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Textbook to self teach 1st year undergrad maths? Watch

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    After self teaching a-level maths I was thinking of doing some further maths modules but I think I'd rather look at some undergrad stuff which focuses more on how mathematicians think and write etc.

    Can someone recommend a good book which is suitable for someone self learning and that has problems with answers I can try?

    Thanks
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    (Original post by Sceptical_John)
    After self teaching a-level maths I was thinking of doing some further maths modules but I think I'd rather look at some undergrad stuff which focuses more on how mathematicians think and write etc.

    Can someone recommend a good book which is suitable for someone self learning and that has problems with answers I can try?

    Thanks

    A calculus book sort of like this: https://www.amazon.co.uk/gp/product/...?ie=UTF8&psc=1 would be good. Undergrad books sometimes only have answers for even questions, and you have to buy a separate book for the odd answers though.
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    thanks will look into that

    (Original post by rayquaza17)
    A calculus book sort of like this: https://www.amazon.co.uk/gp/product/...?ie=UTF8&psc=1 would be good. Undergrad books sometimes only have answers for even questions, and you have to buy a separate book for the odd answers though.
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    Is there anything in particular you would like to learn about?
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    (Original post by Sceptical_John)
    After self teaching a-level maths I was thinking of doing some further maths modules but I think I'd rather look at some undergrad stuff which focuses more on how mathematicians think and write etc.

    Can someone recommend a good book which is suitable for someone self learning and that has problems with answers I can try?

    Thanks
    You can get quite a lot of textbooks online by typing 'pdf' after the book's title.

    I'd recommend:
    The Calculus Lifesaver
    Introduction to Set Theory
    Introduction to Algebra by Peter J. Cameron
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    (Original post by kkboyk)
    You can get quite a lot of textbooks online by typing 'pdf' after the book's title.

    I'd recommend:
    The Calculus Lifesaver
    Introduction to Set Theory
    Introduction to Algebra by Peter J. Cameron
    (Original post by spectral_theory)
    Is there anything in particular you would like to learn about?
    I'd like to avoid massive books (ie ones over 400 pages) as they are quite daunting and as I will be going fairly slow I want to see progress being made. Also I know you can probably get them free as pdf but it's nice to have the physical book I find for maths such as when flicking to the answers.

    Nothing in perticular but having a really good understanding of algebra would be good.
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    Anyone have experiance with these? They look appropiate.

    Springer Undergraduate Mathematics
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    (Original post by Sceptical_John)
    I'd like to avoid massive books (ie ones over 400 pages) as they are quite daunting and as I will be going fairly slow I want to see progress being made. Also I know you can probably get them free as pdf but it's nice to have the physical book I find for maths such as when flicking to the answers.

    Nothing in perticular but having a really good understanding of algebra would be good.
    Shorter books won't be much help and would lack a lot of explanations. With university level mathematics, you shouldn't try to rush and treat it like A-levels as you'll just end up far more confused than you were at the start (honestly, it takes time to understand what you are learning). Large textbooks really aren't that bad, provided you pick a good one that doesn't skip all the basics.

    The algebra book I mentioned is very good intro to abstract algebra, and does go into detail despite being short (though there are some topics that you won't cover until the 2nd yr).

    (Original post by Sceptical_John)
    Anyone have experiance with these? They look appropiate. Springer Undergraduate Mathematics
    I find them to be alright, but sometimes a little confusing, so I use it along with other books.
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    read or die

    https://marinazahara22.files.wordpre...s-wie-1975.pdf
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    Have you tried Mathematical Methods for Physics and Engineering by K.F.Riley ? Its pretty nice imho. Lots of problems and interesting stuff.
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    (Original post by Sceptical_John)
    After self teaching a-level maths I was thinking of doing some further maths modules but I think I'd rather look at some undergrad stuff which focuses more on how mathematicians think and write etc.

    Can someone recommend a good book which is suitable for someone self learning and that has problems with answers I can try?

    Thanks
    Have you tried MIT opencourseware? It has pretty good resources for mathematics.
    Some of the courses have solutions for the assignments.
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    (Original post by Sceptical_John)
    After self teaching a-level maths I was thinking of doing some further maths modules but I think I'd rather look at some undergrad stuff which focuses more on how mathematicians think and write etc.

    Can someone recommend a good book which is suitable for someone self learning and that has problems with answers I can try?
    As a "meta" comment: mathematics at university covers a huge range of topics, and different topics tend to have very different "feels" when it comes to 'thinking like a mathematician'.

    Because of this, you're not really going to find "one book" that covers even all the typical first year topics. You're also probably going to find that there are topics that you really struggle with, because they are so different from A-level. (Analysis seems to be one topic that many many undergraduates 'bounce' off at first - personally it was my favorite, so I don't totally get the reaction, but looking at forums etc. it's clearly a common one).

    For applied material (and applied material at university level is much more like A-level pure maths than you might expect) the "doorstop" maths methods books tend to be reasonably good and cover a reasonable spread of stuff (I used Arfken, but I'm sure there are others than people can recommend). You'll find a fair bit of stuff you don't want to cover, but also a fair amount of relevant stuff to the applied side of first year mathematics.

    Pure is definitely harder, and I think you'll basically need a book for each topic. Which topics you decide to cover can vary quite a lot: typically you might do some kind of linear algebra (matrices) course, some group theory, and some analysis. But other possibilities are complex methods (more geometry/algebra than contour integration), set theory, number theory, combinatorics (and lots more than aren't immediately coming to me).

    Probability is probably a third area that is going to need its own book if you do it.
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    This book is often recommended for people who want to get some insight into undergraduate mathematics prior to starting a degree. It does not go into any great depth though.

    https://www.amazon.co.uk/Concise-Int...dp_ob_title_bk
 
 
 
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