Author: harry

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Mathematics

I’m doing a Mathematics degree with the Open University and I am in my first two of the 4 required level 3 subjects.
I have not really had as much time as I would like to devote to Maths, so, for the most part, I have been reading the material and finishing the course work with as little paper and pen as possible. This system of doing things was working fine up until a few weeks ago when I started to run into trouble with M381 (Number Theory and Mathematical Logic).
The questions in this course have demanded a rigour that has not really been set out in previous courses. When asked “Prove the Following” I was completely baffled and had no idea where to start. This might sound odd for those people who are up to speed with their Math but for me it was an eye opener. For those maths teachers out there you may recognise that I have become a calculator and not a thinker (my own fault) which is fine for doing sums but pretty useless for real Mathematics.
Anyway. Not to be outdone I decided that the only way to get up to speed was to subject myself to more Maths, specifically, more thinking about Maths. I went looking for a text that would have the rigour I was looking for and having searched high and low one text that seemed to appeal was A Course of Pure Mathematics by G. H Hardy
I have been trying to get to grips with this book over the last few weeks and so far I have made the following observations.
The book states in the preface:

This book has been designed primarily for the use of first year students at the Universities whose abilities reach or approach something like what is usually described as “Scholarship Standard”

I am “meant” to be covering 3rd year level material in my degree and a lot of the material in this book appears new to me. This begs the question[s].

  • Have I forgot what I learned previously?
  • Have I not understood the material in previous courses?
  • Has the standard slipped since Hardy’s time?

There are more questions I could ask but these questions alone scared me into checking Google groups for more information and I found the following article on Littlewood which made me think that perhaps the required standard was higher in those days.
Having thought about this for a while I decided that “standards being higher” was a weak excuse at best, and that I should really not be casting historical aspersions when I’m hardly capable of judging a decent book from a bad one due to my lack of mathematical maturity. This left me in a bit of a dilemma.

  • I want to get better at Maths.
  • I have only so many hours in the day (I have bills to pay).
  • I need to teach myself.

The criteria above mean I need to pick an area of mathematics in which I will continually find myself in, regardless of what maths I am doing. From what I could gather there are a few areas that seem to crop up all over the place. Two of these subjects are Calculus and Analysis (I know they are similar subjects), they seem to find their way into everything to some degree or another.
To this end I have decide to spend some of my spare time doing problems from calculus and analysis books. I have also bought Polya’s “How to solve it and am about half way through it” and so far it has been an interesting read.
I have ordered Spivaks Calculus book. I would also like a few other books to read around the area a bit. Again the source I went to for information on this was sci.math. The books I intend to investigate are as follows.

  • Calculus: T. M. Apostol
  • Calculus: Spivak (on order)
  • Calculus Answer book: Spivak (Answer book) (on order)
  • Introduction to Calculus: Courant, John
  • Mathematical Analysis: T. M. Apostol
  • Real Anlysis: Royden
  • Principles of Mathematical Analysis: Rudin (Baby)

I don’t intend to purchase all of the above books although it would be nice to have them. The above list seems to be the most popular recommendations on sci.math (particularly Spivak, it has an answer book so I ordered it). I intend to have a look at each of them and decide which ones would be best suited for me.
I have also heard good things about:
What is Mathematics: Courant Robbins Stewart
which I have been meaning to buy for a long time. Current books I own are:

  • A Course of Pure Mathematics: Hardy
  • Differential and Integral Calculus: Courant Vol 1 (Old Blackie edition).
  • Calculus Made Easy: Silvanus P Thompson and Martin Gardner
  • An Introduction To the Theory of Numbers: Niven and Zuckerman
  • An Introduction To the Theory of Numbers: Hardy and Wright
  • Fundamentals of Number Theory: William J. LeVeque
  • Advanced Mathematics (A pure Course): Perkins and Perkins
  • Engineering Mathematics: K. A. Stroud 4th Ed
  • How to solve it: Polya
  • Fermats Lat Theorem: Simon Singh
  • A concise History of Mathematics: Dirk J. Struik
  • Introductory Logic and Sets for Computer Scientists: Nimal Nissanke
  • A History of Mthematics: Victor J. Katz
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Why blog

When asked why he wanted to climb Mount Everest the climber George Mallory answered,

Because its there

This was a fantastic answer and I wish I had an original one liner to answer the original question. My paltry answer is:
I blog because I blog.

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Google Premium Adsense

I currently use Google Adsense and was wondering just how many hits a second I would need to be receiving in order to apply for their Premium service
You need to be getting 10 million content views per month. This is not the same as hits because images, spider hits etc don’t count.
Last month I got approximately 1020358 hits which sounds impressive but it isn’t that great because this only got me 102,636 content views on google adsense as per their own stats. So approximately every ten hits I get 1 content view.
Using some advanced mathematics based on our very accurate assumptions 😉 This means I need approximately 100 million hits a month to achieve 10 million content views. This is of course pie in the sky.
This is about 40 hits per second. I doubt very much if my little sever would be able to withstand that kind of usage 😉 I suppose if I was getting that many hits per month then I would be able to afford a whole rack full of equipment.

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Emotive entries

Is it just me or do more emotional entries on blogs get more hits. The reason I ask this is due to an entry I made just recently.
I’ve had more comments on that one topic than any other. In fact, its been the most popular topic on my blog for a couple of months. Admitedly this is not a huge achievment but I have found the more controversial or emotional the entry the more comments it seems to collect.

