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> Maths teaching

Holy wars, every profession has them

2008-04-30 12:46:00

Whenever two or more parties are convinced that they're on the side of absolute right holy wars pop up. I'm not just talking about the religious conflicts that we see every day, but also professional debates that are verging on religion.

Windows versus Linux versus Mac OS X. Emacs versus Vi versus Pico. Sendmail versus just about any decent email server. Japanese cars versus American cars versus European cars. Ketchup-on-your-steak versus Ketchup-lovers-should-die. Whatever, there's too much to even think of!

The field of education unfortunately is no different. Many people think that they know what's best for today's kids and thus philosophies about teaching vary greatly! For example, in December I wrote about the Het nieuwe leren versus Het oude leren crowds. The first think that the folks over at BON are decrepit relics from a time better forgotten. The latter think that the HNL crowd are nonsensical managers lusting for new and shiny toys. And neither side is willing to give in one inch, or to even concede that the other side has at least -some- merit.

Great.

One of the stories that's been recently snapped up by the BON-folks, is the story of Jan Verhoeven's family and their experiences with De Nieuwste School in Tilburg (The Newest School). While the Verhoevens are actually quite content in their role as chroniclers, the two battling sides grasp any chance to duke it out. The BON-ers ragged on the school on their fora, in their usual fashion. At the same time the DNS-folks grasp at any chance to portray themselves in an overly positive fashion, by grabbing media attention and by spawn camping the relevant Wikipedia pages. So instead of working on a real solution, both sides are just too fscking concerned with their little battles.

Very productive, que no?

Me, I'm just glad that the Verhoevens are alright and that their daughter's happy at her new school after getting out of De Nieuwste School


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Researching ancient mathematics

2008-04-20 14:16:00

Part of the 1482 print of Euclid's work.

This semester I'm taking the second year's course Geschiedenis 2 Vakgedeelte, which can be translated as History of math 2. Over the next two months we'll be taking a look at math through the ages, starting with the Egyptians and Babylonians.

As part of this course, each student is expected to write a short biography on one of the Great Mathematicians (tm). I was assigned Euclid (Euclides in dutch), which seems to be a very interesting topic. So far I've done some six hours of research and I've gotten a pretty good picture so far.

During my research I've run into some very cool things! Things that may be of interest to a lot of people :)

For instance, there's Rare Book Room.org. This website has gathered thousands and thousands of photographs of antique books. They've created a huge archive, so that mere mortals such as you and I can leaf through tomes that are normally in musea.

A 1482 print of Elements, by Euclid.

A 1613 print of Istoria e Dimostrazioni Intorno Alle Macchie Solar, by Galileo Galilei.

Another neat project is Euclid's elements of geometry by Richard Fitzpatrick. Mr Fitzpatrick has taken the 1883 Heiberg translation and used it to make a completely fresh english translation of Elements (Euclid's most famous work). You can download the book for free as a .PDF at the link provided, or you can fork over $28 to buy the hardcover print from Lulu.com. I'd say the print is definitely worth it! I've just ordered my copy, to support Mr Fitzpatrick's work.


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Oral defense of this semester's project

2008-04-09 11:05:00

Last monday my project team had its appointment for our oral defense of our essays. This was the first time we've had to do such a thing, since most docent's are happy just reading through our papers. In this case however, the teacher wanted to prod our minds a little about some additional questions.

We came well prepared, as each of us had researched the questions we'd been given. In my case, the teach wanted to know about two things:

1. How would you go about planning a big workload for a depressed child, say for example his final exams?

2. What needs to be done if a depressed child becomes the victim of harassment by his peers?

Our defense went very well, with each of us answering all the questions to the teach's satisfaction. We actually had a good time and there was no stress at all :) In the end we were told that we could count on a 90%, assuming he didn't find any flaws in our final process reports. Nice!

I have to say that the docent did come off quite wishy-washy. We'd told him that our fifth group member had quit school no less than three times and he was still surprised when there was noone to answer the questions about the guy's report in depth. Uhm yeah, we told you? He left? Which also explains why he was about to completely skip my part of the interview, since he thought I was the guy who left. Scatterbrained much? :/ Jeez!...


