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A Summer of Maths (ASoM) 2016

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    (Original post by Alex:)
    It's good that you're interested in group theory though. I found groups to not be interesting early on, since I'm more of an analysis person. Groups pop up everywhere, which is why we learn about them.. For instance, Lie groups I quite like, as they are groups and differentiable manifolds, so it has all group properties and you can do analysis on them.
    Oh yea haha a family friend gave me a quick 1 hour condensed intro into Lie groups and tangent bundles and their links to Jacobians and stuff like that. Pretty hard to take it in that time though But yeah I love group theory and enjoy analysis, but have little experience with the latter.

    So you study these areas im guessing?
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    Is there a thread like this for commoners like UCL applicants and even Bath applicants?
    More seriously, I wanted to ask how much time a day or better a week is best to be invested in self study to keep the brain active for the summer? I am keeping the remainder of July free from thought but almost 2 weeks in of no maths and I begin reading analysis books before bed (30 mins or so) and worrying about the difficulty of 1st year at uni; August though I plan to start taking notes alongside reading and some exercises.
    Book I am using is A (so called) Straighforward approach to Analysis by KGB (I also have A first course in Mathematical Analysis but it seems a bit too advanced for myself right now; also a bunch of PDF's of notes from different Unis)
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    (Original post by 130398)
    Is there a thread like this for commoners like UCL applicants and even Bath applicants?
    More seriously, I wanted to ask how much time a day or better a week is best to be invested in self study to keep the brain active for the summer? I am keeping the remainder of July free from thought but almost 2 weeks in of no maths and I begin reading analysis books before bed (30 mins or so) and worrying about the difficulty of 1st year at uni; August though I plan to start taking notes alongside reading and some exercises.
    Book I am using is A (so called) Straighforward approach to Analysis by KGB (I also have A first course in Mathematical Analysis but it seems a bit too advanced for myself right now; also a bunch of PDF's of notes from different Unis)
    Im pretty sure being a UCL/Bath applicant doesnt make you a commoner, the thread is for anyone who wants to do maths
    I use that Binmore book too, nice style.
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    (Original post by EnglishMuon)
    Im pretty sure being a UCL/Bath applicant doesnt make you a commoner, the thread is for anyone who wants to do maths
    I use that Binmore book too, nice style.
    And how many hours do you spend on it? And do you go by step, i.e. Do you go chapter by chapter, in order or pick what you prefer?
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    (Original post by EnglishMuon)
    Oh yea haha a family friend gave me a quick 1 hour condensed intro into Lie groups and tangent bundles and their links to Jacobians and stuff like that. Pretty hard to take it in that time though But yeah I love group theory and enjoy analysis, but have little experience with the latter.

    So you study these areas im guessing?
    My interests lie mainly in PDEs, differential geometry and analysis. I don't usually get to do any abstract algebra apart from Lie groups. You could probably pick up a text on real analysis right now. It'll give you a nice head start into understanding epsilon-delta proofs.
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    (Original post by 130398)
    And how many hours do you spend on it? And do you go by step, i.e. Do you go chapter by chapter, in order or pick what you prefer?
    You should definitely take a look at "How to Think Like a Mathematician" by Houston, which would answer most of your questions about self-studying uni maths. You can pick out whichever chapter you want from this book, but in general, any kind of rigorous, university level mathematics textbook should be read chapter by chapter, unless you are comfortable with the material. More often than not writers like structuring the chapters in order that would best fit the student that is reading them, a prime example of this is Beardon's textbook on V&M and GT where he starts with an introduction of groups and connect it to points made in linear algebra later on. However, chapters that deal with concepts such as, for example, Möbius transformations in Beardon's "Algebra and Geometry" textbook are only used to show you the applications of what is currently being learnt; and thus some textbooks, whose main purpose is to give the fundamentals of a particular course, could use different examples, or may even omit such applications of the theory as a whole.

    I am not sure about others, but I usually self-study for about 5-8 hours, but it heavily fluctuates. Yesterday I managed 8 hours and a half, but the day before that I only did 4 hours. Either way, I would recommend you to take a look at Houston's textbook and manage your time as you wish. Don't look at other people since it solely depends on you, and take it into account that most people do not have any prerequisite knowledge of the material taught at university before October, so you should only decide to self-study if you are really eager to start early. Also, don't think of relaxing during the summer and not doing mathematics as something unproductive, it is important that you do not get 'burnt out' of mathematics before you even start to do 'actual' mathematics.
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    (Original post by 130398)
    And how many hours do you spend on it? And do you go by step, i.e. Do you go chapter by chapter, in order or pick what you prefer?
    Yeah basically what insight said. But if you are starting looking at a completely new topic Id recommend reading the chapters in order until you have a good feel for it (especially the first few ones). and timewise probably upto 8 hours . Basically stop if you feel you arent making much progress due to tiredness etc.
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    Any other dirty physmos looking at dynamics and relativity? (Doing like 45 min a day, don't know how you lot work like five hours a day.)


