A Summer of Maths (ASoM) 2016

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    Hmm. I'm way too nervous about results day to start preparing for uni maths haha.
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    This sounds interesting. I'm doing A levels next year but I think it will be fun to learn some of this stuff.
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    (Original post by 16Characters....)
    Hmm. I'm way too nervous about results day to start preparing for uni maths haha.
    Agreed!! I'm much the same, bit hypocritical since I made the thread, but it's more for the benefit of the others who are fairly sure they have 1's and S's whilst I'm too nervous about my 2 to do anything properly. :lol:
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    (Original post by Kryptonian)
    This sounds interesting. I'm doing A levels next year but I think it will be fun to learn some of this stuff.
    You're welcome to do so, but if you're doing A-Levels next year, then this thread might be a bit out of your reach, since it deals with first year uni work.
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    (Original post by Zacken)
    You're welcome to do so, but if you're doing A-Levels next year, then this thread might be a bit out of your reach, since it deals with first year uni work.
    Unless he is jim leck.


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    (Original post by physicsmaths)
    Im gna let it sit at my desk and not use it so I know how you feel.


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    "Consider the equation z^n = 1. The coefficient of z^{n-1} is the sum of all roots." is that Vieta's formula?

    Also, if w = \exp(\frac{2\pi i}{n}) and  w^n - 1 = (w-1)(1+w+w^2+...+w^{n-1}) where w \neq 1, then why is \frac{w^n - 1}{w -1} = 0 when trying to show that 1 + w + w^2 + ... + w^{n-1} = 0 ?
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    (Original post by physicsmaths)
    Unless he is jim leck.


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    Or physicsmaths... after his two gap years.
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    (Original post by Insight314)
    "Consider the equation z^n = 1. The coefficient of z^{n-1} is the sum of all roots." is that Vieta's formula?
    Yes (ish). Think about expanding the polynomial (z-z_1)(z-z_2) \cdots (z-z_n). The coefficient of z^{n-1} is the ((-1)^{n-1} of) the sum of the roots.

    Also, if w = \exp(\frac{2\pi i}{n}) and  w^n - 1 = (w-1)(1+w+w^2+...+w^{n-1}) where w \neq 1, then why is \frac{w^n - 1}{w -1} = 0 when trying to show that 1 + w + w^2 + ... + w^{n-1} = 0 ?
    Roots of unity, so w^n - 1 = 0 but then it follows that the latter bracket must be 0 for w \neq 1 then geometric series, i.e: sum of the first n terms with first term 1 and common ratio w.
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    (Original post by Insight314)
    "Consider the equation z^n = 1. The coefficient of z^{n-1} is the sum of all roots." is that Vieta's formula?

    Also, if w = \exp(\frac{2\pi i}{n}) and  w^n - 1 = (w-1)(1+w+w^2+...+w^{n-1}) where w \neq 1, then why is \frac{w^n - 1}{w -1} = 0 when trying to show that 1 + w + w^2 + ... + w^{n-1} = 0 ?
    Geometric sum of the right bracket since one is zero.
    Well yeh its application of vietas formula yeh. The wiki page covers it rather well for general terms.


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    (Original post by Insight314)
    "Consider the equation z^n = 1. The coefficient of z^{n-1} is the sum of all roots." is that Vieta's formula?

    Also, if w = \exp(\frac{2\pi i}{n}) and  w^n - 1 = (w-1)(1+w+w^2+...+w^{n-1}) where w \neq 1, then why is \frac{w^n - 1}{w -1} = 0 when trying to show that 1 + w + w^2 + ... + w^{n-1} = 0 ?
     w^n - 1 = 0 by definition, since we is an nth root of unity.
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    (Original post by JackHKeynes)
    ... by definition, since we is an nth root of unity.
    You'll want to use [/latex] and not [\latex].

    (it's not by definition, it's because w is a nth root of unity).
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    (Original post by Zacken)
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    This looks amazing, such a shame I don't have the brain for advanced maths haha. Can you recommend me any resources over the summer to bridge the gap from GCSE to A-level maths? It's been 5 years since I've done maths GCSE and I acheived a B grade. I'm looking at starting an A-level in maths this september coming if my university back up plan does not work out.
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    (Original post by Zacken)
    Agreed!! I'm much the same, bit hypocritical since I made the thread, but it's more for the benefit of the others who are fairly sure they have 1's and S's whilst I'm too nervous about my 2 to do anything properly. :lol:
    I'm sure you'll be fine :-)

    I think I might teach myself the rest of M3 and 4. There is no M5 with MEI but they used to go up to M6 so that might be the extention :-)
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    (Original post by 16Characters....)
    I'm sure you'll be fine :-)

    I think I might teach myself the rest of M3 and 4. There is no M5 with MEI but they used to go up to M6 so that might be the extention :-)
    I've heard some very interesting things about those mechanics modules, stuff like intrinsic co-ordinates and the likes. I think I saw a few resources on the really old A-Level spec with all those things, if I ever track them down again I'll let you know. :-)
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    Right, thanks guys. I don't know why I was this silly not to see the initial point of the argument i.e that it is roots of unity so it must be zero haha.

    Btw, check out what I just printed out.

    Name:  ImageUploadedByStudent Room1467147003.088446.jpg
Views: 133
Size:  94.0 KB

    Anyone have an idea how I can staple the whole thing though? It's 35 double-sided pages lol.


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    (Original post by Zacken)
    I've heard some very interesting things about those mechanics modules, stuff like intrinsic co-ordinates and the likes. I think I saw a few resources on the really old A-Level spec with all those things, if I ever track them down again I'll let you know. :-)
    Tee Em once posted a good intrinsic co-ordinates question, and in the same thread people linked the old Edexcel M6 stuff
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    (Original post by Insight314)
    Anyone have an idea how I can staple the whole thing though? It's 35 double-sided pages lol.

    Get it binded.
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    (Original post by Insight314)
    Right, thanks guys. I don't know why I was this silly not to see the initial point of the argument i.e that it is roots of unity so it must be zero haha.

    Btw, check out what I just printed out.



    Anyone have an idea how I can staple the whole thing though? It's 35 double-sided pages lol.


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    Use a binder clip. Much neater and easier to take out individual notes so things don't get messy

    (Original post by Zacken)
    Get it binded.
    Or that
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    (Original post by AngryRedhead)
    This looks amazing, such a shame I don't have the brain for advanced maths haha. Can you recommend me any resources over the summer to bridge the gap from GCSE to A-level maths? It's been 5 years since I've done maths GCSE and I acheived a B grade. I'm looking at starting an A-level in maths this september coming if my university back up plan does not work out.
    Thanks for quoting the whole thing.


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    (Original post by Zacken)
    Get it binded.
    You mean spiral binding? How do I even do that lol?


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