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    Hi there! My name's George and I'm a student going into year 12 with a particular interest in maths. I thought I'd jump on the current trend of these threads and create my own. I created two GYGs previously but they died due to lack of interest in my part. Hopefully this will not be subject to a similar fate.

    note: this OP is really unfinished

    Boring things
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    GCSEs: 7A*s, 3As (bio, chem, physics (oops)) and a B (french).
    A-level choices: maths (edexcel), further maths (edexcel), physics (edexcel), history (OCR)
    FM units: FP1, D1
    History units: Democracy and Dictatorships in Germany, Britain 1930-1997, Britain and Ireland






    My interests within mathematics
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    todo







    To do
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    to revise



    Where I'm thinking of applying
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    At the moment,
    • Cambridge - Maths - A*A*A+1,1 in STEP II/III
    • Warwick - Maths and philosophy - A*A*A
    • Bath - Maths - A*AB + 2 in any STEP or A*AA
    • UCL - Maths - A*AA + 1 in any STEP or A*A*A
    • Bristol - Maths and philosophy - A*AA

    ultimately I want to get into maths academia. grades wise I'd be going for A*A*A[A/B] but there's no point bothering myself at all atm

    Resources
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    • ProofWiki - an overlooked wiki documenting axioms, definitions, and theorems (and proofs thereof). Definitely worth checking out, considering that proof is often overlooked in high-school mathematics, despite most study of mathematics being vapid in its absence.
    • MathWorld - arguably the best online mathematics encyclopedia out there.
    • Brilliant
    • KhanAcademy
    • MSE
    • Quora
    • MIT OpenCourseware
    • Project Euler Plus - programming challenges specifically pertaining to mathematics. As opposed to "normal" ProjectEuler, ProjectEuler+ features a 1 minute time limit, and several hidden test cases.
    • /r/math - someone recommended this.
    • ArXiv @ Cornell- research papers
    • Paul's Online Maths Notes

    Specifically for maths exams/revision

    Anything that's not maths?
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    no







    people who wanted me to tag them
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    Lemur14, maybe Quizlet, and someone called Sonechka, don't know who she is or why she's interested.:erm:





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    Subbed at Odinspeed~
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    Omg I can't believe you tagged me :O cos that means you've finally shown a sine of acknowledging my existence! What progress(ion)! :heart:
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    (Original post by Sonechka)
    Omg I can't believe you tagged me :O cos that means you've finally shown a sine of acknowledging my existence! What progress(ion)! :heart:
    did you ask me to tag you just so you could make that horrifying pun
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    (Original post by _gcx)
    did you ask me to tag you just so you could make that horrifying pun
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    (Original post by _gcx)
    Resources
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    • ProofWiki - an overlooked wiki documenting axioms, definitions, and theorems (and proofs thereof). Definitely worth checking out, considering that proof is often overlooked in high-school mathematics, despite most study of mathematics being vapid in its absence. I've started contributing and I've probably just gave away what my username is and hence my username on one or two other sites. So much for keeping identities separate.
    • MathWorld - arguably the best online mathematics encyclopedia out there.
    • Brilliant
    • KhanAcademy
    • MSE
    • Quora
    • MIT OpenCourseware
    You have Quora on that list but you don't have Reddit. :confused:
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    (Original post by num.7)
    You have Quora on that list but you don't have Reddit. :confused:
    Yeah I suppose there's /r/6thform but I can't really think of any other useful subs but I'll add it when I get to it. Quora is actually quite good for maths though it does attract some particularly low quality answers.
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    (Original post by _gcx)
    Yeah I suppose there's /r/6thform but I can't really think of any other useful subs but I'll add it when I get to it. Quora is actually quite good for maths though it does attract some particularly low quality answers.
    /r/math, no?

    By the way, why do you have a passion for maths?
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    (Original post by num.7)
    /r/math, no?

    By the way, why do you have a passion for maths?
    i have never actually used /r/math so idk how useful it is.

    I find the subject legitimately interesting and I enjoy it a great deal. Maths is a subject like no other in many ways. Contained with it are some of the most beautiful and elegant one can observe.
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    (Original post by num.7)
    /r/math, no?

    By the way, why do you have a passion for maths?
    What is TSR's obsession with leddit.

