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Preparing for analysis/proofs

  1. Dec 17, 2007 #1
    I want to take a real analysis course, and eventaully an analysis course. I would really like to become fluent in the language of the calculus as well as proofs, almost to make as a second language. (I hear it can take years to master it but is rewarding). I am a physics major so it could be tough going from applied to pure.

    However, I do not have much expierence in proofs. How can I resolve this?
    Show I buy a book on logic? I have "how to prove it," by Daniel J Velleman. It is just hard getting motivated reading it as aposed to a Physics read.

    A thing I notice when I look at a proof sometimes is that complicated notation/symbols are used to express simple ideas. There are tons of subtlies that must be taken into account.
    This gets on my nerves but I can grip through it.
    I hear it is hard getting started in proofs, but it gets easier, is this true?
    Advice would be appreicated.

    By the way I am done with all three semesters of Calc, and will be taking diff eq, and linear algebra.
  2. jcsd
  3. Dec 17, 2007 #2


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    i recommend a good calc book with proofs like spivak. since you know the calc, the proofs will be easier to follow.
  4. Dec 17, 2007 #3
    Mathwonk I have heard Spivak is excellent, how does it compare to Apostoll?

    Also am I right about proofs starting out to be difficult? It might be harder since I am a phys major.
    Being a respectable Professor in Mathematics, can you give me any general advice when it comes to proofs?
    Thank you
  5. Dec 17, 2007 #4


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    Similar to that question; how does the Howard Anton book compare to the Spivak book? I bought an old, thick, Calculus book by Anton but have never seen the Spivak book.
  6. Dec 18, 2007 #5
    You could try a number theory book for learning proof by induction, bu that will only get you so far in Analysis. A good Calculus book is really the way to go. Get very familiar with Epsilon and Delta, as well as terms like increasing, strictly increasing, monotone, convergence, divergence, continuity, uniform continuity. Maybe review sequences and series a bit if you have had them before.
    if you ever find yourself writing "given Epsilon < 0," then you need to go back and start over with your Calculus 1 proofs
  7. Dec 19, 2007 #6
    I was looking at these tow books:
    Mathematical Analysis- by T. Apostol
    Mathematical Analysis- Zador

    Both look really good.
  8. Dec 19, 2007 #7
    Similar to that question; how does the Howard Anton book compare to the Spivak book?

    Not favorably.
  9. Dec 19, 2007 #8
    i would recommend a transition to advanced mathematics by gary chartrand.
  10. Dec 19, 2007 #9
    I just started reading Spivak's book, it's hard and I've already taken Calculus 1 and 2.

    Thinking vs. Computing, it's a big change ... uh. I can't wait for school to start up again, then I can bug my Professors :-]
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