Korner's Korner

Tom Körner's Home Page


Where do Numbers Come From?

Makes a splendid Christmas gift for young and old. The first correction has arrived before the book PDF. Sketch solutions to most of the exercises are at PDF.

Calculus for the Ambitious

the ideal present for every sixteen year old geek has hit the streets. You can read an unbiased comparison of the book with its main competitors at PDF together with some of the preliminary reviews at PDF. There is a genuine review at MAA reviews. (One online bookseller has the book classified under `Fairy Tales, Folk Tales and Myths' which seems a trifle harsh.) You can bring a smile to CUP's careworn features by buying it from their own site. There is an a rather rough and ready partial set of solutions at DVI PS PDF. A first list of corrections is available at DVI PS PDF.

Vectors, Pure and Applied

is another book that does what it says on the tin. The paperback has ISBN-9781107675223 and costs £32.99 but, of course, your library should get the hardback with ISBN-9781107033566, a snip at £75. A non-trivial correction may be found at PDF. Solutions for the exercises incorporated into the main text (not the ones at the end of each chapter) may be found at PS, DVI and PDF.

Naive Decision Making

CUP was anxious that this should not be bought by those seeking a political tract and insisted on the subtitle `Mathematics Applied to the Social World'. However, what it says on the tin is what is in the tin, and the book presents a naive, but mathematical, look at decision making. Intended for readers who have done a first course on calculus, this book is a `cat sat on the mat' first reader for future Masters of the Universe, an ideal birthday present for budding casino owners, bookmakers and card sharps and, I hope, a good read for everybody else. The paperback has ISBN-13 9780521731638 and costs £21.99 but no one who can afford it will wish to miss the privilege of owning the hardback (ISBN-13: 9780521516167) at £60. If (perish the thought) your local bookstore does not stock it, try CUP's own web site.
  • Sketch solutions for some of the exercises in Naive Decision Making PDF LATEX A list of corrections is available at PDF LATEX.

    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.

    Fourier Analysis


    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

    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.)

    Helpful guides on

    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.

    Courses close to those presently given

    Next notes on courses corresponding to past schedules which are still close enough to course presently given.

    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

    Part III courses

    Next various Part III courses.

    New! My 2010/11 Part III course Topics in Analysis in DVI PS PDF LATEX.

    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.

    Notes of little useful relation to current courses

    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.

    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.

    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.

    And Finally

    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.)

    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!

    New! 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?').

    `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.