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# The Official Cambridge Offer Holders Thread 2016 Entry MK II

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Why bother with a post grad? Are they even worth it? Have your say! 26-10-2016
1. (Original post by Insight314)
It's not for us, I don't think we have enough friends to spend the 16GB space with
What do you mean, friends? Is that a term from Group theory? You must be a bit further into the lecture notes than I, for I have not come across that term before

I don't even know what memory my iPhone 6S has lol, I literally haven't had a single problem with it. I think it is the lowest possible memory space.
Perhaps you forget the memory problems, because of all the other problems with Apple products
2. (Original post by Mathemagicien)
What do you mean, friends? Is that a term from Group theory? You must be a bit further into the lecture notes than I, for I have not come across that term before
It's a pretty complicated group with a binary operation of something called "banter", I am not yet experienced with this however.

On a side note, I think I have refuted the friendship paradox, for I can't have fewer friends than my friends if I have no friends to begin with.

The friendship paradox was first observed by the sociologist Scott L. Field in 1991 and it states that most people have fewer friends than their friends have, on average. Mathematically, it is explained through graph theory, and is mainly related to the AM-GM and the Cauchy-Schwarz inequalities. Summarysing from Wikipedia:

Theorem: The average degree of a friend is strictly greater than the average degree of a random node.

Proof:
If you have a social network (which trivially I don't) you can represent it using a graph where the set of vertices corresponds to people in the social network, and the set of edges corresponds to the friendship relation between pairs of people. It is assumed that friendship satisfies symmetry, that is, if is a friend of , then is a friend of ; it is also modelled that the average number of friends of a person in the social network is the average of the degrees of the vertices in the graph. In graph theory, the degree of a vertex of a graph is the number of edges incident to the vertex, with loops counted twice, that is, . The average number of friends that a typical friend has (i.e not someone like me) can be modeled by choosing, uniformly at random, an edge of the graph (pair of friends) and an endpoint of the edge (one of the friends), and calculating the degree of the selected endpoint gives

,

where is the variance of the degrees in the graph and is the average number of friends of a random person in the graph. For a graph that has vertices of varying degrees (as is typical for a social network), both and are positive, which implies that the average degree of a friend is strictly greater than the average degree of a random node.

(Original post by Mathemagicien)
Perhaps you forget the memory problems, because of all the other problems with Apple products
Oh damn, Mathemagicien going savage on Steve Jobs.
3. (Original post by Insight314)
It's a pretty complicated group with a binary operation of something called "banter", I am not yet experienced with this however.

On a side note, I think I have refuted the friendship paradox, for I can't have fewer friends than my friends if I have no friends to begin with.

The friendship paradox was first observed by the sociologist Scott L. Field in 1991 and it states that most people have fewer friends than their friends have, on average. Mathematically, it is explained through graph theory, and is mainly related to the AM-GM and the Cauchy-Schwarz inequalities. Summarysing from Wikipedia:

Theorem: The average degree of a friend is strictly greater than the average degree of a random node.

Proof:
If you have a social network (which trivially I don't) you can represent it using a graph where the set of vertices corresponds to people in the social network, and the set of edges corresponds to the friendship relation between pairs of people. It is assumed that friendship satisfies symmetry, that is, if is a friend of , then is a friend of ; it is also modelled that the average number of friends of a person in the social network is the average of the degrees of the vertices in the graph. In graph theory, the degree of a vertex of a graph is the number of edges incident to the vertex, with loops counted twice, that is, . The average number of friends that a typical friend has (i.e not someone like me) can be modeled by choosing, uniformly at random, an edge of the graph (pair of friends) and an endpoint of the edge (one of the friends), and calculating the degree of the selected endpoint gives

,

where is the variance of the degrees in the graph and is the average number of friends of a random person in the graph. For a graph that has vertices of varying degrees (as is typical for a social network), both and are positive, which implies that the average degree of a friend is strictly greater than the average degree of a random node.

Oh damn, Mathemagicien going savage on Steve Jobs.
Check out friendship theorem proven by Erdos and a few others!

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4. (Original post by physicsmaths)
Check out friendship theorem proven by Erdos and a few others!
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I really want to learn graph theory, just so I can get a taste of what having friends is like.
5. (Original post by Insight314)
Oh damn, Mathemagicien going savage on Steve Jobs.
Can't believe I haven't chanced upon the friendship paradox before

This graph theory is giving me bad memories of the days when I was practicising for the BMO

I have nothing against crApple
6. (Original post by Mathemagicien)
Can't believe I haven't chanced upon the friendship paradox before

This graph theory is giving me bad memories of the days when I was practicising for the BMO

I have nothing against crApple
I have a wonderful problem sheet going from simple D1 graph theory all the way to IMO Graph theory and 3rd year Graph theory.