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Our kids don't need to learn fractions

2008-02-02 08:41:00

Or apparently that's what prof. DeTurck of Penssylvania-U thinks.

DeTurck does not want to abolish the teaching of fractions and long division altogether. He believes fractions are important for high-level mathematics and scientific research. But it could be that the study of fractions should be delayed until it can be understood, perhaps after a student learns calculus, he said. Long division has its uses, too, but maybe it doesn't need to be taught as intensely.

From:

USA Today

and

Good math, bad math

Of course, like many others I believe this notion to be nuts. Decimals have no meaning unless you know what fractions are. It'll be like handing a bunch of powertools to a carpenters apprentice and asking him to build a house. Oh, you don't need to know what everything does, just get to work...

As a future maths teacher I'm scared by this idea. And it's not just limited to the US. A dutch prof by the name of Kees Hoogland shares DeTurck's opinion that kids should be learning less longhand maths and should instead be focusing on using the calculator. Why? Because they'd be stupid not to use the modern materials at their disposal. *sigh*

I've started a forum discussion about this, over at Ars. Obviously, it's gotten some pissed off responses ^_^

EDIT:

In response to my thread over at Ars, GwT has started a new thread asking how important math is in general.


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A different kind of hacking

2007-11-25 22:40:00

You know? This whole college deal, burning the midnight oil over homework, feels like hacking to me. It gives me the same feeling I had during my internships or during late-night projects at the office. A feeling that I'm completely into what I do and that I want to keep on going.

Case in point: tonight I'm working on a report for Analysis 1 - Didactics, scratching away at my whiteboard. And of course I turn to the music I always play at times like these.

If you're curious, the song's Funky doll from the original Bubblegum Crisis soundtrack.

It's awfully eighties, but there's something I just love about that song. Of course, I'm also glad there was no video camera there to register my gay-ass dancing at the board. There's just something weird about a geek dancing, while working ^_^;


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Ouch, Analysis-1 is going to be a toughy

2007-11-17 11:55:00

Careful now, this may sting a little... o_O

This semester we're covering Analysis 1, which requires a wholly new way of thinking. Where Statistics 1 was pure maths and calculation, this course requires something additional: insight and a sense of logic.

The thing about this course is that it's all about proving maths. Not using maths to prove stuff, but proving the mathematic equations themselves.

Folks who aren't too hot on math may want to skip the next section :D

==========

For example, the calculation show is above belongs to the question "Prove or disprove that (k^2 -1) is divisible by eight, for all values of K that are integers and odd". "Odd" in this case is opposed to "even".

So, how do you even get started on such a question?! Well, you start filing in bits and pieces, starting out by equating k to (2n + 1). Why? Because one can make -any- odd number by taking integer n, multiplying it by 2 (thus becoming an even number) and then adding 1.

Once all of that is done we're left with 4(n^2 + n). In order for the original theory to be right, this'd mean that any value of (n^2 + n) needs to be even. And that's what I'm testing in the second and third lines: first for even numbers, then for odd numbers. And indeed, both tests come out positive: any value for n will result in an even number.

Pulling this back to the original theory means that any outcome is indeed divisible by eight, because four times any even number is always divisible by eight.

==========

Joy!... I've always sucked at being insightful, so a lot of these "tricks" don't come natural to me. Then again, I used to get good grades for math and even for stuff like this. I ought to be able to get the hang of it again.

I hope ^_^;;


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How do you make grownups re-learn basic maths?

2007-11-15 13:20:00

This semester, the didactics course that's part of Analysis 1 focuses on the teaching of basic maths to children. What kind of troubles do they run into? What are common mistakes they make? How does learning maths even work?!

Of course it's a bit hard for a bunch of grownups to sympathize with the issues kids run into. Adults have been calculating things in their heads for decades and everything's become an autoamtic process.

8 + 5? The answer "13" automatically pops up in my head. No need to even think about it. 2 x 20? Boom! "40".

So how do you make adults relive their days of learning basic maths?

By making them do maths in base-8, ie octal counting.

