Hey there! Sign in to join this conversationNew here? Join for free
    Offline

    1
    ReputationRep:
    (Original post by shamika)
    Where do you go to university?
    I will be attending UCL starting this September.

    (Original post by ukdragon37)
    Why do you presume he goes to university?
    Well done (for your dissertation)! Although, I have to admit, I am not surprised the slightest.
    Offline

    16
    ReputationRep:
    (Original post by jack.hadamard)
    I will be attending UCL starting this September.
    Consider me really scared (you'll love university I'm sure, and as long as UCL give you room to shine you'll do great).

    Well done (for your dissertation)! Although, I have to admit, I am not surprised the slightest.
    He is really lazy

    Spoiler:
    Show
    Nah I'm kidding ukdragon, my congrats is unreserved


    Have you lot looked at the STEP papers? Some nice questions this year, as always.
    Offline

    18
    ReputationRep:
    (Original post by ukdragon37)
    I got a distinction bring on the girls
    Congratulations!
    Offline

    1
    ReputationRep:
    (Original post by shamika)
    Consider me really scared (you'll love university I'm sure, and as long as UCL give you room to shine you'll do great).
    I'm sure I'll love it. I think there is room to shine, and it's better to be the king of a village than a clerk of a town.
    Offline

    12
    ReputationRep:
    (Original post by shamika)
    Good point. But if this is the new cohort of pre-uni students, then I'm scared...
    I've got past that point aaaages ago. Also considering this year's Senior Wrangler is only 18 I think we should just make peace with the fact that we will never be child prodigies. :laugh:

    (Original post by jack.hadamard)
    Well done (for your dissertation)! Although, I have to admit, I am not surprised the slightest.
    I don't know what causes you to not be surprised, but thanks!

    (Original post by shamika)
    He is really lazy

    Spoiler:
    Show
    Nah I'm kidding ukdragon, my congrats is unreserved
    Thanks! But you are actually correct. I'm incredibly lazy.

    (Original post by shamika)
    Have you lot looked at the STEP papers? Some nice questions this year, as always.
    Nah, I haven't looked at them since I crashed spectacularly when sitting them in 2009. I just hang around the STEP thread to troll.

    (Original post by Lord of the Flies)
    Congratulations!
    Thanks! I'm sure you'll have great fun at Cambridge, a place I am leaving for the foreseeable future on Saturday :cry:

    (Original post by jack.hadamard)
    I'm sure I'll love it. I think there is room to shine, and it's better to be the king of a village than a clerk of a town.
    :lol: From what I've seen even if you went to Cambridge for maths you wouldn't just be a clerk of a town.
    Offline

    0
    ReputationRep:
    (Original post by ukdragon37)
    I've got past that point aaaages ago. Also considering this year's Senior Wrangler is only 18 I think we should just make peace with the fact that we will never be child prodigies. :laugh:
    .
    I know I'm going to spend next year wondering if I deserve my place and that I'm an idiot Can't wait.

    18...what?
    Offline

    16
    ReputationRep:
    (Original post by bananarama2)
    I know I'm going to spend next year wondering if I deserve my place and that I'm an idiot Can't wait.

    18...what?
    Yep! I believe he also got a full set of alphas/betas in the first year (if you don't know what that means, he basically got nearly full marks on every question he needed to attemp)
    • PS Reviewer
    Offline

    20
    ReputationRep:
    PS Reviewer
    (Original post by ukdragon37)
    .
    Congrats on your grade for masters! :awesome:
    Offline

    12
    ReputationRep:
    (Original post by bananarama2)
    I know I'm going to spend next year wondering if I deserve my place and that I'm an idiot Can't wait.

    18...what?
    (Original post by shamika)
    Yep! I believe he also got a full set of alphas/betas in the first year (if you don't know what that means, he basically got nearly full marks on every question he needed to attemp)
    I keep making comments to friends that it would be funny to give supervisions to those older than you. :laugh:

    (Original post by cpdavis)
    Congrats on your grade for masters! :awesome:
    Thanks! :awesome:
    Offline

    2
    ReputationRep:
    Hmm, I think I might make a separate thread for people learning bits of analysis, group theory, etc... over the summer. Anyone up for this? I saw one last year called "A Summer of Maths" (I think?) so I might be a ******* and steal the name :lol:

    Edit: Too late I already made it
    Offline

    1
    ReputationRep:
    Another beautiful combinatorial geometry problem.

    Problem 254**

    Let n be a fixed positive integer. Suppose also that f : \mathbb{C} \to \mathbb{R} is a function such that, for any points P_{i}, i \in \{1,2,\cdots,n \} which are vertices of a regular n-gon, we have \displaystyle \sum_{1 \le i \le n} f(P_{i}) = 0. Show that f \equiv 0 over \mathbb{C}.
    Offline

    0
    ReputationRep:
    (Original post by Mladenov)
    Another beautiful combinatorial geometry problem.

    Problem 254**

    Let n be a fixed positive integer. Suppose also that f : \mathbb{C} \to \mathbb{R} is a function such that, for any points P_{i}, i \in \{1,2,\cdots,n \} which are vertices of a regular n-gon, we have \displaystyle \sum_{1 \le i \le n} f(P_{i}) = 0. Show that f \equiv 0 over \mathbb{C}.
    Crap, sorry for the neg. That was an accident. Mis-click. *Facepalm.
    • Thread Starter
    Offline

    16
    ReputationRep:
    (Original post by jack.hadamard)
    I'm sure I'll love it. I think there is room to shine, and it's better to be the king of a village than a clerk of a town.
    The other day I was speaking to a friend who has just finished his first year at UCL. He said failing STEP was the best thing to happen to him, since he's now doing extremely well there and he says he's having much more fun in London than he would have done at Cambridge. In fact if I understood correctly he came top of his year, and still had a lot of time to go out and enjoy himself. He also mentioned that he's been doing most of the Cambridge problem sheets, and has been finding them surprisingly easy after the UCL course.