    (Original post by _gcx)
    Hi there! My name's George and I'm a student going into year 12 with a particular interest in maths. I thought I'd jump on the current trend of these threads and create my own. I created two GYGs previously but they died due to lack of interest in my part. Hopefully this will not be subject to a similar fate.

    note: this OP is really unfinished

    Boring things
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    Show




    GCSEs: to not bother people with numbers, 7A*s, 3As (bio, chem, physics (oops)) and a B (french).
    A-level choices: maths (edexcel), further maths (edexcel), physics (edexcel), history (OCR)
    FM units: Not sure as of yet, hopefully FP1 and FM1. It could not get worse than FS1 and D1. If that happened, I'd probably bunk D1 lessons and do FP1 instead.
    History units: can't remember, will fill in when I find out





    My interests within mathematics
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    todo






    To do
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    Stuff I should really look in to
    • Modular Arithmetic
    • More differential equations
    • Group theory - know nothing about this field though I probably should.
    • More integral calculus, specifically line/surface/contour/multiple integrals. Started on the latter.
    • Applied maths in any sense whatsoever.


    Books
    Some guy gave me a few pdf books to go through as well as a link to an archive. (would link it, but it probably violates copyright etc.) Some of note are,
    • Rudin's Principles of Analysis, haven't even opened the pdf lol
    • Elementary Analysis by Ross, which is dedicated to real analysis. I've read a few chapters but admittedly not much.
    • Differential and Integral Equations by Collins, probably not going to be looking at this one in a while. Looks intimidating, and I doubt that I have much of the preliminary knowledge required.


    Aspirations
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    maths academia. grades wise I'd be going for A*A*AA but there's no point bothering myself at all atm





    Resources
    Spoiler:
    Show
    • ProofWiki - an overlooked wiki documenting axioms, definitions, and theorems (and proofs thereof). Definitely worth checking out, considering that proof is often overlooked in high-school mathematics, despite most study of mathematics being vapid in its absence. I've started contributing and I've probably just gave away what my username is and hence my username on one or two other sites. So much for keeping identities separate.
    • MathWorld - arguably the best online mathematics encyclopedia out there.
    • Brilliant
    • KhanAcademy
    • MSE
    • Quora
    • MIT OpenCourseware



    Anything that's not maths?

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    no






    people who wanted me to tag them,

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    Lemur14, maybe Quizlet, and someone called Sonechka, don't know who she is or why she's interested.:erm:




    It's a shame you don't want to do FP2, where you actually do group theory and number theory (mod arithmetic), fermat's little <3. I'm actually looking forward to it. Nice way to end A Level Further maths - actually doing fun stuff. I'm just not 100% sure if my school offer it (they really should).

    I was scrolling through what's in cambridge course and found the lecture notes for IA groups. The first chapter is surprisingly quite accessible. As I got towards the end of the first chapter, I just got confused and left it there, Past the first chapter, I don't know what the **** is going on . But I like the way it sets out everything and proves results immediately and is quite concise and dense. If you want to get a grip on group theory (and non-applied modular arithmetic), I would recommend the first 80% of the first chapter on that link. You've given a lot of resources, so I feel as if I have to give one to you.

    The prospect of academia never really appealed to me. But maybe that'll change.

    Good luck with your hopefully somewhat remarkable ventures.

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    I found your old thread where you said you want to do Compsci? Is that still the case :P?

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    (Original post by Eulogy)
    What is TSR's obsession with leddit.



    It's a shame you don't want to do FP2, where you actually do group theory and number theory (mod arithmetic), fermat's little <3. I'm actually looking forward to it. Nice way to end A Level Further maths - actually doing fun stuff. I'm just not 100% sure if my school offer it (they really should).

    I was scrolling through what's in cambridge course and found the lecture notes for IA groups. The first chapter is surprisingly quite accessible. As I got towards the end of the first chapter, I just got confused and left it there, Past the first chapter, I don't know what the **** is going on . But I like the way it sets out everything and proves results immediately and is quite concise and dense. If you want to get a grip on group theory (and non-applied modular arithmetic), I would recommend the first 80% of the first chapter on that link. You've given a lot of resources, so I feel as if I have to give one to you.

    The prospect of academia never really appealed to me. But maybe that'll change.

    Good luck with your hopefully somewhat remarkable ventures.