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    (Original post by Krollo)
    Any other dirty physmos looking at dynamics and relativity? (Doing like 45 min a day, don't know how you lot work like five hours a day.)


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    "8 hours work"= 45 mins work + 7h45 procrastination
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    (Original post by EnglishMuon)
    "8 hours work"= 45 mins work + 7h45 procrastination
    "45 minutes work" = 10 minutes worm + 35 minutes watching Fleabag and getting a magnum

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    (Original post by Krollo)
    Any other dirty physmos looking at dynamics and relativity? (Doing like 45 min a day, don't know how you lot work like five hours a day.)


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    I was going to do D&R during summer, but was told it is best to self-study the fundamentals of high-level mathematics first, so I chose to do V&M and Groups during summer. How are you finding D&R so far? I don't think the content itself requires VC, but the example sheets do seem to include divergence and what not.

    On a side note, are you planning on taking Maths with Physics at Cambridge?
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    (Original post by Krollo)
    "45 minutes work" = 10 minutes worm + 35 minutes watching Fleabag and getting a magnum

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    Id like to see how you spend your 10 minutes worm. Could be quite interesting
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    (Original post by EnglishMuon)
    Id like to see how you spend your 10 minutes worm. Could be quite interesting
    I haven't been on TSR for a while, how is part IA doing? You are working through Beardon's textbook right?
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    (Original post by Insight314)
    I haven't been on TSR for a while, how is part IA doing? You are working through Beardon's textbook right?
    ah yea I was wondering how you were doing the other day . but yeah its great so far! A bit of bad hay fever seemed to reduce my thinking abilities for the first few days but been much better after I realised waking up early helps for some reason . and yea its the beardon I've been going through, been a bit distracted GT though as its so nice. I skipped the section on spherical geometry though, it seemed like one of those topics that'll be more useful for geometry later on but not too important for the other material in the book but idk.
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    (Original post by EnglishMuon)
    ah yea I was wondering how you were doing the other day . but yeah its great so far! A bit of bad hay fever seemed to reduce my thinking abilities for the first few days but been much better after I realised waking up early helps for some reason . and yea its the beardon I've been going through, been a bit distracted GT though as its so nice. I skipped the section on spherical geometry though, it seemed like one of those topics that'll be more useful for geometry later on but not too important for the other material in the book but idk.
    Yeah, I've been pretty busy lately with maths and social life (finally managed to get one) so I haven't been that active on TSR. Definitely gonna be here for results day though!

    I also find Groups pretty nice, I even decided to casually read through (not doing exercises or taking notes) of "A First Course in Abstract Algebra" by Fraleigh, which is a pretty good one on Groups and it even goes in depth with rings, field theory and Galois theory. Definitely recommend it if you are the 'abstract algebra' type. It also has way more exercises than Beardon's after each chapter (one of the reasons I got it), and the only downside to it is that it is not written in LATEX (pretty old one). I am either going to start working through rings and fields from this textbook, or do some Analysis I from Burkill's textbook, after I finish Beardon's. Probably gonna do the former since I am really starting to like abstract algebra, and Analysis I is only in Lent term.

    I don't think spherical geometry is that important, you are right. I really liked it, but I had a bit of trouble with some theorems so gonna have to read through my notes in detail at some point. Are you currently on 'Quaternions and Isometries'? What do you think of quaternions? I had so much fun with them!
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    (Original post by Insight314)
    ...
    Yeah Ive been enjoying quaternions, but I prefer doing it all in terms of the previous group theory stuff and then going back to beardon to get the general ideas refreshed
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    (Original post by EnglishMuon)
    ah yea I was wondering how you were doing the other day . but yeah its great so far! A bit of bad hay fever seemed to reduce my thinking abilities for the first few days but been much better after I realised waking up early helps for some reason . and yea its the beardon I've been going through, been a bit distracted GT though as its so nice. I skipped the section on spherical geometry though, it seemed like one of those topics that'll be more useful for geometry later on but not too important for the other material in the book but idk.
    Spherical geoemtry is IB geometery i think.
    Do not skip, geometry is the best.


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    (Original post by physicsmaths)
    Spherical geoemtry is IB geometery i think.
    Do not skip, geometry is the best.


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    3 different spellings of geometry right there.

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    I feel like i should get some sleep

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    (Original post by Krollo)
    3 different spellings of geometry right there.

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    I feel like i should get some sleep

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    Lol I think im actually retarded.
    ****ing hell. My soelling has gotten even worse. All in two sentences.


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    (Original post by Krollo)
    3 different spellings of geometry right there.

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    I feel like i should get some sleep

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    Dorpus.
    Need not evaluate anything else.


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