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Category: stories

teaching mathematics

Published December 21, 2005 by lievenlb

Tracking an email address from a subscribers’ list to the local news bulletin of a tiny village somewhere in the French mountains, I ended up at the Maths department of Wellington College.

There I found the following partial explanation as to why I find it increasingly difficult to convey mathematics to students (needless to say I got my math-education in the abstract seventies…)

“Teaching Maths in 1950:

A logger sells a truckload of lumber for £ 100. His cost of production is 4/5 of the price. What is his profit?

Teaching Maths in 1960:

A logger sells a truckload of lumber for £ 100. His cost of production is 4/5 of the price, or £80. What is his profit?

Teaching Maths in 1970:

A logger exchanges a set A of lumber for a set M of money. The cardinality of set M is 100. Each element is worth one dollar. The set C the cost of production, contains 20 fewer elements than set M. What is the cardinality of the set P of profits?

Teaching Maths in 1980:

A logger sells a truckload of lumber for £ 100. His cost of production is £80 and his profit is £20. Your assignment: Underline the number 20.

Teaching Maths in 1990:

By cutting down beautiful forest trees, the logger makes £20. What do you think of this way of making a living? How did the forest birds and squirrels feel as the logger cut down the
trees? (There are no wrong answers.)

Teaching Maths in 2000:

Employer X is at loggerheads with his work force. He gives in to union pressure and awards a pay increase of 5% above inflation for the next five years.

Employer Y is at loggerheads with his work force. He refuses to negotiate and insists that salaries be governed by productivity and market forces.

Is there a third way to tackle this problem? (Yes or No).”

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two TA tales

Published December 19, 2005 by lievenlb

situation 1 :
one of the better first year students comes up to TA1’s office.
student : Um, can I ask you a question?
TA1 : Sure!

student : Well, um, about next year… will it be more of
this? … I mean, with proofs and stuff like that?
TA1 :
Heh? Well… eh… yes, I think so…
student : Oh,
in that case, I think I’m going to study something else…
situation 2 : TA2 is showing to second year (an exceptionally
good year) that $SL_2(\\mathbb{Z}_2) \\simeq S_3$. He defined the
groupmorphism, showed injectivity and surjectivity… So, we are
done! Are we? student1 : Surely that’s not enough!
TA2 : Heh?
student1 : Not every mono and epi has to be
an isomorphism.
TA2 : ???
student2 (to student1) :
But clearly it is in this case, stupid. Finite groups is a small
category! I’m not sure what story depresses me
more…

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the Oxford murders

Published October 3, 2005 by lievenlb

Set in the
spring and summer of 1993, the Oxford
Murders by Guillermo Martinez is
a crime-story about a series of murders commited in Oxford. At a certain
moment one even conjectures that the next victim will be Andrew Wiles on the eve of delivering his extra two talks at
a Cambridge seminar and that as a consequence the proof of
Fermat’s last theorem will be lost for another three
centuries… At that particular point in the book, I stopped looking
for the killer and just enjoyed the story (true or false?) of a bus
chartered by the Oxford Maths department to go to Cambridge to witness
the final two talks whereas the betting-rates were still 6 to 1
_against_ Wiles the night before. There are more hilarious
stories about a Russian PostDoc in Oxford, claiming that someone stole
his ideas on Fermat’s theorem and got a Fields Medal for it…
And so on, and so on, probably it gives a pretty accurate picture of the
life of many PostDocs travelling from one place to another to survive
(although, clearly Oxford is not just a place like any other… some
may argue). All in all, it is a rather enjoyable read. It is a
bit short (197 pages) so that there are not that many likely suspects
around to guess the two (!) outcomes way ahead. In fact, in the end I
wasn’t that much interested in the identity of the murderer but
rather in some of the side-line suicide stories. Sure, I was aware that
Taniyama and Turing commited suicide
but whereas I did know Taniyama’s method (and I notice that on the
web one is very cautious about it, so I will not give it away
here…) I never heard that Turing ate an apple laced with cyanide.
Further, I didn’t know of Taniyama’s ‘mysterious
suicide note’. So I looked it
up. It seems that he left a three page note, most of it concerned
with specifying dates when his books should be returned to the library,
indications on how far he got with certain courses and plenty of
apologies. Still, there are these mysterious sentences which some people
used to cook up a conspiracy theory

