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	<title>danielyeow.com &#187; Academia</title>
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	<description>Daniel Yeow and the Quest for World Peace</description>
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		<title>Fluorinated Compounds</title>
		<link>http://www.danielyeow.com/2011/fluorinated-compounds/</link>
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		<pubDate>Mon, 03 Oct 2011 21:43:16 +0000</pubDate>
		<dc:creator>Daniel Yeow</dc:creator>
				<category><![CDATA[Academia]]></category>
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		<category><![CDATA[Science]]></category>
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		<guid isPermaLink="false">http://www.danielyeow.com/?p=4370</guid>
		<description><![CDATA[Last Friday I was fortunate enough to be present at my girlfriend's Ph.D. thesis defence at the University of Copenhagen. In case anyone is wondering, it went very well, and all the opponents spoke highly of her work, and now we can all call her "Doctor". <span style="color:#777"><a href="http://www.danielyeow.com/2011/fluorinated-compounds/">&#8594;more</a></span>]]></description>
			<content:encoded><![CDATA[<p><a href="http://www.danielyeow.com/wp-content/uploads/two_tail.jpg"><img class="alignnone size-medium wp-image-4371" title="front cover image from the thesis" src="http://www.danielyeow.com/wp-content/uploads/two_tail-500x375.jpg" alt="" width="500" height="375" /></a></p>
<p>Last Friday I was fortunate enough to be present at my girlfriend&#8217;s Ph.D. thesis defence at the University of Copenhagen. In case anyone is wondering, it went very well, and all the opponents spoke highly of her work, and now we can all call her &#8220;Doctor&#8221;. I have incidentally included a small photo gallery from the day of the defence at the bottom of this post. However, what I<em> really</em> want to talk about is the subject matter of the thesis itself.</p>
<p>As you may have guessed from the title, the thesis is concerned with fluorinated compounds. The full name of the thesis is <em>Polyfluorinated surfactants in food packaging of paper and board</em>. The research investigates the implications of fluorinated compounds when they are used in food packaging. After the high-profile banning of BPA from water bottles, it doesn&#8217;t take a huge leap of imagination to come up with ways in which other chemicals in food packaging might have adverse effects.</p>
<p>Fortunately (or unfortunately) I have had the privilege of reading through the thesis many times, at various stages of its development. It is written in English, and being a native English speaker, I have some amount of usefulness in spotting odd uses of grammar, and finding better choices of words in certain situations. To be honest, I didn&#8217;t have to correct very much. Most Danes speak English quite fluently, and unsurprisingly, Danes who have been in educational institutions for long enough to get a PhD speak and write better English than many of my Australian friends for whom English is their ONLY language. (I also <a href="http://www.danielyeow.com/2011/drawing-molecules/">drew the molecules</a> for her thesis, including the cover image above).</p>
<p>Anyway, while many (indeed most) of the more technical points of chemistry went straight over my head, I was able to quite easily follow what was going on in the thesis, and I write about it here not only because I find it interesting, but also because I find it concerning from a public health perspective.</p>
<p>So what are fluorinated compounds? They are chemicals with the chemical element fluorine in them. The ones being investigated are ones that have long chains of CF2, that is a carbon atom with two fluorines attached. The carbon acts as a backbone while the fluorine attaches to the outside (they&#8217;re the orange blobs in the drawing above, the carbons are black). They&#8217;re very useful because the bonds don&#8217;t break down easily, and they have the property of being both hydrophobic and lipophobic, which means that they repel both water-based solutions as well as oil-based solutions. Teflon (polytetrofluoroethylene) is a good example of a commonly used fluorinated compound.</p>
<p>Imagine a popcorn bag. In the past, simple popcorn bags were coated with wax so that the paper in the bag wouldn&#8217;t degrade too quickly after coming into contact with the butter in the popcorn. This was all well and good until we invented microwave popcorn. Regular wax breaks down in a microwave, so you have to coat the inside of the bag with something that will withstand the heat, and this is where materials like fluorinated compounds come in.</p>