    Having said that, this guy is insanely clever so it's clear that most people won't have the same experience.
    Offline

    0
    ReputationRep:
    (Original post by und)
    The other day I was speaking to a friend who has just finished his first year at UCL. He said failing STEP was the best thing to happen to him, since he's now doing extremely well there and he says he's having much more fun in London than he would have done at Cambridge. In fact if I understood correctly he came top of his year, and still had a lot of time to go out and enjoy himself. He also mentioned that he's been doing most of the Cambridge problem sheets, and has been finding them surprisingly easy after the UCL course.

    Having said that, this guy is insanely clever so it's clear that most people won't have the same experience.
    Aren't first year courses the same at most universities?
    • Study Helper
    Offline

    3
    ReputationRep:
    Study Helper
    I'm sorry to bother everyone but could someone supply me with some useful links on modular arithmetic as I'm trying to get to grips with it and the stuff I've looked at so far isn't very helpful to me
    Offline

    1
    ReputationRep:
    (Original post by MathsNerd1)
    I'm sorry to bother everyone but could someone supply me with some useful links on modular arithmetic as I'm trying to get to grips with it and the stuff I've looked at so far isn't very helpful to me
    Try this, by Vicky Neale (the notes for the Part II NT course she taught are excellent ).
    Offline

    1
    ReputationRep:
    (Original post by MathsNerd1)
    I'm sorry to bother everyone but could someone supply me with some useful links on modular arithmetic as I'm trying to get to grips with it and the stuff I've looked at so far isn't very helpful to me
    http://www.mathdb.org/notes_download...mber/ne_N2.pdf
    • Study Helper
    Offline

    3
    ReputationRep:
    Study Helper
    (Original post by jack.hadamard)
    Try this, by Vicky Neale (the notes for the Part II NT course she taught are excellent ).
    Thanks I'll take a look at this now This made it all seem so very simple and I finally get it now so thanks for the link!
    Offline

    1
    ReputationRep:
    (Original post by FireGarden)
    Spoiler:
    Show
    Kind of. That is a pretty standard "first question on homeomorphism" problem.

    Something harder would be:

    Define  C = S^1 \times [0,1] and let  ((x,y),t) \sim ((x',y'),t') \iff t=t'=0 or  t=t'=1 . Show that C/\sim is homeomorphic to the sphere, S^2.

    This is a question about a cylinder, formed as the product space of the circle (s^1) and the closed interval, with an equivalence relation on it, which effectively is pulling a drawstring around the open ends of the cylinder (and geometrical intuition should confirm the result is sphere-like!)

    Geometric intuition is probably the most important source of examples in algebraic topology. As you have already pointed out, your example is intuitively true, just as the fact that S^{2} with two holes is homeomorphic to a torus is intuitively true.

    Let me consider your problem more generally. Clearly, S^{n-1} \times I, where, of course, I = [0,1], is a cylinder. The equivalence relation you defined is simply identifying S^{n-1} \times 1 and S^{n-1} \times 0 with two points. It is sometimes called suspension, and is denoted by S(S^{n-1}). We can also interpret S(S^{n-1}) as the union of two copies of C(S^{n-1}) under the identity of S^{n-1}. There exists natural homeomorphism \varphi : C(S^{n-1}) \to B^{n}. I can't draw a diagram to show it...
    Now, from the above interpretation of the suspension as a double cone, it follows that C(S^{n-1}) / S^{n-1} is the suspension of S^{n-1}. But, it is clear that B^{n} / S^{n-1} \cong S^{n} (stereographic projection). Thus, S(S^{n-1}) \cong S^{n}.

    I recently have noticed that I find the double suspension theorem beyond my intuition. What do you think of it?
    Offline

    3
    ReputationRep:
    I have as yet only studied point-set topology, and am not well acquainted with algebraic topology, and know literally nothing about the theorem. I shall learn more of it next year, and for now am preliminarily reading about it (with such things as simplicial complexes and the euler characteristic.. I really haven't seen much!)
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Would you like to hibernate through the winter months?
    Useful resources

    Make your revision easier

    Maths

    Maths Forum posting guidelines

    Not sure where to post? Read the updated guidelines here

    Equations

    How to use LaTex

    Writing equations the easy way

    Student revising

    Study habits of A* students

    Top tips from students who have already aced their exams

    Study Planner

    Create your own Study Planner

    Never miss a deadline again

    Polling station sign

    Thinking about a maths degree?

    Chat with other maths applicants

    Can you help? Study help unanswered threads

    Groups associated with this forum:

    View associated groups
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

    Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

    Quick reply
    Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.