‘’Until yesterday I have had no definite
intention of killing myself. But more than a few must have noticed I
have been tired both physically and mentally. As to the cause of my
suicide, I don’t quite understand it myself, but it is not the
result of a particular incident, nor of a specific matter. Merely may I
say, I am in the frame of mind that I lost confidence in my future.
There may be some to whom my suicide will be troubling or a blow to a
certain degree. I sincerely hope that this incident will cast no dark
shadow over the future of that person. At any rate I cannot deny that
this is a kind of betrayal, but please excuse it as my last act in my
own way, as I have been doing all my
life.\’’

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Mappalujo

Published September 29, 2005 by lievenlb

Together with
Steve Beard, Jeff Noon devised the writing game Mappalujo. The set of rules can be
made applicable (with minor changes) to other situations such as :
writing a mathematical paper or book with a co-author, an idea for a
group-blog or it might be fun to run a seminar with two lecturers
following this idea. All one needs is a good choice of ghosts, perhaps
adding some order structure on them… Needless to say that
mappalujo is (via mamalujo) another tribute to Joyce. Back in the old
UIA-days we shared a building and more importantly a library with the
languages departments. There were times that I took out more Dutch and
English novels and Buffalo
Notebooks than math-books. I’m happy to see that one of my
favourite books The Sigla of Finnegans Wake by McHugh is
now available online. If you ever wondered where my fascination for
strange notation comes from have a look here and if
you want to know more about Mamalujo, read the relevant chapter.

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sudoku mania (bis)

Published September 27, 2005 by lievenlb

Situation : my first class this year, about 20
fresh(wo)men, their second class this year.

Me : Okay, who
did some mathematics this vacation?

(No response
obviously, even if they did, it’s not a cool thing to
admit…)

Me : Sure, let me rephrase the question :
who thought about solving a puzzle or played a strategic game this
vacation?

(No response, or… is there?….. a
timid question :

‘Does Sudoku
count????’

Me : Well, not really but okay
let’s rephrase the question : Who solved at least 1 Sudoku this
vacation?

IMMEDIATE RESPONSE : about three quarters of all
students waving their arms!

Me :
Oof…….Oh…….Yes??? (to an even more timid
student raising his arm)

‘Does doing half a Sudoku
also counts?’

It’s going to be a tough
semester…

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nymphomation

Published September 26, 2005 by lievenlb

If you prefer Neal Stephenson’s Snow crash to his bestseller Cryptonomicon you may have a fun time reading through Jeff Noon’s Nymphomation.

In a
‘parallel’ 1999’s Manchester, blurbflies (blurb stands for Bio-logical-Ultra-Robotic-Broadcasting-System) fill the air chanting their slogans, especially for _DominoBones_, the new lottery game which is on a year trial run in Manchester before going National.

A group of mathematics students are searching for the hidden mysteries behind the game. Their promotor is Prof. Max(imus) Hackle who has written a series of psychedelic sixties papers in a `journal’ called _Number Gumbo: A Mathemagical Grimoire_ with titles like “The No-Win Labyrinth: A solution to any such Hackle maze”, “Maze Dynamics and DNA Codings, a special theory of
Nymphomation” and “Fourth-Dimensional Orgasms and the Casanova Effect.”

He is also keen on using fun-terminology defining processes happening in the ‘Hackle maze’ and as such is a bit like John Conway. In fact, Conway’s Game of Life is a lot like Hackle’s maze.

There is some statistics and game theory in the book but the plot and ending are that of a good Postcyberpunk
novel, that is rather chaotic depending on possible future technological advances rather than the logical and unescapable ending of a good whodunnit.

After reading Nymphomation, a fly or a game of dominoes will never seem quite the same again.

