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Pure mathematics, where to begin?

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  • 12-04-2012 6:06am
    #1
    Squashie
    Registered Users Posts: 67 ✭✭


    Coming near the end of two B.Sc's at the moment, one in applied maths and the other in applied physics, I've become pretty accustomed to the applied aspect of mathematics by now. However I have little to no experience of pure mathematics and abstract reasoning and logic. I've shied away from it, avoided it, shrugged it off mostly until recently. It's only since reading about Principia Mathematica have I decided I'd actually like to understand more. I've no idea where to begin though? Where do people usually start with it? Topics to begin with? Textbooks? Papers to read? Basic proofs to read or work through? I'm used to following and understanding basic logic already lined, but I wouldn't know the first thing about formulating my own proof for something.
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    #2
    seandoiler
    Registered Users Posts: 107 ✭✭seandoiler


    simple book giving a basic overview "All the Mathematics You Missed: But Need to Know for Graduate School" By Thomas A. Garrity

    a fairly simple straight forward book that will give you a good overview of a number of different mathematical topics


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    #3
    equivariant
    Registered Users Posts: 966 ✭✭✭equivariant


    For the OP - how about something like http://www.amazon.com/Proofs-THE-BOOK-Martin-Aigner/dp/3540636986

    Its a beautiful book and if you want to learn about mathematical proof, one of the best things to do is to read and understand beautiful examples. Anyone with a degree in applied mathematics should be well equipped to read this book.

    Also a good introductory text on abstract algebra might be interesting for someone from an applied maths background looking to learn some pure mathematics. I'm sure that there is lots of stuff on that topic only a google search away


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    #4
    TheBody
    Registered Users Posts: 5,619 ✭✭✭TheBody


    As the poster above suggested, abstract algebra might be a good place to start. I recommend Topics in Algebra by I.N Herstein. It contains all the basics of Group theory, and Rings and Fields. Very accessible and contains problems to try. Excellent book.

    http://www.amazon.co.uk/Topics-Algebra-I-N-Herstein/dp/8126510188/ref=sr_1_4?ie=UTF8&qid=1334249981&sr=8-4


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