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Books for self-study in pure areas of mathematics

  1. Jan 1, 2010 #1
    Books for self-study in "pure areas" of mathematics

    Hi,
    I am starting an applied mathematics course this year at university. Unfortunately I don't have the option to study "pure" areas of mathematics, but I would like to learn more about them to become a more complete mathematician at the end of the course, as I understand that areas such as topology also have important practical applications and also because of my intelectual curiosity.

    Therefore I would like to know if you guys could recommend good books for self study in topology, graph theory, number theory and group theory, or any other "purer" area that I may be forgetting and you think is important/interesting.

    I like books that have many examples or worked problems but also present proofs. I recently studied linear algebra using Gilbert Strang's video lectures and David Poole's book, and I thought this was a good method and the syllabus was of sufficient depth and difficulty for my current conditions, so I believe this would be the level I am looking for (first years of undergradute school).

    Thanks for your help!
     
  2. jcsd
  3. Jan 1, 2010 #2
    Re: Books for self-study in "pure areas" of mathematics

    Here are a few books I used that I really liked and I think are suitable for self-study.

    If you want a nice, easy introduction to real analysis, I recommend Elementary Analysis by Ross. This is below the level of Rudin's Principles of Mathematical Analysis, but it's easy for self-study. It has hints and solutions in the back for proof problems. This book is also very cheap, which makes it nice.

    https://www.amazon.com/Elementary-A...=sr_1_1?ie=UTF8&s=books&qid=1262409298&sr=8-1

    For a more advanced analysis book, Carothers' Real Analysis is fantastic and it has a very different style than other books. I highly recommend it. I used this for self study of some more advanced analysis concepts.

    https://www.amazon.com/Real-Analysi...=sr_1_1?ie=UTF8&s=books&qid=1262409627&sr=1-1

    For Algebra (Groups, Rings, Fields), I really liked Abstract Algebra: An Introduction by Hungerford. For some reason, it's ridiculously expensive though. However, it has lots of examples and problems sorted by difficulty and it has hints in the back.

    https://www.amazon.com/Abstract-Alg...=sr_1_1?ie=UTF8&s=books&qid=1262409347&sr=1-1

    For topology, Munkres' text is great.
    https://www.amazon.com/Topology-2nd...=sr_1_1?ie=UTF8&s=books&qid=1262409466&sr=1-1

    If you have any interest in pursuing analysis, Kreyszig's Functional Analysis book is very easy and readable with tons of examples. The only background required is linear algebra and some analysis.

    https://www.amazon.com/Introductory...=sr_1_1?ie=UTF8&s=books&qid=1262409528&sr=1-1
     
    Last edited by a moderator: Apr 24, 2017
  4. Jan 3, 2010 #3
    Re: Books for self-study in "pure areas" of mathematics

    What do you currently know?
     
  5. Jan 3, 2010 #4
    Re: Books for self-study in "pure areas" of mathematics

    The most advanced things I know in calculus are integration by parts and partial derivatives, I know the basics of group theory and have a good knowledge of linear algebra, actually the whole content of Poole's Linear Algebra book, besides the usual high-school math.
    Ebolapox, thank you for your recommendations. I really liked the topology book and have access to it here in Brazil, so I think that issue is settled, but the other ones on algebra are too expensive and I don't have access to them, do you have any other recommendation?
    Regarding analysis, thanks for the books, but I will have this subject covered in college, so I don't need the books right now, but thank you anyway!
     
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