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    (Original post by Jkn)
    Is this correct? (It lacks the symmetry the inequalities you set tend to have )
    Nope, I have messed it; it is now correct. Apologies.

    (Original post by Slumpy)
    x=0 gives y+f(y)=2, so f(x)=2-x. Quick check shows this satisfies the original equation.
    Feels like I must've missed something!
    Ah, of course, I've entirely omitted when f(0)=0. Give me a couple of minutes...

    Edit; f(0)=0, set y=0, f(x^2)=xf(x), so f(x)= +/-x
    From f(x^{2})=xf(x) follows that f(x) =  \pm x when we know that the function is monotone, or bounded, or continuous, etc.
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    (Original post by bananarama2)
    I wondered whether this is what you were hinting at when you said about a compsci being around.
    Yes.

    (Original post by Jkn)
    I don't know why that would be assumed, it changes everything and is crucial to the question! That's like asking "how likely is it that I will go inside the white house today?" and forgetting to say that we are assuming I'm Barack Obama :lol:
    Because there's no point in the question being asked if it wasn't assumed, and I know what the asker actually meant and he knows what he meant but he just didn't express it carefully enough.
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    (Original post by Mladenov)
    Nope, I have messed it; it is now correct. Apologies.



    From f(x^{2})=xf(x) follows that f(x) =  x when we know that the function is monotone, or bounded, or continuous, etc.
    Doh. I thought about it for like 2 minutes to decide if I thought f(x) was only x or -x. Ta.
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    (Original post by Slumpy)
    Doh. I thought about it for like 2 minutes to decide if I thought f(x) was only x or -x. Ta.
    f(x)=x is not a solution.

    Spoiler:
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    You have found all the solutions, however, you have not proved that are no other solutions.
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    (Original post by Jkn)
    Hmm, that's quite cool Is optimising mathematical processes in this way the kinds of things you do in compsci, or is it programming and stuff like that? I literally have no idea what computer scientists even do... :ninja:
    That is a small part of what we do. It's very much a mixture of engineering, logic, design and discrete mathematics. I guess it's best described as the science of computation and manipulating information, both in terms of how to model them in theory and how to design the machinery to carry them out in practice.
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    (Original post by Mladenov)
    Nope, I have messed it; it is now correct. Apologies.
    Thank god! There's nothing scarier than an ugly problem :|

    In that case, please check the infamous problem 74 in case I ever return to it :lol:
    (Original post by ukdragon37)
    Because there's no point in the question being asked if it wasn't assumed, and I know what the asker actually meant and he knows what he meant but he just didn't express it carefully enough.
    Well yeah, fair enough. I just felt it needed a bit of common sense to define (something that, in my opinion, is non-existent and based solely on past experience) Because when I saw it I just instantly thought of splitting x into 1+...+1 (x times) and then assigning x a value equal to whatever algebraic quantity is desired :lol:

    Btw, out of interest, being a graduate-level computer scientist, do you generally find the questions on this thread to be rather trivial? i.e. Can you do all of the questions on here, all except some of the crazy *** ones mladenov posts occasionally or do you still find challenge in the same ones we STEP-takers wrestle with? (sorry if this is really nosy and/or rude )
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    (Original post by ukdragon37)
    That is a small part of what we do. It's very much a mixture of engineering, logic, design and discrete mathematics. I guess it's best described as the science of computation and manipulating information, both in terms of how to model them in theory and how to design the machinery to carry them out in practice.
    Oh right, I never thought there were such practical aspects to computer science (in my ignorance!)

    So do you, in a sense, continue from D1 and D2 in the same way that we continue from the other 16 modules? Note that when I say "continue from" I mean that is the same way a Law degree follows from a Law A-Level (same topics, different methods/skills etc..)
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    [QUOTE=Jkn;43048736]I'm confused... what do you want us to do? I don't believe it makes sense to assign a "number of times" to a process of multiplication. Here, only one multiplication is performed if you chose to see it that way.

    (a+ib)(c+id)=(ac-bd)+i(ad+bc)[/qoute]

    (Original post by ukdragon37)
    He means given a, b, c and d you need to compute e and f from them with only three multiplications. Both of you have clearly used four.



    You can try the AEA, but most people who start STEP actually does just jump straight in to its style of questions. The books "Advanced Problems in Core Mathematics" and "Advanced Problems in Mathematics" published by one of the examiners (Siklos) gives examples and solutions in additional to the thought processes involved. Other than that some STEP questions are easier than others, and I'm sure people here can point you to them.



    Solution 218

    Unfortunately you picked a time when a CompSci is present

    Spoiler:
    Show

    Let r_1 = a(c + d), r_2 = d(a + b) and r_3 = c(b - a). Then e = r_1 - r_2 and f = r_1 + r_3. This recipe has significance in Digital Signal Processing.
    Sorry if it wasn't clear, that above is what I was looking for.
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    (Original post by Jkn)
    Thank god! There's nothing scarier than an ugly problem :|

    In that case, please check the infamous problem 74 in case I ever return to it :lol:
    I hereby assure you that problem 74 is correct.
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    (Original post by Jkn)
    Btw, out of interest, being a graduate-level computer scientist, do you generally find the questions on this thread to be rather trivial? i.e. Can you do all of the questions on here, all except some of the crazy *** ones mladenov posts occasionally or do you still find challenge in the same ones we STEP-takers wrestle with? (sorry if this is really nosy and/or rude )
    I think if I want to I could solve most of the ones on this thread if I sit down and put my mind to it, but I'm by no means good at it anymore since I'm out of practice in doing these questions as they are very much not related to what I do as maths after about second year of university. I'm being entirely serious when I say that many people on this thread will be able to solve the problems faster than I can, but that is expected.
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    (Original post by Jkn)
    Oh right, I never thought there were such practical aspects to computer science (in my ignorance!)

