A Summer of Maths (ASoM) 2016

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    (Original post by ThatPerson)
    The parametrisation is fine. The required integral is  I(2) - I(0) .
    Ahhh, I hadn't thought about that - that's a useful thing to bear in mind, thanks!
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    (Original post by EricPiphany)
    Are any improvements on Dijkstra's Algorithm taught in Dx modules for x more or equal to 2?
    No, can confirm D2 is the *****est module in all of A level.


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    (Original post by physicsmaths)
    No, can confirm D2 is the *****est module in all of A level.


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    Thanks, I ask because I stumbled across something called the 'A* search algorithm'.
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    (Original post by Kadak)
    I read A Mathematician`s Apology a while ago,and while I did enjoy it,I still don`t get why it held in such reverence by pure mathematicians.
    Plenty of us mathematicians feel the same way! It's a good read, but as a late romantic take on mathematics from a Bloomsbury angle, it's not the be all and end-all. Hardy's partner in crime John Littlewood wrote a little book ("A Mathematician's Miscellany" ) that was later edited by Bela Bollobas to incorporate more material and appeared as "Littlewood's Miscellany". Well worth a read to give a different perspective from that era.
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    Does the course content for part IA change from time to time, are the lecture notes from previous years likely to cover/not cover topics which are/aren't on the course for next year?
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    For probability theory, a very useful book is Grimmett and Stirzaker's "Probability and Random Processes", which will see you though to part II or until you really need to start studying measure theory. The trouble with G&S is that it covers a huge amount of ground - so you might prefer Grimmett & Welsh's "Probability: an Introduction" or Stirzaker's "Elementary Probability". The former is at a level just below that of G&S and covers less (so is less intimidating as a book); but the last chapter on markov chains strikes me as being a bit obscure. The latter is longer than G&W but at a slower pace. All three of these are very useful.

    A left field recommendation is Cinlar's "Introduction to Stochastic Processes" - very clear and very cheap! Also Cinlar has written "Probability and Stochastics"; another very good book, but at Part II/III level.
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    (Original post by liamm691)
    Does the course content for part IA change from time to time, are the lecture notes from previous years likely to cover/not cover topics which are/aren't on the course for next year?
    It does change from time to time; but for most purposes it is realistic to treat it as quasi-stationary.
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    A book that is recommended under IA vector calculus is Riley, Hobson & Bence's "Mathematical Methods for Physics and Engineering". This is one of those portmanteau books that will see you through "methods" for much of the tripos.

    It's a very well written book, and I'd recommend it to pure mathmos as well as to applied - simply because it's got so much material on how to calculate stuff - including vectors/matrices/tensors.
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    (Original post by Gregorius)
    A book that is recommended under IA vector calculus is Riley, Hobson & Bence's "Mathematical Methods for Physics and Engineering". This is one of those portmanteau books that will see you through "methods" for much of the tripos.

    It's a very well written book, and I'd recommend it to pure mathmos as well as to applied - simply because it's got so much material on how to calculate stuff - including vectors/matrices/tensors.
    Would you agree that Beardon's "Algebra and Geometry" is best for both Groups and V&M in part IA?
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    The Archimedeans :cry2: Archimedes is my hero :cry2:
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    (Original post by Insight314)
    Would you agree that Beardon's "Algebra and Geometry" is best for both Groups and V&M in part IA?
    I've not read it, so I can't really give you a direct answer! But, scanning through the index, it does seem to cover much of the syllabus for both courses. I will add that, when I was at Cambridge, Alan Bearodn was regarded as a superb lecturer; I loved his courses!

    One thing that must be considered is: what do you want a textbook for? Are you looking for a book that covers what will be in the lecture notes in more detail? Or which extends beyond the lectures to tell you what is going to come next? Or do you want a reference book that will last you a lifetime?
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    (Original post by Gregorius)
    I've not read it, so I can't really give you a direct answer! But, scanning through the index, it does seem to cover much of the syllabus for both courses. I will add that, when I was at Cambridge, Alan Bearodn was regarded as a superb lecturer; I loved his courses!

    One thing that must be considered is: what do you want a textbook for? Are you looking for a book that covers what will be in the lecture notes in more detail? Or which extends beyond the lectures to tell you what is going to come next? Or do you want a reference book that will last you a lifetime?
    Ahm, I am not quite sure. I am thinking of reading through the textbook, working through the exercises/example sheets and maybe take a look at the lecture notes from time to time.
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    (Original post by Gregorius)
    I've not read it, so I can't really give you a direct answer! But, scanning through the index, it does seem to cover much of the syllabus for both courses. I will add that, when I was at Cambridge, Alan Bearodn was regarded as a superb lecturer; I loved his courses!

