13: 9780521389914,
cost £51) and then work through
Exercises in Fourier Analysis (ISBN13: 9780521438490,
cost £33.99). If you prefer your books in Japanese,
there is a translation of Fourier Analysis
by Yoichiro Takahashi.
Helpful Guides and Sundries
Helpful guides on
Great musical moments
Next notes on courses presently given in the Tripos.
Course Notes
Courses presently given in the Tripos
Courses close to those presently given
Next notes on courses corresponding to past schedules
which are still close enough to course presently given.
Part III courses
My 2010/11 Part III course Topics in Analysis in
DVI
PS
PDF
LATEX.
Notes of little useful relation to current courses
Notes describing my own work
These notes give the background to and proofs of most of the results
I obtained in the last few years of my career.
DVI
PS
PDF
LATEX.
And Finally
You have read the book and studied the pamphlets BUT NOW
in glowing LMScolour you can watch the film (video actually).
In response to overwhelming lack of demand the video
of my lecture
`Marrying, Voting, Choosing' is now available for the
price of £10 including postage and packing (a reader writes
`Worth it for the postage and packing alone')
from the LMS, De Morgan House, 57-58 Russell Square, London
WC1B 4HP. Be the first person on your street to have
your own copy!
Or, if you are one of those who wants everything to be free
you can go to
Gresham College
and watch me pontificating on `Mathematics and Smallpox'
(a reviewer writes `Mathematics and Smallpox, what's not to like?').
