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# A Summer of Maths (ASoM) 2016

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1. (Original post by Insight314)
I was talking about the second theorem, I know the first theorem has its proof above the theorem. But now I just realised that the second theorem also has its proof above the theorem, lol. Sorry about that.
Yeah, I was talking about the second one as well. S'alright - I can see how that'd be confusing.

FWIW, I'd advise trying to prove everything yourself in at least the beginning portions of the notes - they should be easily provable with your existing knowledge.
2. (Original post by krishdesai7)
You might want to try Dr Cawley's noted for V&M. Those are the ones I'm using for the most part, and they're really very good
Nevermind m8, thanks for suggesting but I am already working through the Dexter notes. I just went full retard there and got confused by the way he structures "Theorem: ... Proof: ... " and then he starts to put proofs and then give Theorems. I guess I need to get more used to university textbooks (lecture notes in this case).
3. (Original post by Zacken)
Yeah, I was talking about the second one as well. S'alright - I can see how that'd be confusing.

FWIW, I'd advise trying to prove everything yourself in at least the beginning portions of the notes - they should be easily provable with your existing knowledge.
Yeah, I got confused due to the fact that he structures "Theorem: ... Proof: ... " and then he stops doing that lol. I was thinking of doing that, but don't you think it is a bit pointless for the beginning portions of the notes? I already know how to prove them from A-level (De Moivre's theorem, roots of unity etc.) but I think it's more important to see the rigor at which they are proven, which differs much more than at A-level. Like, I literally just found out what a "Lemma" is, and I don't think I would be able to copy mathematical rigor without even seeing a rigorous proof in the first place. Btw, am I the only one whos TSR is broken with Google Chrome? I can't separate paragraphs and number of posts/rep is missing from the interface for each post. Weird.
4. (Original post by Insight314)
13 1 20 8 42, Zacken, Mathemagicien, physicsmaths,

Do you guys know why Dexter's notes are incomplete, and where can I find ones which are fully complete?

Page 10 of V&M lecture notes is missing the proof to the theorem. Or is that left as an exercise to the reader?
yah what Zacken said
5. For anyone who's doing D&R or wants to pick up some special relativity in general with a full fledged maths framework, Taylor wheeler's Spacetime Physics is amazing. It starts right from scratch and takes you through the subject with amazing grace, in very lucid terms
6. What the hell did they do to TSR? But nice thread
7. http://ocw.mit.edu/courses/mathemati...2010/index.htm

first project
8. Going through the groups notes... So much notation to learn

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9. (Original post by drandy76)
Going through the groups notes... So much notation to learn

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Ahm. I think it's best to go through V&M and then Groups? Unless you are working through textbooks like Beardon's which cover both courses, I feel like you need to know the fundamentals in V&M in order to be able to have an in depth understanding of Groups.
10. (Original post by Insight314)
Ahm. I think it's best to go through V&M and then Groups? Unless you are working through textbooks like Beardon's which cover both courses, I feel like you need to know the fundamentals in V&M in order to be able to have an in depth understanding of Groups.
It seems fine so far, but I'll take your word for it before it gets too far into the meat of the course

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11. You are something else, Zacken!
I won't be studying Mathematics at university; good luck to those who will!
12. Mathemagicien, physicsmaths, shamika, Zacken, raff97, (I am tagging quite a few people since there isn't one person (yet) in this thread that these questions can be addressed to; maybe get more Camb undegrads in here?)

How do I know when to start working through the example sheets?

I've done first chapter of V&M Dexter's notes, and I am not sure if the letter/number on the top-left corner (A1a, A1b etc.) of the example sheets (https://dec41.user.srcf.net/notes/IA...atrices_eg.pdf) is in any kind of chronological order. First six questions seem to be accessible to me at first glance (after finishing complex numbers chapter) but in the future how should I manage my time between working through textbook/lecture notes and doing the example sheets? How can I be certain that I have covered enough knowledge on that specific topic that I can attempt some examples?
13. (Original post by Insight314)
Ahm. I think it's best to go through V&M and then Groups? Unless you are working through textbooks like Beardon's which cover both courses, I feel like you need to know the fundamentals in V&M in order to be able to have an in depth understanding of Groups.
What?
Vectors and matrices and groups are completely different no?
I duno. I thought they were pretty much independant.

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14. (Original post by Insight314)
Ahm. I think it's best to go through V&M and then Groups? Unless you are working through textbooks like Beardon's which cover both courses, I feel like you need to know the fundamentals in V&M in order to be able to have an in depth understanding of Groups.
How come Cambridge lecture both V&M and Groups at the same time, then?
15. (Original post by physicsmaths)
What?
Vectors and matrices and groups are completely different no?
I duno. I thought they were pretty much independant.

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Not really. The recommended book for both courses is the one by Beardon. Groups is pretty dependent on V&M due to its dependence on matrices, and V&M is a very fundamental course so makes sense that it must be a prerequisite to Groups. I think they teach them at the same time which also proves my point since they would try to connect the material from different courses together (just like they give Lorentz transforms at the end of V&M to connect it with D&R later on).
16. (Original post by Zacken)
How come Cambridge lecture both V&M and Groups at the same time, then?
Read my post above, and they try to be flexible. They make sure that required knowledge of V&M is covered first there and then they teach Groups. Also, I am talking about Groups later on, if you check the contents page you can see that one of the topics in Groups is "Matrix groups" which is pretty dependent on V&M. Also, Mobius transforms and symmetries I think are described through matrcies, but I am taking a big leap here (haven't touched Groups so might be wrong about this).
17. (Original post by Zacken)
How come Cambridge lecture both V&M and Groups at the same time, then?
Yeah, check out Dexter's lecture notes on Groups. At the start you don't really need any V&M knowledge, which is what I told drandy76, but then you get to matrix groups and transforms which requires V&M knowledge. Even if you only plan to go through the start of Groups and then start V&M, I feel like it is best to do V&M completely first and then work through Groups since, as I said before, it is a fundamental course so it gives you the initial 'step' into university maths. Again, I know it is taught first but they try to make sure that they give lectures on V&M first and then Groups, or at least structure the lectures in such a way that the person is shown V&M first.
18. (Original post by Insight314)
Not really. The recommended book for both courses is the one by Beardon. Groups is pretty dependent on V&M due to its dependence on matrices, and V&M is a very fundamental course so makes sense that it must be a prerequisite to Groups. I think they teach them at the same time which also proves my point since they would try to connect the material from different courses together (just like they give Lorentz transforms at the end of V&M to connect it with D&R later on).
I have beardons book.
Kool.

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19. (Original post by physicsmaths)
I have beardons book.
Kool.

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I have to wait until 30th.

I hate you.
20. (Original post by Insight314)
I have to wait until 30th.

I hate you.
Im gna let it sit at my desk and not use it so I know how you feel.

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