    One thing that must be considered is: what do you want a textbook for? Are you looking for a book that covers what will be in the lecture notes in more detail? Or which extends beyond the lectures to tell you what is going to come next? Or do you want a reference book that will last you a lifetime?
    On a side note, how do I know when I am ready to tackle the example sheets? For example, I've just finished the complex numbers chapter of the V&M lecture notes (Dexter's notes) and I think the first 6 questions of A1a example sheet are accessible to me, so are the questions ordered in some particular way?
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    (Original post by Insight314)
    On a side note, how do I know when I am ready to tackle the example sheets? For example, I've just finished the complex numbers chapter of the V&M lecture notes (Dexter's notes) and I think the first 6 questions of A1a example sheet are accessible to me, so are the questions ordered in some particular way?
    I must admit that they look much of a muchness to me (assuming that you're looking at the Michaelmas 2015 set from DAMTP). Dive in and try!
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    Hey heres a fun problem.
    We have a scale and we place weights of size 1,a,a^2,\cdots,a^{n-1} such that at no step, the right scale weighs heavier than the left scale (and we place all weights). Find the number of ways to do this.
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    (Original post by Gregorius)
    I must admit that they look much of a muchness to me (assuming that you're looking at the Michaelmas 2015 set from DAMTP). Dive in and try!
    Oh, I am definitely gonna work through the example sheets. My question was more about when I should work through them while I study the material. Like, when do I know I have enough of the knowledge I have gained from reading the textbook/lecture notes in order to attempt them? Are they usually given to undegrads after their first lecture and then told to only do the first questions (since the lecture has only covered the first questions)?
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    (Original post by Insight314)
    Like, when do I know I have enough of the knowledge I have gained from reading the textbook/lecture notes in order to attempt them?
    You're ready when (a) you understand the question and (b) when you can make a fair fist of answering it. I would say that those questions look accessible to someone who has done FM at A-level.

    Once you're there you're only going to get the lecture notes and a few hints and tips from your supervisor (if you are lucky) and then you attempt the example sheets.

    Are they usually given to undegrads after their first lecture and then told to only do the first questions (since the lecture has only covered the first questions)?
    I'll leave this for more recent Cambridge students to answer; but when I was there, the first sheets came out pretty rapidly, as it was assumed that the college would have organized supervisions to start PDQ. Supervisions in my time were 90% example sheets 10% tring to fathom out what the lecturer had said/meant.
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    (Original post by Gregorius)
    You're ready when (a) you understand the question and (b) when you can make a fair fist of answering it. I would say that those questions look accessible to someone who has done FM at A-level.

    Once you're there you're only going to get the lecture notes and a few hints and tips from your supervisor (if you are lucky) and then you attempt the example sheets.


    I'll leave this for more recent Cambridge students to answer; but when I was there, the first sheets came out pretty rapidly, as it was assumed that the college would have organized supervisions to start PDQ. Supervisions in my time were 90% example sheets 10% tring to fathom out what the lecturer had said/meant.

    All right, I see. Thanks!
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    Gregorius,

    This might be a very stupid question, and it probably is, but Edexcel FP2 doesn't really teach this properly so I couldn't get the intuition behind it.

    If S is the interior of the circle |z - (1 + i)| = 1 and if z \in S then is |z-(1+i)| < 1? Or is it > sign? How do I get intuition behind this, it makes more sense for it to be less than 1 since it is the interior of the circle, but then I don't get the necessary inequalities.

    Again, I am pretty embarrassed of this, so don't judge.
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    (Original post by Insight314)
    Gregorius,

    This might be a very stupid question, and it probably is, but Edexcel FP2 doesn't really teach this properly so I couldn't get the intuition behind it.

    If S is the interior of the circle |z - (1 + i)| = 1 and if z \in S then is |z-(1+i)| < 1? Or is it > sign? How do I get intuition behind this, it makes more sense for it to be less than 1 since it is the interior of the circle, but then I don't get the necessary inequalities.

    Again, I am pretty embarrassed of this, so don't judge.
    Do the normal z=x+iy and look at the distances.


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