<p>So what&#8217;s the problem? As mentioned above, they are useful because the carbon-fluorine bonds are strong and don&#8217;t break down easily. It is also for precisely this reason that these compounds accumulate in nature. It gets worse though, these compounds are bioaccumulative &#8211; they accumulate in living organisms. It was at this point where I was surprised to learn that most people living in the western world live with significant amounts of chemicals and plastics in their bodies that have slowly accumulated over time.</p>
<p>Many of these substances are mostly harmless, but the long-term effects of most of them are unknown. There is mounting evidence now that fluorinated compounds fall into the category of being endocrine disruptors, meaning that (like BPA) they can disrupt your hormones. That has a number of bad effects, notable among them being lower sperm counts (leading to infertility) as well as babies being born with underdeveloped genitalia.</p>
<p>So this was the crux of the thesis &#8211; do fluorinated compounds used in food packaging contaminate our food? It turns out that finding an answer to this question requires some impressive instrumental trickery and knowledge of chemistry. I used to think that you just put a bunch of samples through a very large and expensive machine and then it would tell you if what you were looking for was there, and how much there was. Turns out that there&#8217;s quite a lot more to it.</p>
<p>The short answer is yes. In most cases, there was significant <em>migration</em> (that&#8217;s what they call it) of these compounds from the packaging to the food. We should all be concerned. Since this result would be considered quite recent, there has not been sufficient time to develop and implement regulations on fluorinated compounds in food packaging materials. In the meantime, we should make an attempt to avoid exposure to them wherever possible.</p>
<p><a href="http://www.danielyeow.com/wp-content/uploads/fig1.jpg"><img class="alignnone size-medium wp-image-4402" title="fluorinated compounds, having a high surface energy, cause droplets to be very round" src="http://www.danielyeow.com/wp-content/uploads/fig1-500x375.jpg" alt="" width="500" height="375" /></a></p>
<p>But how? First we have the droplet test. Since fluorinated compounds are very strong surfactants, they have a very high surface energy. This causes droplets on the surface to form into tight balls. In particular, pay close attention to the angle of contact between the droplet and the surface. In the diagram above, the droplet on the right would indicate that fluorinated compounds were being used.</p>
<p>The next test is called the &#8220;tear test&#8221;. Since these compounds are used to <em>impregnate</em> paper and (card)board, the materials can be torn. When the packaging material is torn, pay close attention to where the tear takes place. If there is a separation, that is &#8211; if there is one layer of paper and a separate layer of clear plastic, then there&#8217;s no need to worry about fluorinated compounds. In this case, you have a plastic coating, and plastics have been around for longer and have regulations in place. If, however, you find that there is no separation, then you most likely have yourself a fluorinated compound.</p>
<p>Don&#8217;t despair though, there are varying degrees of badness. The greatest amount of migration tends to occur when the packaging is used on wet, and especially greasy foods. Also of concern is when the content of the packaging is intended to be heated with the packaging still in contact with it (remember those bags of microwave popcorn). Thirdly, more flexible packaging materials, like thin paper, are worse because they require a higher amount of fluorinated compounds to effectively impregnate them. For reasons that should be obvious, the longer something is in contact with its fluorinated compound-impregnated packaging material, the worse you can expect it to be. Dried foods and frozen foods are often ok though.</p>
<p>So there you have it, advance notice on the next widely-used chemical that will probably eventually get banned. Just the tip of the iceberg in the slow chemical contamination of our biosphere. And now, as promised, photos from the day of the thesis defence (click the images for a larger view):</p>

<a href='http://www.danielyeow.com/2011/fluorinated-compounds/20110930-dsc_3400/' title='A corridor at KU (Københavns Universitet)'><img width="100" height="100" src="http://www.danielyeow.com/wp-content/uploads/20110930-DSC_3400-100x100.jpg" class="attachment-thumbnail" alt="A corridor at KU (Københavns Universitet)" title="A corridor at KU (Københavns Universitet)" /></a>