Another nice feature are the non-sensical beginning sentences of every ‘chapter’. To some they seem like the rantings of a mad mathematician. To me they sound like a tribute to Finnegan’s Wake…

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fall again

Published September 20, 2005 by lievenlb

When the leaves start falling, so does the plane Jacobian conjecture,
or so it seems. The comparison is a bit weak in this case as two of the
authors of the preprint posted today at the arXiv A Proof of the Plane
Jacobian Conjecture are based in Sydney, Australia… A
first glance through the paper shows that it uses Newton-polygons and
the 1975 Abyankar-Moh result on
embeddings of the line in the plane. Techniques that have been tried
before by numerous people in their attempts to tackle the plane Jacobian
conjecture (the reference to Dean in this wikipedia entry is
outdated, as mentioned in an old blog
entry). Still, the paper just might be correct. As there
are several editors chasing me for overdue referee reports I have no
time to go through the proof in detail, but if you hear more on this
paper or have the energy to go through it, please leave a comment.

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work in progress

Published August 22, 2005 by lievenlb

The third volume in the NeverEndingBooks-series will be written by Geert Van de Weyer and will
be about (double) Poisson structures in the noncommutative world. Volume
4&5 are becoming clearer every day and if you think you have a
project fitting in this series, you can always email to
[info@neverenedingbooks.org][3].

As for the NeverEndingBooks-URL, I will
probably close this blog by the end of the month (at its first
birthday). The main reason is that I found out that it takes several
people to maintain a mathematical blog for some time. So, if you want to
co-author a group-blog on noncommutative algebra and/or noncommutative
geometry, please [email me][5] (or even better, leave a comment here so
that other people may be willing to join in too) and if there is enough
critical mass to go ahead with the plan I will be happy to set up a
group-blog at noncommutative.org.

At
this URL I’ll probably put a frontpage for the book-series we started
and which you can buy at all times via lulu.com/neverendingbooks. It will contain errata- and suggestions-pages for each volume and
details about forthcoming books, links etc… Btw. it would probably
be a good commercial move to delete TheLibrary links sooner, now that
even String Theorists are driven to this site via
Lazariou’s paper On
the non-commutative geometry of topological D-branes

As my
main objective next year will be to write courses (from first year down
to post-doc level) I will set up (again) a Moodle site (mainly in English,
although UA-students will be free to add to it in Dutch). News about it
will be posted eventually at my regular, but forgotten
homepage and perhaps here.

Once again, if you are interested
to contribute at unregular intervals to a noncommutative group-blog,
please leave a comment!

[3]: mailto: info@neverendingbooks.org
[5]: mailto: lieven.lebruyn@ua.ac.be

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publish

Published July 27, 2005 by lievenlb

A quick reply to some of the comments
to the lulu/neverendingbooks post.

_Are they also
responsible for the graphical design in your books ?_ No! In fact it
was one of the more pleasant experiences of the last couple of weeks to
develop our own format, LaTeX-style and covers. The usual gang had their
say in all of this but it is only fair to say that Jan did most of the work. We developed
the cover-concept (that is, macro shots of games in duotones and placing
of titles etc) by trial and error. Jan is responsible for the
photo-shoot, I did choose the shots to be used and did the initial
coloring and placing of titles and left the final tweaking to Jan, who
did some lay-out work before. We, at least, are happy with the
result… As mentioned before, the LaTeX-style sheets were made
using the
memoir package.