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    I found your old thread where you said you want to do Compsci? Is that still the case :P?




    I doubt that my school will offer FP2. That's fair enough I suppose, though, as it comprises almost solely new content, and hence would be intimidating for schools to teach, preferring the more familiar content of FM1/FS1 etc., unless a school previously taught OCR MEI I suppose. It would be a pain in the arse to convince my school to enter me for FP2, so if I end up doing FP1/FM1 I wouldn't be too fussed, though I probably will be learning the content.

    I've had a brief skim over those notes and I do very much appreciate the inclusion of proofs. Not sure if I've really talked about it here, but the lack of rigour and proof in A-level/GCSE mathematics really grinds my gears because it encourages mindless computation and memorisation as opposed to actual maths. Yeah I'll be working on the resource list a bit more when more pop to mind.

    Academia is the only thing that I can envisage doing right now but that may well change through the course of a-level/uni. Thank you, good luck in yours too

    Yeah I kind of abandoned compsci. I was originally shooting for a maths and compsci degree, but I found myself becoming more interested in maths. Learning to program was too slow-paced for me, and I ended up losing interest unfortunately.
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    Update 1 (I guess?)

    Tomorrow is enrolment day, and I can imagine my chemistry and physics teachers both being particularly disappointed that I didn't get an A* in their respective subjects, that only hit me recently lol. I also failed to do any further reading in physics as I planned to, so I can expect an unforgiving lecture. At least I'm pretty set on my options now, unless I have a sudden revelation, or I'm suddenly told that I can take RS/philsophy at a partner school despite no contact in regards to that for 8 months or so.

    Now the slightly less (or immensely more, depending on how you're inclined) boring stuff,

    Differential Equations

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    Still haven't read any of the pdf books that I have on hand, but I did introduce myself to Laplace Transforms, through KhanAcademy, and applied it to a few examples. (though I just used symbolab to get the inverse transforms, not sure of any other way to obtain them bar prior knowledge or a transform table) Though, I did stumble across some strange "function" through doing \mathcal L^{-1} \left\{\exp(-s)\right\}, \delta, which behaves in a particularly confusing but interesting manner, though not technically a function.

    Resources


    Fourier series'
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    When I was looking at proofs for \zeta(4), and \zeta(2) on MSE I stumbled across Fourier series'. In brief, it's a series expansion of a function that consists of trigonometric functions. They're quite nifty to derive, not too hard either, though ProofWiki surprisingly didn't document any of them, (particularly odd because they're quite useful in proofs) bar a definition, so I added a few, with proofs for 2. I suppose not particularly interesting to most people, but I like them.

    Resources


    tagging people who might be vaguely interested,

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    You're passion for maths is amazing. We're taking the same A levels apart from history swapped with chemistry for me. Could you tag me in your future posts? I'm looking forward to following
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    (Original post by Tormund)
    You're passion for maths is amazing. We're taking the same A levels apart from history swapped with chemistry for me. Could you tag me in your future posts? I'm looking forward to following
    I was originally going to take maths, further maths, physics and chemistry, but seeing as I got nearly full UMS in history, I was compelled to take it at A-level. I do hope that it's not a boring slog however. I can always swap to chemistry if it's too boring. Yup, sure!
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    Update 2

    Not a productive day at all by any means. I finally confirmed my options, so I'm definitely doing maths, further maths, physics and history. I should find what units I'm doing for further maths and history shortly into the term. I seem to remember Nazi Germany and Ireland with history, but the further maths units were not decided the last I spoke with my teacher, Let's just hope that it's a tolerable combination. I was originally planning to do RS as my fourth subject, so I put it down back in like, February, but I received no contact in regards to it since then. Apparently the partner school didn't get enough students to run it, but they didn't actually tell me until I went to finalise my choices. Loving the organisation on the part of my school :rofl: In regards to work, I did quite little.

    Maths
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    I hoped to actually make some headway on group theory, but I just didn't I looked at the basic definition of a group, then group axioms and then shortly got distracted on YouTube. Not at all satisfied, certainly not enough knowledge to do anything of substance :rofl: Did a piss easy proof of \sum_{n \ge 0} (2n + 1)^{-2} = \pi^2/8 using the Fourier series of |x| for proofwiki, but that's about it as far as maths goes. I really should be doing more.