<a href='http://www.danielyeow.com/2011/fluorinated-compounds/20110930-dsc_3401/' title='Printed and ready to go'><img width="100" height="100" src="http://www.danielyeow.com/wp-content/uploads/20110930-DSC_3401-100x100.jpg" class="attachment-thumbnail" alt="Printed and ready to go" title="Printed and ready to go" /></a>
<a href='http://www.danielyeow.com/2011/fluorinated-compounds/20110930-dsc_3409/' title='not distracted by the art in the room, everyone turns their attention to the thesis presentation'><img width="100" height="100" src="http://www.danielyeow.com/wp-content/uploads/20110930-DSC_3409-100x100.jpg" class="attachment-thumbnail" alt="not distracted by the art in the room, everyone turns their attention to the thesis presentation" title="not distracted by the art in the room, everyone turns their attention to the thesis presentation" /></a>
<a href='http://www.danielyeow.com/2011/fluorinated-compounds/20110930-dsc_3417/' title='a glass of water in a plastic cup - no fluorinated compounds here'><img width="100" height="100" src="http://www.danielyeow.com/wp-content/uploads/20110930-DSC_3417-100x100.jpg" class="attachment-thumbnail" alt="a glass of water in a plastic cup - no fluorinated compounds here" title="a glass of water in a plastic cup - no fluorinated compounds here" /></a>
<a href='http://www.danielyeow.com/2011/fluorinated-compounds/20110930-dsc_3418/' title='...and the fish we caught was THIS big'><img width="100" height="100" src="http://www.danielyeow.com/wp-content/uploads/20110930-DSC_3418-100x100.jpg" class="attachment-thumbnail" alt="...and the fish we caught was THIS big" title="...and the fish we caught was THIS big" /></a>
<a href='http://www.danielyeow.com/2011/fluorinated-compounds/20110930-dsc_3423/' title='question time (the defending part of the thesis defence)'><img width="100" height="100" src="http://www.danielyeow.com/wp-content/uploads/20110930-DSC_3423-100x100.jpg" class="attachment-thumbnail" alt="question time (the defending part of the thesis defence)" title="question time (the defending part of the thesis defence)" /></a>
<a href='http://www.danielyeow.com/2011/fluorinated-compounds/20110930-dsc_3427/' title='I thought it was funny how they always seemed to stand at opposite ends of the room'><img width="100" height="100" src="http://www.danielyeow.com/wp-content/uploads/20110930-DSC_3427-100x100.jpg" class="attachment-thumbnail" alt="I thought it was funny how they always seemed to stand at opposite ends of the room" title="I thought it was funny how they always seemed to stand at opposite ends of the room" /></a>
<a href='http://www.danielyeow.com/2011/fluorinated-compounds/20110930-dsc_3432/' title='things seem to be going well'><img width="100" height="100" src="http://www.danielyeow.com/wp-content/uploads/20110930-DSC_3432-100x100.jpg" class="attachment-thumbnail" alt="things seem to be going well" title="things seem to be going well" /></a>
<a href='http://www.danielyeow.com/2011/fluorinated-compounds/20110930-dsc_3436/' title='dont let the water on top fool you, that cart is almost completely loaded with alcoholic beverages'><img width="100" height="100" src="http://www.danielyeow.com/wp-content/uploads/20110930-DSC_3436-100x100.jpg" class="attachment-thumbnail" alt="dont let the water on top fool you, that cart is almost completely loaded with alcoholic beverages" title="dont let the water on top fool you, that cart is almost completely loaded with alcoholic beverages" /></a>
<a href='http://www.danielyeow.com/2011/fluorinated-compounds/20110930-dsc_3438/' title='finger food...'><img width="100" height="100" src="http://www.danielyeow.com/wp-content/uploads/20110930-DSC_3438-100x100.jpg" class="attachment-thumbnail" alt="finger food..." title="finger food..." /></a>
<a href='http://www.danielyeow.com/2011/fluorinated-compounds/20110930-dsc_3439/' title='for the reception... it was quite yummy'><img width="100" height="100" src="http://www.danielyeow.com/wp-content/uploads/20110930-DSC_3439-100x100.jpg" class="attachment-thumbnail" alt="for the reception... it was quite yummy" title="for the reception... it was quite yummy" /></a>
<a href='http://www.danielyeow.com/2011/fluorinated-compounds/20110930-dsc_3443/' title='I wonder why my mum wrote all this stuff... I cant even read!'><img width="100" height="100" src="http://www.danielyeow.com/wp-content/uploads/20110930-DSC_3443-100x100.jpg" class="attachment-thumbnail" alt="I wonder why my mum wrote all this stuff... I cant even read!" title="I wonder why my mum wrote all this stuff... I cant even read!" /></a>