Using the classic method known as the Land of Okt (het land van Okt), aspiring teachers are introduced to the problems of learning maths. We're using a book published by APS, though there's also a book dedicated to this specific subject.

I have to say that it's an interesting and somewhat frustrating experience. It feels odd break down addition and multiplication into steps again. Ie: 3 + 9 = 3 + 5 + 4 = 14. Or: 4 x 5 = 2 x 12 = 24. Don't even get me started about fractions :D

Yeah... Good stuff! If you're curious to see some of the assignments we're doing, check the Wiki page for week 1.


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Here I go: my first exams in college

2007-11-05 09:57:00

My calculator, my pens, my reports and my summaries.

So... Exciting day! Today's the first time I'm taking exams for my new college education. Of course I've done all of this before, but that was years ago!

I've got two tests scheduled for today:

* 1200 - 1400 = Statistics 1.

* 1800 - 2000 = Didactics 2.

So yeah, I've got four hours of wasted time in between my tests. I'll use that to go through the summaries some more and to relax a little.

Well, here I go ^_^ Faito!


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W00t! New books have arrived.

2007-10-31 20:22:00

Three new books and a pamphlet

This year's second semester will start in about a week. In preparation for my new courses I've been ordering books left and right. Luckily I already own the most expensive book on the list, so I won't have to get that one.

On the pile on the left you see:

* Identity development and student counseling

* Maths for students between 12 and 16

* Teaching effectively: learning maths

* A pamphlet entitled Don't touch me!

The last two items weren't on the official book list, but I decided to get them anyway. Learning maths because it will make a nice addition to my current library. Don't touch me! because I am very curious how one would handle a situation where kids are harassed by others.

This leaves two syllabi that I should buy at school. After that I'm all set.


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Math revision

2007-08-14 21:36:00

Seven math books.

Since school starts in about three weeks I thought it was about damn time to start getting prepared! It's one thing to make all arrangements with the school, taking care of paperwork and talking to people. But it's another thing entirely to actually be prepared for the course material!

I graduated from college a little over seven years ago. For about half of my college years I was very busy with maths, learning all kinds of new tricks. All the other time was spent programming, doing web design and learning about Unix. Since my career progressed with the latter half of what I just described, it's only natural for my maths to be a little rusty.

Well, rusty would be an understatement. Consider if you will one of the original, iron nails that Noah had used in his arc. Having been exposed to tremendous amounts of sea water and ages upon ages of time it's sure to be a bit rusty. Now, let's assume that ever since that flood the nail had been exposed to corrosives, acid rain and various other nasties. Not much would be left of it, right? A nasty, little chunk of iron would be all that's left.

Well, that's where my current grasp of maths is.

Thankfully I am confident that I can at least completely revive my high school math skills, considering this blog post. Back in 2005 I prepped Marlijne for an exam that consisted of all my HS maths in only a few hours.

Also thankfully, unlike what I wrote in that blog post, I did -not- throw away my math books! /o/

The picture above shows all of the books that I want to go through before school starts. The bottom row (plus the b/w book at the top left) are all high school books from my final two years. They cover everything from functions and equations, through trigonometry, to differentials and logarithms.

The top row is the stuff I went through in college. It's also the stuff that currently gives me a dread feeling in my stomach because it is way beyond me. They start out by repeating a little bit of HS stuff (differentials, functions), but then quickly move on to limits, logarithms, partial differentials, integrals, multiple variable equations and vectors. Zounds! I won't even mention the two other books that cover Laplace transforms and Fourier strains. Although I doubt whether I'll need to know any of that stuff.

Unfortunately I -have- thrown out all of my syllabi, meaning that I'm out of materials on chance calculation and on matrices. Luckily my friend The Saint is willing to lend me his copies. Apparently his storage space is larger than mine and he's hung onto most of the stuff from our college years ^_^

Well! Here I go! Study study study!


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Training to be a safety steward

2007-06-24 10:24:00

A safety steward's jacket

Yesterday was a very well spent day! I may have been way too busy and I may have gotten way too little sleep, but it was damn well worth it. For yesterday was the first of two whole-day training sessions to become a BHV worker.