_Who is responsible for trying to sell
the book, you or them?_ I dont think we are doing great efforts to
try to sell the books, yet. Up to now, you can only get to the
book-sites via this blog or via my homepage. Lulu claims that they will only make
money if we do… and as this is clearly sales-talk (they make money
on every book they print) it involves no (or a very small) financial
risk on our part. Anyone who wants to have a copy of one of our books,
orders them at Lulu, they print it and ship it to you. But beware! They
have several shipping options and for most of them it costs you more to
get them shipped than to buy the books… In fact, that was the main
reason why we didnt put the URL online before we had two volumes out.
The reason being that if you buy for over 25dollars you can have them
shipped via their “SuperSaver” option, that is, shipping is free (but
probably slow). But, based on my own experience it works well (I ordered
a few copies of book 1 via SuperSaver and another one via their
InternationalShipment and got the free SuperSaver package a day before
the costly other shipment…). Our real investment is that we have
bought ISBN-numbers for the books (at a price of 35dollars/book) and
hope to earn this back from a small royalty we get from each book (the
Lulu-rule is that they get 25% of any royalties you set). Even though we
are not entirely happy with the distribution process we opted for this
series for an unusual book-format making it handy and fun to use (the
square 7.5 x 7.5 inch format is very pleasing to read and the
coil-binding makes it extremely handy to lay flat on the table). So we
view this series as a student-edition of the books and we keep them as
cheap as possible. At a later stage it may happen that we will also have
a library-edition of the books which will have global distribution
(meaning that you can order them via Amazon or your local bookshop). For
this to work, you have not so much freedom in your book-format and can
only have regular binding. Besides, buying such a global-ISBN is more
costly and will make this edition (a lot) more expensive. But, as you
can see from the picture, the books get printed and shipped and look
VERY nice. In fact, of the few copies I ordered, I had to hand out
already two because some people just liked the feel and touch of it. I
think, people will only gradually be willing to buy their own copy when
(1) they have glanced through a copy at some meeting or seminar and (2)
if more volumes come out and they have a greater choice in bying 2
volumes to get free shipping. On this last issue : already three people
have expressed interest in writing a book in our series. My own hunch is
that the next book out will have to do with Poisson noncommutative
geometry and will have a macro shot of a war-game on its cover (authors
can give suggestions for which games they want on their cover), curious
how this will work out…

_How many have you sold so
far?_ Well, not enough so far to get our ISBN-investment back…
But, once again, I think it will take some time for people to trust the
series enough to buy a volume or two. In the first week we made the URL
available we sold 16 books, so if you want to increase our sales-index
please do by going to this
page for the first volume and to this page for the second
volume. But perhaps it is easier to bookmark the lulu/neverendingbooks if
you want the latest news on the series. I”ll keep you posted on our
sales via this page. If you buy a book and like the result, please tell
others about it (or even better, let them see and feel the copy.
Hopefully you will get it back…)

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sudoku mania

Published June 26, 2005 by lievenlb


I never pay
much attention to the crossword-puzzle page of our regular newspaper DeMorgen. I did notice that they
started a new sort of puzzle a few weeks ago but figured it had to be
some bingo-like stupidity. It wasn’t until last friday that I had a
look at the simple set of rules and I was immediately addicted (as I am
mostly when the rules are simple enough!). One is given a 9×9 grid
filled with numbers from 1 to 9. You have to fill in the full grid
making sure that each number appears just once on each _horizontal
line_, on each _vertical line_ and in each
of the indicated 3×3 subgrids!

It is amazing how quickly one learns
the basic tricks to solve such _sudoku_s. At first, one plays by
the horizontal-vertical rule trying to find forbidden positions for
certain numbers but rapidly one fails to make more progress. Then, it
takes a while before you realize that the empty squares on a given line
in a 3×3 subgrid cannot be filled with any of the numbers already
present in the 3×3 subgrid. Easy enough, but it takes your
sudoku-experience to the next level. Anther simple trick I found useful
it to keep track how many times (from 0 to 9) you have already filled
out a given number. If it is 9, you may as well forget about this number
for elimination purposes and if it is 0 it will be hard to use it.
Optimal numbers to use are those that are already 4 to 6 times on the
board. And so on, and so on.

After having traced all back-copies
of the newspaper I ran out of sudokus but fortunately there is a
neverending (sic!) supply of them on the web. For example, try out the
archive of Daily
Sudoku, and there are plenty of similar sites as, no doubt, you’ll
find by Googling.

An intruiging fact I learned from my newspaper
is that there are exactly 6,670,903,752,021,072,936,960 different
filled-out Sudoku grids. You then think : this should be easy enough to
prove using some simple combi- and factorials until you give this number
to Mathematica to factor it and find that it is

$2^{20} \\times
3^{8} \\times 5 \\times 7 \\times 27704267971$

and hence has a
pretty big unexplained prime factor! This fact needed clarification, so
a little bit later I found this Sodoku
players forum page and shortly afterwards an excellent (really
excellent) Wikipedia on
Sudoku. There is enough material on that page to keep you interested
for a while (e.g. the fact that nxn sudoku is NP-complete).

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