<a href='http://www.danielyeow.com/2011/fluorinated-compounds/20110930-dsc_3447/' title='Mette, Mette, and Mette - all three are old school friends of Xenias'><img width="100" height="100" src="http://www.danielyeow.com/wp-content/uploads/20110930-DSC_3447-100x100.jpg" class="attachment-thumbnail" alt="Mette, Mette, and Mette - all three are old school friends of Xenias" title="Mette, Mette, and Mette - all three are old school friends of Xenias" /></a>
<a href='http://www.danielyeow.com/2011/fluorinated-compounds/20110930-dsc_3453/' title='at the reception, the three opponents congratulate the candidate'><img width="100" height="100" src="http://www.danielyeow.com/wp-content/uploads/20110930-DSC_3453-100x100.jpg" class="attachment-thumbnail" alt="at the reception, the three opponents congratulate the candidate" title="at the reception, the three opponents congratulate the candidate" /></a>
<a href='http://www.danielyeow.com/2011/fluorinated-compounds/20110930-dsc_3454/' title='candidate and opponent have a chat'><img width="100" height="100" src="http://www.danielyeow.com/wp-content/uploads/20110930-DSC_3454-100x100.jpg" class="attachment-thumbnail" alt="candidate and opponent have a chat" title="candidate and opponent have a chat" /></a>
<a href='http://www.danielyeow.com/2011/fluorinated-compounds/20110930-dsc_3458/' title='many relatives were on hand to share in the celebrations'><img width="100" height="100" src="http://www.danielyeow.com/wp-content/uploads/20110930-DSC_3458-100x100.jpg" class="attachment-thumbnail" alt="many relatives were on hand to share in the celebrations" title="many relatives were on hand to share in the celebrations" /></a>
<a href='http://www.danielyeow.com/2011/fluorinated-compounds/20110930-dsc_3471/' title='10-second exposure of the view out the window - over the courtyard of the main entrance to the campus'><img width="100" height="100" src="http://www.danielyeow.com/wp-content/uploads/20110930-DSC_3471-100x100.jpg" class="attachment-thumbnail" alt="10-second exposure of the view out the window - over the courtyard of the main entrance to the campus" title="10-second exposure of the view out the window - over the courtyard of the main entrance to the campus" /></a>
<a href='http://www.danielyeow.com/2011/fluorinated-compounds/20110930-dsc_3485/' title='walking to the afterparty'><img width="100" height="100" src="http://www.danielyeow.com/wp-content/uploads/20110930-DSC_3485-100x100.jpg" class="attachment-thumbnail" alt="walking to the afterparty" title="walking to the afterparty" /></a>
<a href='http://www.danielyeow.com/2011/fluorinated-compounds/20110930-dsc_3489/' title='Frederiksberg metro... near where the party was to happen'><img width="100" height="100" src="http://www.danielyeow.com/wp-content/uploads/20110930-DSC_3489-100x100.jpg" class="attachment-thumbnail" alt="Frederiksberg metro... near where the party was to happen" title="Frederiksberg metro... near where the party was to happen" /></a>
<a href='http://www.danielyeow.com/2011/fluorinated-compounds/20110930-dsc_3502/' title='coincidentally, that Friday was the last Friday Night Skate, and their afterparty joined ours'><img width="100" height="100" src="http://www.danielyeow.com/wp-content/uploads/20110930-DSC_3502-100x100.jpg" class="attachment-thumbnail" alt="coincidentally, that Friday was the last Friday Night Skate, and their afterparty joined ours" title="coincidentally, that Friday was the last Friday Night Skate, and their afterparty joined ours" /></a>
<a href='http://www.danielyeow.com/2011/fluorinated-compounds/20110930-dsc_3506/' title='skaters begin to pour in... we would have been among them, had it not been for the free food at the reception'><img width="100" height="100" src="http://www.danielyeow.com/wp-content/uploads/20110930-DSC_3506-100x100.jpg" class="attachment-thumbnail" alt="skaters begin to pour in... we would have been among them, had it not been for the free food at the reception" title="skaters begin to pour in... we would have been among them, had it not been for the free food at the reception" /></a>
<a href='http://www.danielyeow.com/2011/fluorinated-compounds/20110930-dsc_3511/' title='Olympian Cathrine Grage says hi'><img width="100" height="100" src="http://www.danielyeow.com/wp-content/uploads/20110930-DSC_3511-100x100.jpg" class="attachment-thumbnail" alt="Olympian Cathrine Grage says hi" title="Olympian Cathrine Grage says hi" /></a>