In dutch, BHV is an abbreviation for Bedrijfs HulpVerlener, which can be roughly translated as Company Safety Steward. In short, these are the people who are there to limit the scope of a disaster on the workfloor, while waiting for the professionals to arrive. They apply first aid, the guide an evacuation and they fight a starting fire. All in all a very important job!

Over here, in the Netherlands, every company is required by law to have BHVs on hand. Originally the law required a minimum of one BHV per fifty people, but these days it just calls for an appropriate amount. This means that it could be anything between 1:10 (retirement homes, hospitals) to 1:50 (office buildings). BHVs should be sufficiently trained a know how to prevent panic and/or casualties.

Yesterday's session focussed on an intro to BHV, communcations during an incident an on fighting fires. This also included fighting gas and petrol fires using CO2 and foam extinguishers. This was a truly awesome day!

Our training was delivered by the good fellows of TBT fire and medical. If you're looking for a good BHV training, give these guys a ring.


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w00t! Passed my LPIC-102!

2007-04-06 10:57:00

Yay! There wasn't much reason for my doubting :) I passed with a 690 score (on a 200-930 scale), which boils down to 87% of 73 questions answered correctly. Not bad... Not bad at all...

Next up: ITIL Foundations!


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LPIC-102 summary

2007-04-03 23:41:00

The LPIC-102 summary is done. You can find it over here, or in the menu on the left. Enjoy!


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Preparing for LPIC-102

2007-03-20 21:01:00

Cailin working hard

One of the rules my employer Snow imposes on its employees is a rather strict certification track. Technically speaking each employee progresses through five C-levels, starting at 0 and ending up at 4. As you reach new levels of certification you will also reap benefits of your hard work.

Let's take the track that applies to me as an example:

C0 = no certification

C1 = LPIC1 (101 and 102) and ITIL Fundamentals

C2 = LPIC2 (201 and 202)

C3 = SCSA1 and SCSA2

C4 = SCNA and others

The irony of the matter is that I've already achieved both SCSA exams and the SCNA exam a long time ago, but that I'm still stuck at C0 because I haven't done my LPICs. So to work myself up the ladder I'm slogging my way through the requisite LPIC stuff, even though I'm not that fond of Linux.

The challenge here lies in the fact that haven't used Linux in a professional environment that much, so I'm at a disadvantage when compared to the rest of my colleagues. I'm really glad I've always been a rather good student, so cramming with a few books should get me through. I managed to score a 660 (87%) at my LPIC-101, so that brings some hope :)

And now I'm cramming for the 102 exam! Since I was postponing it way too long, I reckoned I'd better get my act together! This week I took two days off to dedicate myself completely to studying. I managed to work through six of the nine objectives in these two days, resulting in a thirty-one page summary so far. In two weeks time I'll take another two days and then I'll be ready!

Like last time I'll post my summary over here, to help out all those other souls trundling through their LPICs.


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As promised: adding a new LUN to Tru64

2006-12-22 09:00:00

As I promised a few days ago I'd also give you guys the quick description of how to add a new LUN to a Tru64 box. Instead of what I told you earlier, I thought I'd put it in a separate blog post instead. No need to edit the original one, since it's right below this one.

Adding a new LUN to a Tru64 box with TruCluster

1. Assign new LUn in the SAN fabric.

No something I usually do.

2. Let the system search for new hardware.

hwmgr scan scsi

3. Label the "disk".

disklabel -rw $DISK

4. Add the disk to a file domain (volume group).

mkfdmn $DISK $DOMAIN

5. Create a file set (logical volume).

mkfset $DOMAIN $FILESET

6. Create a file system.

Not required on Tru64. Done by the mkfset command.

7. Test mount.

Mount.

8. Add to fstab.

vi /etc/fstab

Also, if you want to make the new file system fail over with your clustered application, add the appropriate cfsmgr command to the stop/start script in /var/cluster/caa/bin.


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Crash course in new OSes

2006-12-20 20:20:00

The past two weeks I've been learning new stuff at a very rapid pace, because my client uses only a few Solaris boxen and has no Linux whatsoever. So now I need to give myself a crash course in both AIX and Tru64 to do stuff that I used to do in a snap.