    So do you, in a sense, continue from D1 and D2 in the same way that we continue from the other 16 modules? Note that when I say "continue from" I mean that is the same way a Law degree follows from a Law A-Level (same topics, different methods/skills etc..)
    Lol no, the D modules are a pale imitation of computer science that really only bears resemblance because it tells you about things related to algorithms. For a good cross section of what we do you can look at this year's third year CompSci exam papers: One Two Three

    EDIT: I want to bring out the fact that the courses available range from Business Studies (yuck yuck yuck) to Quantum Computing, things stats-related to logic-related, applications-based to theory-based and engineering to mathematics.
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    (Original post by james22)
    Sorry if it wasn't clear, that above is what I was looking for.
    No worries!
    (Original post by Mladenov)
    I hereby assure you that problem 74 is correct.
    :pierre:
    (Original post by ukdragon37)
    I think if I want to I could solve most of the ones on this thread if I sit down and put my mind to it, but I'm by no means good at it anymore since I'm out of practice in doing these questions as they are very much not related to what I do as maths after about second year of university. I'm being entirely serious when I say that many people on this thread will be able to solve the problems faster than I can, but that is expected.
    Do you still use algebra, calculus and stuff like that though? :eek:

    You should do some of the unsolved ones! If you can find them that is! I swear there were one or two integration problems I was working on the Mladenov set last week that were too hard to find I'm not sure if one of them got solved or not!
    (Original post by ukdragon37)
    Lol no, the D modules are a pale imitation of computer science that really only bears resemblance because it tells you about things related to algorithms. For a good cross section of what we do you can look at this year's third year CompSci exam papers: One Two Three
    Haha, well that's what I suspected! A pale imitation though an imitation none the less

    **** that looks so far removed from the maths and science papers!
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    (Original post by Jkn)
    Do you still use algebra, calculus and stuff like that though? :eek:

    You should do some of the unsolved ones! If you can find them that is! I swear there were one or two integration problems I was working on the Mladenov set last week that were too hard to find I'm not sure if one of them got solved or not!
    In fact, I don't, but why must I for it to be mathematical?

    (Original post by Jkn)
    **** that looks so far removed from the maths and science papers!
    What I do looks much more mathematical, but I was trying to say there is the option in the subject to go either way.
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    Solution 213

    Not complex analysis, but an alternative way of immediately solving this is to use one of the sums derived from here (142).

    Plug in x=\dfrac{\pi}{2} and we get \displaystyle \sum_{k\geq 0}\frac{(-1)^k}{(2k+1)^5}=\frac{5\pi^5}{15  36}
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    (Original post by ukdragon37)
    In fact, I don't, but why must I for it to be mathematical?

    What I do looks much more mathematical, but I was trying to say there is the option in the subject to go either way.
    Oh right, have you taken the mathematical route?


    Has problem 166 been solved yet? Just been giving it a go and managed to make a dent in it by splitting off a chunk and analysing it using Beta and Gamma functions. The problem's *** so I'm not sure if I'm lacking the knowledge to do the next bit... hmm... or I've what I've done even helps...

    So far I have \displaystyle \int_0^2 \frac{x^4}{(x^2+1)(x(2-x)^3)^{\frac{1}{4}}} \ dx = \frac{1}{2} \int_0^1 \frac{1}{(4x^2+1)(x(1-x)^3)^{\frac{1}{4}}} \ dx + \frac{13 \sqrt{2} \pi}{16}
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    By the way, do we have to know the solution to the problem (or, for that matter, if the solution exists in closed form) to post a question here (perhaps with a warning)?
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    (Original post by Jkn)
    Oh right, have you taken the mathematical route?
    One of the mathematical routes.
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    (Original post by henpen)
    By the way, do we have to know the solution to the problem (or, for that matter, if the solution exists in closed form) to post a question here (perhaps with a warning)?
    Taken from the OP

    Please don't post questions that you're not able or willing to provide solutions to.
    So no :P However, with LotF and Mladenov around, as long as you don't post something ridiculous like the Riemann hypothesis, it'll probably get solved anyway xD
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    (Original post by henpen)
    By the way, do we have to know the solution to the problem (or, for that matter, if the solution exists in closed form) to post a question here (perhaps with a warning)?
    I agree with harry potter potion over there^ But I will add that, whilst it's not the end of the world if you post a problem you haven't done or can't do, make sure that it's not just going to be tedious and boring. For example, be cautious if it's a problem you have invented but if it a problem you have found in a random competition paper somewhere on the internet, the chances are that it wouldn't've been there in the first place unless it was interesting and/or do-able

    I have occasionally posted problems I haven't been able to do but I wouldn't post such a problem if I didn't know anyone on here who would specifically enjoy or benefit from attempting it. For example, a few months ago I posted some ridiculous inequality and Mladenov (the god that he is) solved it!

    Also, if it's a problem you genuinely really want to know the answer to then there's no harm in posting it!
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    (Original post by Jkn)
    ...
    Okay, I'm going to post a nor overtly boring problem on inequalities. Sorry if it's easy or overly well-known, I don't think it is.

    Problem 222*

    Prove that if p_k \ge 0 for k \in \{ 1,2,...,n\} and \sum_{k=1}^np_k=1, then f(x)= \sum_{k=1}^n p_k \cos(\beta_k x) satisfies f^2(x) \le \frac{1}{2} \left( 1+f(2x)\right) , with (I assume) \beta_k, x, p_k \in \mathbb{R}.
 
 
 
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