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Newly found interest in maths

  1. Oct 18, 2011 #1

    First of all, sorry if this kind of thread has been posted before. If so, then a reference to that thread would be appreciated :)

    So here we go.
    I always found maths to be boring in school, I did ok, but I didn't like it. But lately I've started to become fascinated by it. String- or M-theory is particularly fascinating to me.
    So I decided to learn maths again. But I'm struggling, even with the most basic of basics.

    I got the book 'Calculus' by Michael Spivak (1994 edition) but, I'm already having problems with the first few exercises on the basic properties of numbers (proving certain things). The answers to the questions all seem logical to me, but I don't know how to come up with the right ways to prove something without cheating and looking at the answer.

    Is this book too advanced for someone as inexperienced in maths as me? And if so, what else would you suggest?

    - Enclose
  2. jcsd
  3. Oct 18, 2011 #2
    Have you ever read a book in College Algebra ?
  4. Oct 18, 2011 #3
    My maths knowledge is limited to what I saw in high school. I studied ICT in high school so we got quite a lot of maths compared to most other study-directions.

    I live in Belgium though, our school system and standards are quite different to american and UK ones (better in my opinion).
  5. Oct 18, 2011 #4
    But I see it is wrong to begin reading Michael spivak's without even reading a book on pre-Calculus , so I recommend you to read first a pre-Calculus book , and you will see after , that you can easily handle Michael spivak's ( in my opinion that is What I have done before reading a book in Calculus , I was like you )
  6. Oct 18, 2011 #5
    Alright, any pre-Calculus book you particularly recommend or will any do?

    I thought I'd give Spivak's book a try cause I've seen all of the formulae on the first pages before. Sadly though, I've apparently no idea how to use them :(
  7. Oct 18, 2011 #6
    Last edited: Oct 18, 2011
  8. Oct 18, 2011 #7
    If you believe you have a good algebra (i.e. symbol manipulation) background, and understanding of basic and transcendental functions and basic geometry (polynomials, exponentials/logarithms, trigonometric functions; geometry of the circle, triangle and line), then I think Spivak is a great introduction to basic abstract thinking and mathematical "open-mindedness".

    A good intro to calculus with special care to carrying out "attentive algebra" is Stewart's "Calculus: Early Transcendentals". It's not as rigorous as abstract as Spivak, but it will give you a good intuition for a lot of ideas in calculus. Once you have obtained this comfort with calculus, trying out Spivak will be beneficial.

    "Analysis By Its History" is a really cool book I've been reading recently -- it includes very basic analysis topics, but presents it in a historical manner with lots of pictures, quotations, and citations. For example, theorems are stated with who and when they were published. Also, the history of the proof and examination of each important theorem is detailed, which is really cool. It's a good reference book and "glossing" for your analysis skills.
  9. Oct 18, 2011 #8
    Last edited by a moderator: Apr 26, 2017
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