For example, there's adding a new SAN device to a box, so it can use it for a new file system. Luckily most of the steps that you need to take are the same on each platform. It's just that you need to use different commands and terms and that you can skip certain steps. The lists below show the instructions for creating a simple volume (no mirroring, striping, RAID tricks, whatever) on all three platforms.

Adding a new LUN to a Solaris box with SDS

1. Assign new LUN in the SAN fabric.

Not something I usually do.

2. Let the system search for new hardware.

devfsadm -C disks

3. Label the "disk".

format -> confirm label request

When using Solaris Volume Manager

4. Add the disk to the volume manager.

metainit -f $META 1 1 $DISK

5. Create a logical volume.

metainit $META -p $SOFTPART $SIZE

6. Create a filesystem

newfs /dev/md/rdsk/$META

7. Test mount.

mount $MOUNT

8 Add to fstab.

vi /etc/vfstab

When using Veritas Volume Manager

4. Let Veritas find the new disk.

vxdctl enable

5. Initialize the disk for VXVM usage and add it to a disk group.

vxdiskadm -> initialize

6. Create a new volume in the diskgroup.

Use the vxassist command.

7. Create a file system.

newfs /dev/vx/rdsk/$VOLUME

8. Test mount

mount $MOUNT

9. Add to vfstab

vi /etc/vfstab

Adding a new LUN to an AIX box with LVM

1. Assign new LUN in the SAN fabric.

Not something I usually do.

2. Let the system search for new hardware.

cfgmgr

3. Label the "disk".

Not required on AIX.

4. Add the disk to a volume group.

mkvg -y $VOLGRP -s 64 -S $DISK

5. Create a logical volume.

mklv -y $VOLNAME -t jfs2 -c1 $VOLGRP $SIZE

6. Create a filesystem

crfs -v jfs2 -d '$VOLNAME' -m '$MOUNT' -p 'rw' -a agblksize='4096' -a logname='INLINE'

7. Test mount

mount $MOUNT

8 Add to fstab.

vi /etc/filesystems

Adding a new LUN to a Tru64 box running TruCluster

I'll edit this post to add these instructions tomorrow, or on Friday. I still need to try them out on a live box ;)

Anywho. It's all pretty damn interesting and it's a blast having to almost instantly know stuff that's completely new to me. An absolute challenge! It's also given me a bunch of eye openers!

For example I've always thought it natural that, in order to make a file system switch between nodes in your cluster, you'd have to jump through a bunch of hoops to make it happen. Well, not so with TruCluster! Here, you add the LUN, go through the hoops described above and that's it! The OS automagically takes care of the rest. That took my brain a few minutes to process ^_^


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LPIC-101 Summary

2006-12-12 22:38:00

Version 1.0 of my LPIC-101 study notes is available. I bashed it together using the two books mentioned below. A word of caution though: this summary was made with my previous knowledge of Solaris and Linux in mind. This means that I'm skipping over a shitload of stuff that might still be interesting to others. Please only use my summary as something extra when studying for your own exam.

I'm up for my exam next Thursday, at ten in the morning. =_=;

Oh yeah... The books:

Ross Brunson - "Exam cram 2: LPIC 1", 0-7897-3127-4

Roderick W. Smith - "LPIC 1 study guide", 978-0-7821-4425-3


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Two days of training

2006-10-17 19:38:00

Monday and Tuesday were not spent with the usual Nagios project in Amersfoort. Instead, I spent two days cooped up in a small hotel, somewhere in the Achterhoek (for my foreign visitors: one of the Netherlands' rural, backwater areas). It was time well spent, on a inter-personal communications course from CCCM.

While originally quite sceptic, the course turned out fine. About halfway Monday things took a course that made me decide that their approach might not fit my preferences, but half an hour later I also decided that _sticking_ with the course would help me in achieving one of my goals: learning to play my cards close to my chest and not letting a group of people on to my emotions regarding a subject. So even though the course may not be 100% up my alley, I may as well take the time to get some practice in :)

Anywho... November and January will see two additional training days, with a few personal talks at the CCCM office thrown in as well.