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7. You mathmos are hardcore

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8. (Original post by Messier31)
You mathmos are hardcore

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I just don't bother trying to read their posts anymore
(Sos guys)
9. (Original post by physicsmaths)
I have a wonderful problem sheet going from simple D1 graph theory all the way to IMO Graph theory and 3rd year Graph theory.

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Is it online? If so, could you share it please?

(Original post by Serine Soul)
I just don't bother trying to read their posts anymore
(Sos guys)
10. (Original post by Mathemagicien)
Is it online? If so, could you share it please?

Na i got it at a maths camp. Will share if you quote me tmmrw wen Im back home. Away atm till tmmrw. Sheet r at home.

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11. I never knew jneill got promoted to "Clearing and Applications Advisor", climbing up that TSR ladder fast, haha.
12. (Original post by Insight314)
I never knew jneill got promoted to "Clearing and Applications Advisor", climbing up that TSR ladder fast, haha.
I reported it as a bug already...
13. Out of interest, how likely is a new diagnosis of learning disabilities likely to effect my place? So long as the papers are marked properly I should hopefully have my place, but within the recent weeks following Ive been assessed and being on the dyspraxia/dyslexia part of the spectrum. I will let cambridge know when ive got the final report through, but is this something they are likely to frown upon? e.g. if for some reason I were to miss out on a grade needed would they think "oh another person whos not that great and will require lots of help here so we'll get rid of them" or would they think "They got their offer nearenough without extra time/ a scribe etc. they should now have so imagine how much better if they did have help". I was just a bit hesitant to go through this procedure as Im worried people will think im doing it for pity marks :/
14. (Original post by physicsmaths)
Na i got it at a maths camp. Will share if you quote me tmmrw wen Im back home. Away atm till tmmrw. Sheet r at home.

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Thanks
15. (Original post by EnglishMuon)
Out of interest, how likely is a new diagnosis of learning disabilities likely to effect my place? So long as the papers are marked properly I should hopefully have my place, but within the recent weeks following Ive been assessed and being on the dyspraxia/dyslexia part of the spectrum. I will let cambridge know when ive got the final report through, but is this something they are likely to frown upon? e.g. if for some reason I were to miss out on a grade needed would they think "oh another person whos not that great and will require lots of help here so we'll get rid of them" or would they think "They got their offer nearenough without extra time/ a scribe etc. they should now have so imagine how much better if they did have help". I was just a bit hesitant to go through this procedure as Im worried people will think im doing it for pity marks :/
It will NOT disadvantage you. At all.

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16. (Original post by jneill)
It will NOT disadvantage you. At all.

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Ok, thanks
17. (Original post by EnglishMuon)
Ok, thanks
Yeah, there's laws about this kind of thing, it can't go against you or it would be considered discrimination. Worst case scenario it has no effect, since the diagnosis wasn't in time to do anything for your exams, best case scenario they might be more lenient (like in the case of a near miss, as you suggested). I have a diagnosis not wildly different to yours, and Cambridge (and every other uni I've interacted with) have been very professional and positive about it, I definitely don't feel like it was seen negatively at all.
18. (Original post by Mathemagicien)
Thanks
Ello.
Here it is the (+) questions are pretty challenging. Last one is obviously the famous friendship theorem.

Q8 is decent. Was my favourite.
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19. (Original post by Mostly_Crazy)
Yeah, there's laws about this kind of thing, it can't go against you or it would be considered discrimination. Worst case scenario it has no effect, since the diagnosis wasn't in time to do anything for your exams, best case scenario they might be more lenient (like in the case of a near miss, as you suggested). I have a diagnosis not wildly different to yours, and Cambridge (and every other uni I've interacted with) have been very professional and positive about it, I definitely don't feel like it was seen negatively at all.
Thanks, thats nice to know. I have no experience with this stuff at all so yea
20. (Original post by physicsmaths)
Ello.
Here it is the (+) questions are pretty challenging. Last one is obviously the famous friendship theorem.

Q8 is decent. Was my favourite.
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Thanks mate, it looks fun (and probably largely beyond me, but I'll give it a shot)

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