<a href='http://www.danielyeow.com/2011/fluorinated-compounds/20110930-dsc_3514/' title='Xenia announces the party to the skaters, and was surprised when someone embarrassed her by mentioning her PhD and congratulating her'><img width="100" height="100" src="http://www.danielyeow.com/wp-content/uploads/20110930-DSC_3514-100x100.jpg" class="attachment-thumbnail" alt="Xenia announces the party to the skaters, and was surprised when someone embarrassed her by mentioning her PhD and congratulating her" title="Xenia announces the party to the skaters, and was surprised when someone embarrassed her by mentioning her PhD and congratulating her" /></a>
<a href='http://www.danielyeow.com/2011/fluorinated-compounds/20110930-dsc_3519/' title='the photographer photographed!'><img width="100" height="100" src="http://www.danielyeow.com/wp-content/uploads/20110930-DSC_3519-100x100.jpg" class="attachment-thumbnail" alt="the photographer photographed!" title="the photographer photographed!" /></a>
<a href='http://www.danielyeow.com/2011/fluorinated-compounds/20110930-dsc_3537/' title='some friends pose for a paparazzi shot'><img width="100" height="100" src="http://www.danielyeow.com/wp-content/uploads/20110930-DSC_3537-100x100.jpg" class="attachment-thumbnail" alt="some friends pose for a paparazzi shot" title="some friends pose for a paparazzi shot" /></a>
<a href='http://www.danielyeow.com/2011/fluorinated-compounds/20110930-dsc_3539/' title='...and with the successful candidate'><img width="100" height="100" src="http://www.danielyeow.com/wp-content/uploads/20110930-DSC_3539-100x100.jpg" class="attachment-thumbnail" alt="...and with the successful candidate" title="...and with the successful candidate" /></a>
<a href='http://www.danielyeow.com/2011/fluorinated-compounds/20110930-dsc_3541/' title='the celebrations went well, and eventually wound down at about 2am with some nice chit chat'><img width="100" height="100" src="http://www.danielyeow.com/wp-content/uploads/20110930-DSC_3541-100x100.jpg" class="attachment-thumbnail" alt="the celebrations went well, and eventually wound down at about 2am with some nice chit chat" title="the celebrations went well, and eventually wound down at about 2am with some nice chit chat" /></a>
<a href='http://www.danielyeow.com/2011/fluorinated-compounds/untitled-3-2/' title='fluorinated compounds, having a high surface energy, cause droplets to be very round'><img width="100" height="100" src="http://www.danielyeow.com/wp-content/uploads/fig1-100x100.jpg" class="attachment-thumbnail" alt="fluorinated compounds, having a high surface energy, cause droplets to be very round" title="fluorinated compounds, having a high surface energy, cause droplets to be very round" /></a>
<a href='http://www.danielyeow.com/2011/fluorinated-compounds/untitled-3/' title='front cover image from the thesis'><img width="100" height="100" src="http://www.danielyeow.com/wp-content/uploads/two_tail-100x100.jpg" class="attachment-thumbnail" alt="front cover image from the thesis" title="front cover image from the thesis" /></a>

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		<title>Consilience</title>
		<link>http://www.danielyeow.com/2008/consilience/</link>
		<comments>http://www.danielyeow.com/2008/consilience/#comments</comments>
		<pubDate>Mon, 18 Feb 2008 13:48:31 +0000</pubDate>
		<dc:creator>Daniel Yeow</dc:creator>
				<category><![CDATA[Academia]]></category>
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		<description><![CDATA[ New York Tonight saw the launch of &#8220;Consilience: The Journal of Sustainable Development&#8221;. It is the first student-run <span style="color:#777"><a href="http://www.danielyeow.com/2008/consilience/">&#8594;more</a></span>]]></description>
			<content:encoded><![CDATA[<p><img class="size-full wp-image-279 alignnone" title="Josh Zivin, Jeffrey Sachs, and Anubha Agarwal sit" src="http://www.danielyeow.com/wp-content/uploads/2009/06/consiliencelaunch1.jpg" alt="Josh Zivin, Jeffrey Sachs, and Anubha Agarwal sit" width="300" height="200" /></p>
<p>New York</p>
<p>Tonight saw the launch of &#8220;Consilience: The Journal of Sustainable Development&#8221;. It is the first student-run interdisciplinary journal of sustainable development&#8230; ever. That&#8217;s pretty cool. It will be an annual publication and the first issue consists of 12 articles. Now here&#8217;s the kicker &#8211; one of those articles was penned by me!</p>