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SANE 2006 conference notes

2006-08-09 07:35:00

After months and months I've uploaded the notes that I took at the various lectures at SANE 2006. They might be usefull to -someone- out there. Who knows. Be aware though that portions of the notes are a mishmash of dutch and english :) The notes can be found as .PDFs in the menu on the left.


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Listen up. Here's da plan...

2006-08-08 16:52:00

Because I've got all kinds of things lined up for me to do, I'm going to put them into order. That way both you and I will know what to expect. Here's my priorities:

1. Make the requisite changes to my website, so that it plays nicely with search engines. This shouldn't be more than an evening or two of work (barring any reruns of Doctor Who on BBC3).

2. Study for my two LPIC1 exams.

3. Revive the manga and anime section of the website. This needs regular updates, so I'm going to have to think of a few nice things to add to this. I'm thinking "reviews"... It's also meant to give me a couple of days off between studying for my four exams.

4. Study for my two LPIC2 exams.

5. Move other parts of the website into the mySQL database as well.

6. Improve the PHP code that gets data from the database. It could be much cleaner, safer and efficient.

7. Build some form of CMS for myself, so I don't have to work in the database manually.

So there you have it boys! The next few months of my life lined out for ya.

Parallel to da plan I will keep on expanding the Sysadmin section with new stuff I discover every week. And I will try to fit in a week or two of vacation somewhere along the line. I have a big bunch of video games that I finally want to finish!


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Attending the SANE 2006 conference

2006-05-18 14:31:00

Thought I'd give you a little update from SANE'06. I'll keep it short, since there isn't a horrible lot to tell.

* Monday: Linux SysAd course was cancelled so me and Frank switched over to the IPSec course. This was 100% new material to me and (while boring at times) it was quite interesting. Now I'll at least know what people are talking about.

* Tuesday: The Solaris SMF tutorial was well worth the money, although a full day would've suited the material -much- better than half a day. In the AM I decided to crash the BSD Packet Filter tutorial and I guess the tutor should be happy I did. He had some trouble with the Powerbook used for the presentation and I was able to resolve his problems :)

* Wednesday: A full day of CF Engine, which was -totally- worth the money! Mark Burgess is an awesome speaker! Funny, smart and capable of conveying the heart of the matter I'd have loved to have this guy as a teacher in college!

* Thursday: As I suspected the conference itself is quite "meh". A few interesting speeches throughout the day, but I'm mostly taking things slowly. Instead I'm reading a bit in my new books. Unfortunately I slept -horribly- last night, so I'll be skipping the Social Event in the evening. :(


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Hacked admin mode into Syslog-ng

2005-11-22 11:09:00

At $CLIENT I've built a centralised logging environment based on Syslog-ng, combined with MySQL. To make any useful from all the data going into the database we use PHP-syslog-ng. However, I've found a bit of a flaw with that software: any account you create has the ability to add, remove or change other accounts... Which kinda makes things insecure.

So yesterday was spent teaching myself PHP and MySQL to such a degree that I'd be able to modify the guy's source code. In the end I managed to bolt on some sort of "admin-mode" which allows you to set an "admin" flag on certain user accounts (thus giving them the capabilities mentioned above).

The updated PHP files can be found in the TAR-ball in the menu of the Sysadmin section. The only thing you'll need to do to make things work is to either:

1. Re-create your databases using the dbsetup.sql script.

2. Add the "admin" column to the "users" table using the following command. ALTER TABLE users ADD COLUMN baka BOOLEAN;


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Passed my SCNA exam

2004-09-22 13:26:00

Booyeah! While I can't say that I aced the SCNA exam, I'm still extremely happy with my score: an 89% (52 out of 58 scored questions).


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SCNA summary done!

2004-09-15 22:13:00

Well, it took me a couple of days, but finally it's done: my summary own the "SCNA study guide" by Rick Bushnell (see the book list). I'll be taking my first shot at the SCNA exam in about a week (the 22nd, keeping my fingers crossed), so I'm happy that I've finished the document. I thought I'd share it with the rest of you; maybe it'll be of some use.

All 29 pages are available for download as a PDF from the Sysadmin section.


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