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FT Search Engine Spam

Just noticed the following on Jeremy Zawodny’s blog. This is a pretty shit way to make money.
Basically moneysupermarket.com have paid the Financial Times (FT) to add some hidden links to their website. Of course when Google finds the link it will assign a hefty amount of PageRank to the page that’s linked to (FT has a PageRank of 8). I wonder how much the ask for this type of service.
Google’s Quality Guidelines specifically states:

Quality Guidelines – Specific recommendations:
* Avoid hidden text or hidden links.

I wonder what the penalty is (if any) for this sort of search engine spam. I don’t do it for fear of loosing what little Ranking I have with Google. I suppose I could report them but I doubt anything would be done to the FT.

Original Story

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Upgrading Woody to Sarge

Debian have just released sarge as the new stable distribution which means I need to start upgrading my machines. Before I upgraded the main machine though I decided to run through it on a UML machine first to see where the gotchas are.
Things to watch out for
1. The sshd config file gets an extra parameter added to it ie.
UsePAM yes
When I tested ssh after the upgrade I was unable to log into the machine and I found that I had to remove this option or set it to “no” to get ssh to work. This surprised me because I was not expecting Debian to modify config file without my knowledge.
2. The RECORD option is no longer valid
xinetd[5691]: Bad log_on_failure flag: RECORD [file=/etc/xinetd.conf] [line=13]
xinetd[5691]: A fatal error was encountered while parsing the default section. xinetd will exit.
xinetd[5691]: Exiting…
this prevents xinetd from starting up. This was also noticed while testing the machine after the upgrade.
What follows is roughly the files the upgrade offered to update to new versions. Since I had modified most of these I selected the default option which is “N” ie do not upgrade to the maintainers version. This may have been the reason the ssh upgrade wasn’t too smooth. However I would not recommend taking the maintainers version if you have customized the files.
Configuration file `/etc/pam.d/login’
Configuration file `/etc/securetty’
Configuration file `/etc/pam.d/passwd’
Configuration file `/etc/bash.bashrc’
Configuration file `/etc/init.d/sysklogd’
Configuration file `/etc/services’
Configuration file `/etc/init.d/bind9′
Configuration file `/etc/bind/named.conf’
Configuration file `/etc/bind/db.root’
Configuration file `/etc/init.d/xinetd’
Configuration file `/etc/xinetd.conf’
During the upgrade you may also be asked to add any users and groups that are
missing from the default debian lot. The following bits are just the output of some other configurations options and warnings of things that have changed between the woody and sarge.
Configuring ssh
Environment options on keys have been deprecated This version of OpenSSH
disables the environment option for public keys by default, in order to avoid
certain attacks (for example, LD_PRELOAD). If you are using this option in an
authorized_keys file, beware that the keys in question will no longer work
until the option is removed. To re-enable this option, set
“PermitUserEnvironment yes” in /etc/ssh/sshd_config after the upgrade is
complete, taking note of the warning in the sshd_config(5) manual page.

Configuring man-db
This version of man-db is incompatible with your existing database of manual
page descriptions, so that database needs to be x rebuilt. This may take some
time, depending on how many pages you have installed; it will happen in the
background, possibly slowing down the installation of other packages. If you do
not build the database now, it will be built the next time
/etc/cron.weekly/mandb runs, or you can do it yourself using ‘mandb -c’ as user
‘man’. In the meantime, the ‘whatis’ and ‘apropos’ commands will not be able to
display any output. Incompatible changes like this should happen rarely. Should
mandb build its database now?

So far I have upgraded two machines and had the same trouble with ssh and xinetd both times. If I encounter any mmore trouble I will add more here.

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Blogs SpamAssassin and Trackbacks

I disabled the trackback facility on my blog months ago because I was getting a lot of trackback spam. Around the same time I wrote a SpamAssassin Plugin for Movable Type. I effectively took MT-Blacklists regex database and converted into a form compatible for SpamAssassin and then wrote the plugin. Of course at the time I had disabled trackbacks so I only wrote it to handle comments and it has been going a great job because I get virtually zero blog spam now that the database is trained.
Of course now that I have turned on the trackback facility again I now have trackback spam to deal with. Of course this time I am not going to forget about it so await an update and I will release anther version that will handle trackbacks as well.
As promised this is the extended entry. I have now just added trackbacks to the spamassassin plugin. It was easier than I thought. It took 2 hours to finish it, now all I need is someone to test it. As soon as I have packaged it up into a tar ball I will release it.

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df reports wrong size

I had a weird problem the other day when I seemed to be getting inconsistencies between du and df. The two command where in disagreement about what the disk usage was on my box.
thing:/# du -hax –max-depth=1 /
104M total
thing:/# df -h
Filesystem Size Used Avail Use% Mounted on
/dev/sda2 3.7G 3.4G 118M 97% /
The first thing I thought was that there was a corruption on the partition table or some other terrible bug. I asked around and got no answers so I went Googling. I came up with nothing although there seemed to be plenty of people with a similar problem.
It then dawned on me what I might have done. I had originally created the Postgres database under /var/lib/postgres under the root file system. As this database got bigger and bigger I had to move it onto its own file system and mount it there. What I had forgot to do was remove the files from the root filesystem after I had confirmed the move was successful. This meant that 2.4Gb of disk space had not been freed on the root file system. Of course when you use du it only adds up the sizes of the files it sees whereas df reports the device usage. So there where no bugs in this case just simple human error.
thingthong:/home/harry# df -h
Filesystem Size Used Avail Use% Mounted on
/dev/sda2 3.7G 1.1G 2.6G 31% /