<p>The event was a tad nerve-wracking not only for the obvious reasons&#8230; but also because the man on the left of the photo is the head of the advisory board to Consilience &#8211; Dr Joshua Zivin who also happens to be the director of the PhD program in Sustainable Development (which I have applied for <em>again</em>). The man in the centre of the photo is Jeffrey Sachs himself (who probably doesn&#8217;t recognize me from class) and to his left is Anubha Agarwal, the editor-in-chief of Consilience (although she is considerably less scary than the other two).</p>
<p>The website for <a href="http://www.consiliencejournal.org" target="_blank">Consilience can be found here</a>. The <a href="http://journals.cdrs.columbia.edu/consilience/index.php/consilience/issue/view/1" target="_blank">first issue is here</a>, and <a href="http://journals.cdrs.columbia.edu/consilience/index.php/consilience/article/view/15">my article can be found here</a>.</p>
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		<title>Apples!</title>
		<link>http://www.danielyeow.com/2007/apples/</link>
		<comments>http://www.danielyeow.com/2007/apples/#comments</comments>
		<pubDate>Fri, 04 May 2007 09:15:58 +0000</pubDate>
		<dc:creator>Daniel Yeow</dc:creator>
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		<description><![CDATA[ Asuncion Do you like apples? Well&#8230; I&#8217;m going to one, a big one! How do you like them <span style="color:#777"><a href="http://www.danielyeow.com/2007/apples/">&#8594;more</a></span>]]></description>
			<content:encoded><![CDATA[<p><img class="alignnone size-full wp-image-351" title="apple" src="http://www.danielyeow.com/wp-content/uploads/2009/06/apple.jpg" alt="apple" width="200" height="200" /></p>
<p>Asuncion</p>
<p>Do you like apples? Well&#8230; I&#8217;m going to one, a <span>big</span> one! How do you like them apples?</p>
<h6><strong>Fine print: After a long and nail-biting wait, I have been admitted to the<a href="http://www.columbia.edu/cu/climatesociety/" target="_blank"> M.A. in Climate and Society</a> at <a href="http://www.columbia.edu/" target="_blank">Columbia University in the City of New York</a>. I still can&#8217;t quite believe it. Some fans have asked me when I begin. Orientation is on the 28th of August and classes start on the 4th of September. I am superlitavely excited about it.</strong></h6>
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		<title>Thesis of Doom</title>
		<link>http://www.danielyeow.com/2006/thesis-of-doom/</link>
		<comments>http://www.danielyeow.com/2006/thesis-of-doom/#comments</comments>
		<pubDate>Fri, 03 Nov 2006 12:44:27 +0000</pubDate>
		<dc:creator>Daniel Yeow</dc:creator>
				<category><![CDATA[Academia]]></category>
		<category><![CDATA[Blog]]></category>
		<category><![CDATA[mathematics]]></category>
		<category><![CDATA[melbourne university]]></category>
		<category><![CDATA[thesis]]></category>

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		<description><![CDATA[Remember remember the third of November My Thompson&#8217;s Group thesis was due I look through the pieces of my <span style="color:#777"><a href="http://www.danielyeow.com/2006/thesis-of-doom/">&#8594;more</a></span>]]></description>
			<content:encoded><![CDATA[<p style="text-align: center;">Remember remember the third of November<br />
My Thompson&#8217;s Group thesis was due<br />
I look through the pieces of my Thompson&#8217;s Group thesis<br />
And still haven&#8217;t got a clue</p>
<p>It came right down to the wire. I was still writing at 4pm&#8230; while the earlier pages of my thesis were simultaneously being printed. Despite the mad rush approaching 5pm, I actually managed to get the thesis in on time. Some of the other honours students got caught up with binder difficulties, but not me. My dexterity and ability not to flail and crack the shits when a binding machine was being stupid held me in good stead. With a sweaty brow and steely nerves, I bound both copies of my thesis in record time and submitted them before the due date (which is unusual for me).</p>
<p>For those who are interested, i have provided a copy of my thesis here (<a href="http://www.danielyeow.com/wp-content/uploads/2009/06/honoursthesisfinal.pdf">PDF 489KB</a>). It is written in a way as to be easily understood (at least to those who understand it). I would recommend at least 2nd year algebra although 3rd year algebra would be an ideal base for being able to comprehend what I have written. It is 60 pages long so you might want to grab a drink. Its not particularly good.</p>
<p><strong><span style="color: #ff0000;">Important note</span></strong> to those who read my thesis (my thesis examiner&#8217;s excepted, of course): If you spot a mistake, typo, badly-drawn picture <strong><span style="color: #ff0000;">I DON&#8217;T WANT TO KNOW</span></strong>!</p>
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