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A Summer of Maths (ASoM) 2016 Watch

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    I've seen a lot of book requests on this thread, so here are three lists that I've found helpful:
    Undergraduate mathematics bibliography.
    How to become a pure mathematician.
    Archived pure mathematics for grad school.

    There's probably a few people who want to get a head start in maths at university, or don't want to go to university and want to study maths themselves or just want to know what they actually learn. I'd say the bottom line should be:
    • Calculus: vector calculus, ordinary and partial DEs
    • Analysis: real analysis, complex analysis
    • Algebra: linear algebra, abstract algebra
    • Geometry/Topology: point-set topology, differential geometry.
    • Other things you might consider: number theory, combinatorics, logic and all of the applied areas.
    All of this grounds you for more advanced maths. For instance in analysis, this includes: measure theory, probability theory, functional analysis, fourier analysis and PDEs.
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    (Original post by physicsmaths)
    I guess more different questions is what he wants rather then redoing them.Me personally will be doing oxford **** when i get around to it. Maybe Imperial if they are online. Then cambridge ones if i get in.
    chat **** get banged
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    (Original post by Gome44)
    chat **** get banged
    Come at me blud.
    Decked in one blow.


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    I've been quietly stalking this thread for a few weeks now, but most of what you guys are talking about is way beyond me

    What would you recommend is a good way to get into some of this stuff?
    My background is A level Maths and 1st year Physics at York
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    (Original post by l1lvink)
    I've been quietly stalking this thread for a few weeks now, but most of what you guys are talking about is way beyond me

    What would you recommend is a good way to get into some of this stuff?
    My background is A level Maths and 1st year Physics at York
    What topics are you interested in?


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    (Original post by l1lvink)
    I've been quietly stalking this thread for a few weeks now, but most of what you guys are talking about is way beyond me

    What would you recommend is a good way to get into some of this stuff?
    My background is A level Maths and 1st year Physics at York
    I'm assuming you've met basic single-variable calculus at A-level and multi-variable or vector calculus in your physics course, as well as complex numbers and introductory differential equations.

    If you then get comfortable with linear algebra and real analysis, that opens a huge amount of topics for you. Partial differential equations is the obvious one, but related to that is calculus of variations which is used in Hamiltonian mechanics and Fourier analysis which is like everywhere in physics. Differential geometry is the language of general relativity; group theory is used in quantum theory; probability theory in statistical mechanics.
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    (Original post by drandy76)
    What topics are you interested in?
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    Really, I don't know, whatever is somewhat more 'beginner' maybe?

    (Original post by Alex:)
    I'm assuming you've met basic single-variable calculus at A-level and multi-variable or vector calculus in your physics course, as well as complex numbers and introductory differential equations.

    If you then get comfortable with linear algebra and real analysis, that opens a huge amount of topics for you. Partial differential equations is the obvious one, but related to that is calculus of variations which is used in Hamiltonian mechanics and Fourier analysis which is like everywhere in physics. Differential geometry is the language of general relativity; group theory is used in quantum theory; probability theory in statistical mechanics.
    So, where would you recommend I start with linear algebra and real analysis?
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    (Original post by l1lvink)
    Really, I don't know, whatever is somewhat more 'beginner' maybe?



    So, where would you recommend I start with linear algebra and real analysis?
    Heard numbers and sets is meant to be comparatively easy


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    (Original post by drandy76)
    Heard numbers and sets is meant to be comparatively easy


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    Alright, are there any good resources that you can recommend for those?
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    (Original post by l1lvink)
    Alright, are there any good resources that you can recommend for those?
    1st page has some Cambridge notes on them, the Dexter ones, haven't gone through them myself so not too certain of the quality however


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    (Original post by drandy76)
    Heard numbers and sets is meant to be comparatively easy


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    Recommending N&S to a 1st Year Physics student? I think it's better for him to start with something like V&M or Groups which is also comparatively easy, and yet fundamental to both pure and applied mathematics.

    (Original post by l1lvink)
    So, where would you recommend I start with linear algebra and real analysis?
    Dexter's notes on V&M and Groups:
    V&M: https://dec41.user.srcf.net/notes/IA...d_matrices.pdf
    Groups: https://dec41.user.srcf.net/notes/IA_M/groups.pdf

    There are some mistakes in the lecture notes, if you are really troubled by that, or just prefer to study from a textbook, most of us in this thread (who are working through V&M and Groups) are studying from Beardon's "Algebra and Geometry" which covers both courses.

    V&M covers the basics of linear algebra, and Groups gives an introduction into abstract algebra. If you want to get familiar with real analysis, you can work through Dexter's corresponding lecture notes (https://dec41.user.srcf.net/notes/IA_L/analysis_i.pdf) or get the book "A First Course in Mathematical Analysis" by Burkill which is a highly recommended reading for the Analysis I course in IA of the Tripos.
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    (Original post by drandy76)
    1st page has some Cambridge notes on them, the Dexter ones, haven't gone through them myself so not too certain of the quality however
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    They are good but quite a bit of typos/mistakes in them. Unless buying/borrowing a textbook is a problem, I would recommend to work through a textbook over Dexter's lecture notes. I feel like textbooks explain the content better, and they also contain exercises which are fundamental in understanding the material in depth.
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    Thanks a lot for the suggestions, I'll have a look at them

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    Has anyone else noticed how many typos Beardon's textbook has?
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    (Original post by Insight314)
    Has anyone else noticed how many typos Beardon's textbook has?
    yes, they're a few. any particularly bad ones you've noticed?
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    What should I study if I want to make my life as easy as possible next year?
    I'll be going to imp if it matters
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    (Original post by KFazza)
    What should I study if I want to make my life as easy as possible next year?
    I'll be going to imp if it matters
    anything you're interested in really. probably number theory is the most basic to start off with.
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    Anyone know of some good questions on Cayley's theorem? (In particular its implications/ on the theorem "If  G is a group,  H a subgroup of  G , and  S is the set of all right cosets of  H in  G , then there is a homomorphism  \theta of  G into  A(S) and the kernel of  \theta is the largest normal subgroup of  G which is contained in  H ".
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    (Original post by EnglishMuon)
    Anyone know of some good questions on Cayley's theorem? (In particular its implications/ on the theorem "If  G is a group,  H a subgroup of  G , and  S is the set of all right cosets of  H in  G , then there is a homomorphism  \theta of  G into  A(S) and the kernel of  \theta is the largest normal subgroup of  G which is contained in  H ".
    I am not sure if this is what you are looking for, but I have quite a few on isomorphisms (not sure if they include isomorphisms on a group of permutations though).

    Name:  ImageUploadedByStudent Room1470244480.918540.jpg
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    Name:  ImageUploadedByStudent Room1470244514.061150.jpg
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    Start from 7.6 since the first ones are a bit too basic for you.

    These exercises are from an old textbook so tell me if you don't understand the notation that Fraleigh has used.


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    (Original post by EnglishMuon)
    yes, they're a few. any particularly bad ones you've noticed?
    Not really, most of them are not that fatal but it is a bit irritating to have typos on definitions and theorems.
 
 
 
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