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Posts posted by Lyssia

  1. During a maths lesson in primary school in which we were flipping coins and doing other prob-related stuff, my coin landed on its edge. The girl I was working with and I just sat there and gawped before telling our teacher, who didn't believe us. It was seen by one other kid, and for the rest of the lesson and the lunch break afterwards the three of us tried to recreate it.


    Of course it all gets simplified, otherwise prob textbooks wouldn't talk about P(head) = P(tails) = 0.5. This is why I prefer something like algebra (in the main): simplifications make me nervous.

  2. I've only read it a couple of times through, and not in any great detail, but it doesn't seem to make any glaring errors (not that I'm an expert of anything, however). I'm not sure if it's been submitted anywhere, so I wonder what kind of peer reviewing it would get.

  3. I'm one of those people that can't just wing it; when I do I tend to just whitter away the entire day in front of the tv or something. I usually use a program like Korganiser to make to-do lists (not just relating to work - I'm as scatterbrained with everything else too) and organise what I'm doing each day.

  4. All right, I'm looking for text recommendations now. Anyone (looks significantly at Matt Grime in particular) have any blisteringly good experiences with texts about abelian varieties?


    Thanks in advance!

  5. Undergraduates all over the UK (and probably some other countries too) do it every year. Whackloads of international students do it too. I've just done it for the upteenth time but I'm suffering from worse-than-average culture shock - and it's not like I live a huge distance away from the UK normally anyway.


    This afternoon I got on a bus and spoke to the driver in Dutch. When I walk along the street I automatically step to the right. I've lost any sense of "If someone's in your way, you'll apologise politely and step round them" - rather I've become a Brush-Your-Way-Past-And-Glare-If-They-Don't-Like-It rotter. I actually miss my bike (given my physique, that's laughable) and got lost in the University Library earlier because the signs to everything were in English.


    On the plus side though, my bed here is much more comfortable!


    Anyone else travelled "home" for Christmas? Any expats? Any similar weird stories?

  6. I've just realised that I didn't post the image of my own result. Of course there's not much difference in any of the books as they're all yellow. But that's not the point. Here we go (hoping that the image attachment will work):


    If I were a Springer-Verlag Graduate Text in Mathematics, I would be Frank Warner's Foundations of Differentiable Manifolds and Lie Groups


    I give a clear, detailed, and careful development of the basic facts on manifold theory and Lie Groups. I include differentiable manifolds, tensors and differentiable forms. Lie groups and homogenous spaces, integration on manifolds, and in addition provide a proof of the de Rham theorem via sheaf cohomology theory, and develop the local theory of elliptic operators culminating in a proof of the Hodge theorem. Those interested in any of the diverse areas of mathematics requiring the notion of a differentiable manifold will find me extremely useful.


  7. Unless you specify some total ordering of the numbers there is no canonical way to add up the infinite set.


    But the rationals are countable, right? A countable set isn't necessarily well-ordered?


    Hm, but the rationals are dense.


    Don't mind me, I forgot all my maths soon after I graduated.

  8. how about composition, surley that is completely unrelated to science?


    I think that depends a lot on what kind of composer you're talking about. Webern championed a type of music called serialism which is literally composing by numbers (and the analysis of such pieces is great fun to boot!). Contrarily, many of the Romantic-era works seem to have absolutely no semblence of a structure to them at all. Bach's works could be said to be somewhere in the middle (although harmony and counterpoint are much more structured than most other types of music anyway) - almost composition by numbers, but still with the odd unpredicted surprise here and there.


    When it comes to modern popular music, the progressions involved are often so dull that you wonder if many artists just have a machine that churns stuff out when you turn a handle.


    As for the original question, I always had the idea that music was more closely related to maths than to anything involving the scientific method.

  9. Right, this is the infinity book I'm reading at the moment: Everything and More. The Amazon page comes with some impressive-looking reviews but the only customer review is disappointing. To be honest, I can see both points of view. The front of the book carries a one-liner: "If Terry Pratchett wrote a book about mathematics, it would look uncannily like this."


    Which is true, in a way. Wallace's prose is easy to read, his language is about as far from stuffy as you can get (cf. footnote 29 on p. 114, which begins "Sh*t. All right. The strict truth is more complicated than that....") and sometimes it's just downright funny. It's a book that attempts to present the story of [math]\infty[/math] at least somewhat comprehensively and yet in a way that makes it accessible to those without university level maths.


    It sounds a tall order, and it is. Does Wallace manage it? I'm only about half way through at the moment but so far, I have to say I have my doubts. The main stumbling block for me is the most obvious: there isn't a contents page. I don't know how he (or his editor) justifies it - throughout the book is referred to as "a booklet" but it's just over an inch thick: much bigger than your average "booklet" and certainly big enough to make a ToC necessary, let alone a good idea.

    Other than that, the Amazon reviewer's concern about the proliferation of abbreviations is also something that bugs me. Well, it wouldn't bug me so much if all the abbreviations Wallace were actually given in the Foreword. A third and more minor annoyance is the way that everything carries a heavy US-bias. Continual references to Calc 1 don't mean much to a European who has no experience of the USA university system.


    If you can ignore (or at least live with) those two down points, then the book's quite good style-wise. I still have doubts about the way Wallace gets through the maths - can it really be said that someone with no higher maths experience will understand it as an "armchair book"? I'll reserve judgement for when I've finished reading it. In the meantime, I'll recommend it - for mathmos, at least - simply because it's got a very blue cover, and blue is my favourite colour.

  10. I have a plethora of books about infinity. Well, all right, about four or something (which I still think is a bit excessive). Later on today I'll draw up A List and you can all gawk at it.

  11. I don't think there's anything in it that you wouldn't find in any other "reacreational" book about pi, but I haven't read that many so I can't make a good comparison. Having said that, I do like the way it's all presented. It's probably not worth the hardback price so if you want to ask for it for Christmas or something, the paperback is better in terms of the money.


    Ooooh, I could start off on a rant about the price of maths books here, but I won't.

  12. Currently reading "Algebraic Number Theory and Fermat's Last Theorem" by Stewart and Tall. Can't be bothered googling, but for those with some experience with ring theory and some basic algebra, it's quite an interesting insite into the problem. Also contains a lot of historical motiviation, which I find to be essential for a good maths book.


    Ooh I have that book! It doesn't mollycoddle you at all, but given that it's a great intro into ANT, I think. Its predecessor ("Algebraic Number Theory"; it was first published well before Wiles' proof) was the starting point for my reading on the topic; it was a favourite of my supervisor but with good reason, I think.


    The measure theory book I had was Lebesgue Integration and Measure. I have emotional scars from that course so I probably can't be unbiased about the book. Anyone else read it?

  13. I've read that book. It's really rather good, and for those that haven't touched Lattice Theory it's ideal for starters :)


    Weren't you the person who recommended it to me in the first place? :D


    I like how thick it is - about half an inch. A nice, non-intimidating thickness for a maths text like this from the 1960s!

  14. Maths is fun! Although most people would argue with that.


    I'm currenty looking through the CRC Concise Encyclopedia Of Mathematics and thats one hell of a great book' date=' just about everything in there!


    Other than that I'm reading a book on the Golden Ratio and another on Pi and Irrational numbers.




    Ryan Jones[/quote']


    Have you read The Joy of Pi?

  15. Why worry about books from that period? I don't not much about lattices... I'm reading a book from 1969 by H.S.M. Coxeter called Introduction to Geometry[/u'], incredible reference!


    Bitter experience, I'm afraid!

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