    Resources


    And that's pretty much it. Briefly looked over the physics spec just to say that I have actually looked at some physics. I also need to actually finish the OP at some point.

    tags,

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    (Original post by _gcx)
    Update 2

    Not a productive day at all by any means. I finally confirmed my options, so I'm definitely doing maths, further maths, physics and history. I should find what units I'm doing for further maths and history shortly into the term. I seem to remember Nazi Germany and Ireland with history, but the further maths units were not decided the last I spoke with my teacher, Let's just hope that it's a tolerable combination. I was originally planning to do RS as my fourth subject, so I put it down back in like, February, but I received no contact in regards to it since then. Apparently the partner school didn't get enough students to run it, but they didn't actually tell me until I went to finalise my choices. Loving the organisation on the part of my school :rofl: In regards to work, I did quite little.

    Maths
    Spoiler:
    Show




    I hoped to actually make some headway on group theory, but I just didn't I looked at the basic definition of a group, then group axioms and then shortly got distracted on YouTube. Not at all satisfied, certainly not enough knowledge to do anything of substance :rofl: Did a piss easy proof of \sum_{n \ge 0} (2n + 1)^{-2} = \pi^2/8 using the Fourier series of |x| for proofwiki, but that's about it as far as maths goes. I really should be doing more.

    Resources


    And that's pretty much it. Briefly looked over the physics spec just to say that I have actually looked at some physics. I also need to actually finish the OP at some point.

    tags,

    You've done so much work for maths, it's really making me feel inadequate. I got my timetable today though so I know when my frees are so perhaps I can somewhat get caught up

    Your post made me realise that this emoticon :rofl: wasn't someone drinking coffee. I feel so stupid.
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    (Original post by Tormund)
    You've done so much work for maths, it's really making me feel inadequate. I got my timetable today though so I know when my frees are so perhaps I can somewhat get caught up

    Your post made me realise that this emoticon :rofl: wasn't someone drinking coffee. I feel so stupid.
    It's just because I read ahead in my free time, because in the end maths is a hobby of mine. That's why I've read so far ahead, it doesn't really reflect my ability. I don't see how :rofl: could possibly look like a person drinking coffee but ok :rofl: I have done absolutely zilch today so I won't be posting an update today. Probably tomorrow after my first day.
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    I've been working on FP1 notes/a guide (old FP3) with the intention on putting them (though they're not done yet) on here so do let me know if you'd be interested, similar to what I would've done if that guide idea passed in f31 a few weeks ago. I'll just need to ensure that they're actually useful beforehand lol. I probably should be spending my time elsewhere but oh well, I don't really have much work to do yet, and I thought I'd make myself useful. If people find it useful I'll make more, for the compulsory core unit. A full update will come when I can be bothered.

    Tagging people who I think are doing further maths

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    Sonechka Lemur14 num.7 Tormund DeepInTheMeadow (as you've added me to your tag list I thought I'd add you to mine )


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    (Original post by _gcx)
    I've been working on FP1 notes/a guide (old FP3) with the intention on putting them (though they're not done yet) on here so do let me know if you'd be interested, similar to what I would've done if that guide idea passed in f31 a few weeks ago. I'll just need to ensure that they're actually useful beforehand lol. I probably should be spending my time elsewhere but oh well, I don't really have much work to do yet, and I thought I'd make myself useful. If people find it useful I'll make more, for the compulsory core unit. A full update will come when I can be bothered.

    Tagging people who I think are doing further maths

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    Sonechka Lemur14 num.7 Tormund DeepInTheMeadow (as you've added me to your tag list I thought I'd add you to mine )



    Yay, nice to see you have a thread! (They're really becoming like a thing this year, aren't they?) And yes, please add me to your tag list, it'll make me feel better about spamming you with daily posts
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    (Original post by DeepInTheMeadow)
    Yay, nice to see you have a thread! (They're really becoming like a thing this year, aren't they?) And yes, please add me to your tag list, it'll make me feel better about spamming you with daily posts
    Yeah, my previous two attempts were really too dry for me to really keep up. I didn't end up doing nearly as much revision as I imagined that I'd do, and that shows in the sciences, but it wasn't too bad for cramming. I shall! I might start writing an update now though admittedly I've been neglectful this weekend.
 
 
 
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