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Book similar to Basic Mathematics by Serge Lang

  1. Sep 29, 2011 #1
    Book similar to "Basic Mathematics by Serge Lang"

    I'm looking for a good book for my son, who wants to be a mathematician like me. He is totally into mathematics!

    Basically what I need is a "Apostol or Spivak for High School Math". What I mean is: I need a "rigorous mathematician's book".

    I think that "Basic Mathematics by Serge Lang" would be perfect, since I could take a look at it's table of contents and first pages at Amazon, but I cannot find it here in my country.

    Does anybody knows similar books?

    THANKS!
     
  2. jcsd
  3. Oct 7, 2011 #2
  4. Nov 21, 2011 #3
    Re: Book similar to "Basic Mathematics by Serge Lang"

    bump cuz i am wondering the same thing. Are there any books that treat high school math "rigorously"? I am taking calculus next semester and I want to get a very strong understanding on all the topics leading up to it while also gaining exposure to rigourous math in preparation for proof-based courses down the road.

    I have Lang's Basic Mathematics, do you think it fits the bill? Any other books that meet my criteria?
     
  5. Nov 22, 2011 #4

    mathwonk

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    Re: Book similar to "Basic Mathematics by Serge Lang"

    i would suggest the 1955 edition of allendoerfer and oakley as much better than lang. but they assume some of the basic math lang covers. so it depends how basic you want your book to be. If you want material more elementary than A and O, gelfand's book Algebra is also very basic and seems much better written than lang's book. lang was a brilliant man but he wrote his books generally very carelessly, just the opposite of gelfand and others of the russian school of mathematics, where outstanding exposition is the norm.
     
  6. Nov 22, 2011 #5
    Re: Book similar to "Basic Mathematics by Serge Lang"

    Thanks mathwonk. My library has the 1955, 1963, and 1963 versions of Principles of Mathematics. Do you believe the 1955 version to be the best?

    Also, the sole review on amazon describes the book's content as "assorted fun topics in the theory of functions as well as good stuff on sequences and series." Are those the crucial topics of high school math? I was hoping to build a strong understanding of all things that should be known before starting calculus while also getting introduced to the rigorous style that will be used in later math classes. (one of my loftier goals is to eventually be able to work my way through spivak :shy:)

    I trust your opinion way more than that reviewers for obvious reasons, but I still wanted to make sure the book fits what I'm looking for.


    Edit: It doesn't have to be just 1 book either thanks to how long christmas break is in college!
     
    Last edited: Nov 22, 2011
  7. Nov 22, 2011 #6

    mathwonk

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    Re: Book similar to "Basic Mathematics by Serge Lang"

    i used the 1955 edition myself and liked it. usually the earliest edition of a good book is the best.

    this book goes well beyond what used to be taught in hugh school, and is excellent prep for spivak. it cannot be read over even a long xmas break, but contains plenty for a long year course. the logic at the beginning is one of the best parts, and is usually missing in many high school preparations. the complex numbers are clearly explained, another valuable topic.


    say, you might enjoy euler's elements of algebra, free on the web. there is no magic choice, the one that you enjoy and feel connected to is the one for you. math is not a list of topics but an experience of motivation and communication. the one that has you thinking about the concepts afterwards and wanting to know more is the one you want. euclid's elements is also quite wonderful.


    look on my webpage for some free stuff. you might appreciate my epsilon camp notes and my math 4000 notes there.
     
  8. Nov 22, 2011 #7
    Re: Book similar to "Basic Mathematics by Serge Lang"

    Thank mathwonk, but if I can't finish the book over winter break do you still think it would prepare me for calculus? I am taking that in the spring and I have a really weak high school math background that I wanted to strengthen over winter break so i don't fail...
     
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