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Apostol or Spivak?

  1. Dec 15, 2006 #1
    I own both volumes of Apostol, but I must confess that when I bought them I had never heard of Spivak's book. I think it's pretty much a toss up for me now. What about you guys?
     
  2. jcsd
  3. Dec 15, 2006 #2

    verty

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    If you own both volumes, read them.
     
  4. Jan 4, 2007 #3
    heh, you guys misunderstood me. I've already taken my calculus courses, and use both Apostol and Spivak from time to time to refresh my memory and learn new stuff. The question was, which one do YOU prefer?
     
  5. Jan 4, 2007 #4

    morphism

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    I like both so much it's hard to decide which I like more. :smile:
     
  6. Jan 4, 2007 #5

    mathwonk

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    i have taught most of the way through spivak and i and the clas really enjoyed it. as i did so i began to realize some of his proofs were roughly the same as the ones in courant, but written up in a much more accessible and fun style.

    spivak is a ntural born teacher of tremendous ability and it comes LL THE WAY THROUGH IN HIS BOOK.

    apostol i got into later, and began to aPPRECIATE it for the niceties of some arguments. it is very very scholarly and precise, but a bit eccentric in order of rpesentation. it is a superb work and since you already know calculus, should serve you very well.

    apostol is relatively dry comopared to the fun of spivak, but ok for serious advanced students. one of my friends took beginning calc from apostol at MIT and loved it.

    As one of wine dealers said when asked to choose betwen two fine wines "you are asking me to choose between my father and my mother!".

    so there is no way really to prefer one to the other except by personal taste. I enjoy owning both, and also courant, hardy, goursat, and dieudonne!

    great books are uniquely different from each other enough not to be interchangeable, but any one is also sufficient.
     
  7. Jan 4, 2007 #6
    I have only seen Spivak but one problem with Spivak is that he dosen't provide all the solutions to his problems. In general why is more and more authors not providing full solutions to all questions?
     
  8. Jan 4, 2007 #7

    mathwonk

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    my dad used to have a book of riddles and he would not let us see the answers when he read the riddles to us. i think its the same principle. something to hold over your head.
     
  9. Jan 4, 2007 #8

    morphism

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    When I first started reading Apostol I found it dry and switched to Spivak instead, which was more enjoyable as mathwonk says. But a year or so later I began appreciating Apostol's style - so much so I used his analysis text when I did my first real analysis course.
     
  10. Jan 4, 2007 #9

    symbolipoint

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    from Mathwonk:
    What level of Calculus were you teaching when you used this Spivak book? How does it compare the (don't get upset at me...) the Larson & Hostetler undergraduate Calculus book and the Salas & Hill undergraduate Calculus book?

    Symbolipoint
     
  11. Jan 4, 2007 #10

    mathwonk

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    i dont know the hostetler book, but salas and hille is excellent. but spivak is uniquely fun and inspired, much different in flavor from salas hille.
     
  12. Jan 5, 2007 #11
    i think if you studied calculus before, the Apostol is better for review the calculus. buti think spivak's problems is normal and better.

    but i think if anyone wants to learn Calculus the stewart's books for some reasons and in my experience is the best. if you do all the problems, you can see that most of the top universities picked up it. but Apostol is good for any who wants to review and be more exact means that Apostol 's books is suitable for math students mostly, and has a unique subject order.
     
    Last edited: Jan 5, 2007
  13. Jan 5, 2007 #12
    Is it better to not know how to do a problem after spending ages on it or read a bit of the answers in the hope of receiving some clue.

    Also its good to confirm that you got the right answer - espeically if you are not a confident student.

    Also the suggested answers might be different and more likely better than what the student has done so it would be good to see the author's thinking process.

    I have the habit of not doing a problem if the answer isn't immediately avaliable in the fear of not being able to do a problem and not getting to see the solution.
     
  14. Jan 5, 2007 #13

    mathwonk

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    fear (often of embarrassment or failure) is a big enemy of learning. keep fighting it.

    there is almost no limit to what we can do when we RE NOT AFRAID TO TRY.
     
  15. Jan 5, 2007 #14
    I think Apostol isn't THAT dry. I mean, you learn to like it. Oh, and there's a problem in the part of induction that just cracks me, I laughed so hard when I read it. (The "suggestion" made me laugh for about an hour.) I transcribed it for your enjoyment:

    LOL, induction is alright, but go get a GIRL!
    (I know I know, I laugh at stupid things.)
     
  16. Jan 5, 2007 #15
    In books with large numbers of problems its quite commmon to find mistakes in the solutions, its better to learn how to analyze your solution to determine how correct it is.

    So sometimes the author's put in fewer solutions, just so they can check the solutions over a bit more.
     
    Last edited: Jan 5, 2007
  17. Jan 5, 2007 #16
    eGuevara, is that proof really given by Polya?

    I know its meant to be a joke but it is a wrong illustration of proof by induction - there is a fundalmental error.

    In proof by induction one must show in general k=>k+1 for any k

    In the proof it had "The step from k to k+1 can be illustrated by going from n = 3 to n = 4." This is fundalmentally wrong!? Just because it works going from n=3 to n=4 dosen't mean it will go from n=45 to n=46. So the corollary and theorem is logically wrong!?

    Even though its a joke, It might mislead people into thinking this is really how a proof by induction works. I don't find this point funny.
     
    Last edited: Jan 5, 2007
  18. Jan 5, 2007 #17

    Hurkyl

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    pivoxa15: it's simply a more advanced version of "Find the mistake in this attempted proof that 0 = 1" type problems. (incidentally, the method in the inductive step does work from 45 to 46)
     
    Last edited: Jan 5, 2007
  19. Jan 5, 2007 #18
    pivoxa15: the top of the excercise reads:
    Describe the fallacy in the following "proof" by induction
    :smile: it IS wrong.
     
  20. Jan 5, 2007 #19

    radou

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    I got Apostol for Christmas, and it's a great book. But I combine it with another book, since I like some proofs and formulations better. For example, I just reached the section about continuity and limits of functions in Apostol, and got confused with a simple proof of the basic limit theorems. I opened the other book at that section and I immediately understood everything. So, no matter if you're not talented (as in my case) or talented, it's always good to learn from more different sources. In my case, it simply helps, and in the case of someone with talent or more sense for math, it enables one to learn on a slightly higher level - the level of comparsion.
     
  21. Jan 6, 2007 #20

    mathwonk

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    the same proof can be used to show that all posters here agree with one another. i.e. obviously all sets of one poster agree. then the above argument shows if all sets of three posters agree, then so do all sets of 4 posters......so???
     
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