Have finally found a way to describe my research area to 8 year olds. If they know about Scrabble that is. Essentially I work on proving extension theorems about weights on ring linear codes. If one really simplifies this you can think of it as follows. Think of the words we make in scrabble as being codewords, out of the set of possible combinations of the letters only some of them are actually words. Every letter has a score assosciated with it, usually on the letter tile. If we call this the weight of the letter and the total score (neglecting any triple-letter-score bonuses etc) we call the weight of the word. Then the possible scores that we can attatch to the letters and the repercussions of these changes are essentially what I work on. Not much help in real scrabble though! Of course the alphabets I use are different, the rules for making 'valid' words must have certain properties and there are infinitely many of each letter in the imaginary scrabble bag.
A wonderful book. A fantastic view of life from a man who could only move his left eyelid to communicate. Humbling and instills one with a renewed love and appreciation of life and all those things we take for granted. Read it, it won't take you long and it will change your perspective.
This book reminded me of Tony Hawks' 'Round Ireland with a fridge' a book I greatly enjoyed. Both follow the near-random wanderings of an Englishman around Ireland. Pete Mc Carthy's travels centre mostly around West Cork, the idyllic setting of his childhood holidays and a place he has never lost his grá for. Through the humour of bizarre happenings we glimpse the changes brought on by the 'celtic tiger'. Although intended as a comic story, and parts can be funny, I felt a melancholy undertone borne out of our narrator's longing to rightfully claim Ireland as his home, despite his English birth. The book characterises certain elements of Irish culture and landscape that escape many writers and makes an intersting read for any Irish person, or potential visitor.
If I were a turkey-loving American traditionalist and lover-of-holidays I would be celebrating thanksgiving today. Although I will be saving myself for Christmas-day-turkey in less than a month I will share some little things I'm thankful for in a small way today:
sunshine + dry weather on my walk into work. ESB (electricity bill) not as scarily big as the last one. free cake + fizzy lemonade for the arrival of IRU chocolates from Belgium courtesy of Vijay warm clothes fresh from the drier feast of boris three times in one month (pity no-one was ready to ascend) having lunch with a brilliant book and the guts to do so being able to do more than blink one eyelid
things I thank my lucky stars for everyday include: greg (everything about him) my family + their health + well being my friends my health (being able to dance, walk, laugh and have fun) nature ( from kicking fallen leaves to being mesmerised by waterfalls) life!
I had a nice formula for something. Then I couldn't prove its validity when I went to type up my results. Wrote up things the awkward formula-free way. Asked my supervisor for help because I'd found a flaw in the formula. So he gave me a helpful idea. Which was great, I wrote up a nice new proof of the formula. Except I then realised I still have the same little flaw. Have now eventually found a work-around, which is a pain, and can continue. Continue and completely re-write and re-latex all my major work that is. So relieved and dejected. An interesting combination, added to which we have the nerves about the poster I'm trying to design. Lots of working late this week will probably be continuing for some weeks.
Ok, I've decided that for future reviews each book, author, series etc. will be given a rating from the list: Insomnia Inducing Socially Detrimental Addictive Pleasant Put-down-able Tedious Soul Destroying
or some variations thereof. In general the first three indicate that the book is great, though a bit too good. The second two show a book that is good to read if you feel like reading but won't inhibit your ability to live your life independent of it. The last two mean you would really need a reason to read them.
Ok. Sort of fell of the face of the blogosphere for a while there. Things were incredibly busy in both personal life and work and then I got sick. Back in business now and hopefully will have a few new reviews in the offing :)
Sorry to anyone who was confused by my latest post in my native language. I've decided to create a new, separate, blog for all my ramblings in Irish. It's called Grá agus Gaeilge and you can find a link in my blog list or just go direc to gaeilgelecaitlin.blogspot.com if you're interested.
Le deanaí bhí mé ag éisteacht le cheol 08 ar 'youtube'. Is breá liom an idirlíon :) Tháinig mé trasna 'playlist' duine éigin a bhfuil go h-íontach.
Bhí mo dhreathair ag obair mar Chinnire an samhraidh seo chaite igColáiste Sheosaimh, áit a chaith mé an-chuid ám blianta ó shin. Thaispeáin sé dom an t-amhrán seo de Seán ag canadh ar an oíche deireanach den chúrsa. Tháinig na cuimhní go léir ar ais agus na deora leo. Níor thuig mé go dtí an buamaite sin nach mbeadh Dónal ann aris go deo. Fuair sé bás i rith mo scrúdaithe agus ní raibh seans agam glacáil leis ag an ám. Ní bheidh a leithéid ann arís.
Had a very exciting day yesterday, mathematically. I think the insomnia gave me lots of time to think things over so that I came up with ways to solve the problems I was working on. Then proceeded to show all sorts of wonderful correspondances between the ring and the algebra I'm working with. Hooray! Plodding throught the details today and hopefully there'll not be too many fiddly bits. One of the best meetings with my supervisor I've had in a while. He had vision and I had an idea of how these things connected. Great Stuff! If I've it all written up my friday I can have a fun weekend of LaTeX :)
As mathsoc librarian I feel obliged to provide the current list of available books belonging to mathsoc. If anyone would like to borrow any of these books just contact me, eg by leaving a comment to this post, and I will arrange it. After October 1st you will need a current mathsoc membership number. Or maybe just a chocolate brownie for me...
Anyone willing to loan items from their personal collection to mathsoc members just email me the details of the book: title, author, publisher etc and I will arrange it to be added to the list as appropriate. Lending will be on your terms only and you may choose on each occasion if you wish to lend it or not.
Ok, I think I have the radical of the algebra in terms of the radical of the underlying ring. Hooray! A tiny step along the way but it might be as far as it's possible to go so I'm pleased, provided it's all correct of course and I don't wake up in the middle of the night realising I've made a mistake somewhere along the way....*fingers crossed*
Now just the invisible theorem and the tricky review to finish...
Ok, at the moment I'm trying to characterise the Jacobson radical of the factor algebra of the algebra of complex functions from a ring under multiplicative convolution. If you think that sounds convoluted I probably shouldn't add that this was the simplest explanation I could come up with. I've typed up a rough sketch of some of the background work I've done on this algebra, what it is and how it works. The Jacobson radical however is proving elusive, despite all my best efforts. Essentially I've a big set of objects with some structure and I'm trying to find a little very structured bit inside it that has special properties. Tricky stuff :) Hopefully once I've found out what it looks like I'll be able to use it to prove a theorem that another researcher in the field has already proved a different way. Made especially difficult since I can't seem to find his proof or any mention of it.
Also, I've been aksed to review an article on an area related to mine for a recognised journal. Unfortunately I've not much experience with this area which means an awful lot of background reading. I don't think my review will be up to much although I think I've found a neater way to define one of the objects they use. My lack of global vision on the topic precludes any idea of the overall relevence of the work.
Please go to the Science for a succesul Ireland website, watch the three videos and vote for the one you think is best. Personally I think this is video B and I'm not at all biased by the fact that Suzanne is my friend...
Contrary to my most recent post I would now advise that the book 'The Phd Process' be read ONLY before starting a phd. Under no circumstances should this book be read during a particular tough part of one's phd adventure. Unless you wish to be filled with dread, depression and self-loathing. Consider yourselves warned.
'Mathematics: A very short introduction' by Timothy Gowers 'Letters to a young mathematician' by Ian Stewart 'A mathematician's apology' by G.H. Hardy with foreword by J.P. Snow (brilliant!) Currently reading the 'further reading' sections of these books.
Also reading 'The Ph.D. Process: A student's guide to Graduate school in the sciences'. Heavily lab-science based but still has some interesting and noteworthy ideas. Everyone should read this before they graduate if they're even considering a postgraduate degree in the sciences.
Please take 30 mins of your day to enjoy the delights of Dr. Horrible's Sing-Along Blog. You will then find yourself inexorably impatient for the next act. For your convenience there is currently Act I and Act II provided.
It looks like most of the work I've been doing for the past while on weights over Frobenius rings has already been done/published by someone else in a series of 3 papers. He went about it a different way and the three papers overlap heavily, it's hard telling which order they were written in, so hopefully the alternate approach will still be worth something. Probably not. It's difficult even figuring out exactly what he has proved and where it leaves me.
The Fire of Heaven Trilogy by Russell Kirkpatrick consists of:
Across the Face of the World (2005)
In the Earth Abides the Flame (2005)
The Right Hand of God (2006)
Personally I found them very enjoyable, although the final book wasn't quite as engaging perhaps as the first two. A highly addictive series, prepare to be reading through the night. A truely epic tale and many elements were left to the reader to decide: characters' motivation for actions and the consequences of certain events being the primary of these. I felt the ending was a little rushed with many strings left untied. Perhaps this was intentional. All in all it's a great read and will be staying on my shelf to read again and lend to others.
Think i might be one the verge of a breakthrough in proving a certain isomorphism i've been working on :) hooray! i just need to try get the formulation of the map right. Could be tricky though. I'll keep working at it nonetheless!
Just finished my exams yesterday evening and was looking forward to my first sleep in since sometime in April. Unfortunately was woken up by the fire alarm in residences going off at the crack of dawn this morning! One of the pressure pipes/valves upstairs was pumping water out everywhere. I was freezing outside in my pjs and bare feet while they temporarily fixed the problem! Still possible that the water might leak down into our apartment, especially as we could hear it flowing down in the water cupboard. Here's hoping it doesn't ruin our rooms!
So stressed about tomorrow's Calculus on manifolds exam that I've been feeling sick all day :( not to mention the panic attacks :( I can't honestly see myself passing in this state, especially if the exam hall is full. Makes me want to run away and never go back to ucd.
I just ate my last figroll. Apparently there is a shortage of figrolls in England, according to an article in the Guardian. While the shops on campus still have limited supplies of figrolls I wonder how long this will last. Perhaps Irish figroll makers have different suppliers. For the benefit of Cormac I've included a picture of a fig and figtree.
I am giving a short talk on ring-linear coding today. I have put the pdf of my talk on my website for anyone who might be interested in learning about rings, codes and Mac Williams' Equivalence Theorem extended to codes over Frobenius rings. Wish me luck!
For all those who believe in the notion of putting the month before the day I wish you a happy pi approximation day: 3/14 as you would have it in your notation. In my world I prefer to celebrate pi approximation day on 22/7 , in day/month notation. Or even not at all, what with pi being transcendental and all that....
Found a lovely paper from the 1940's detailing how monomials are made up of normal cycles and then some papers by Ralph B. Crouch(1) based on that work. Not directly related to my current work but could be underlying Ioana Constantinescu's Monomialsatz paper. Also cool and interesting :)