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Learning math from scratch

  1. Jul 17, 2011 #1
    So a few years after school, I managed to forget most of what I learned in math class. I'm planning on reteaching myself from elementary arithmetic to calculus. I'm requesting a sequence of books to get me there. Looking for something rigorous, that actually explains why algorithms work, etc. Something that won't bore me when it comes to the basics. Should I learn set theory to start off with, or just go with the more traditional approach?

    Also, apologies for not posting in the learning materials forum, PF won't let me for some reason.
  2. jcsd
  3. Jul 17, 2011 #2
    I would recommend getting a calculus book. The one calculus book that I use for calculus covers Calculus 1, Calculus 2, and multivariable calculus all in one book. Most calculus books have a couple chapters in the back of the book, or the very first couple, that review basic arithmetic for those who haven't studied math in a while. If you learned the material already at one point in your life, you will most likely be bored with books that attempt to teach these topics as if they are presented to you for the very first time.
    Last edited: Jul 17, 2011
  4. Jul 17, 2011 #3

    Ray Vickson

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    Why would you fail to mention the title and author of this wonderful book?

  5. Jul 17, 2011 #4


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    How would you describe your current math skills? I find it hard to believe you need to reteach yourself something like elementary arithmetic.
  6. Jul 17, 2011 #5
    As far as basic math goes, I could do with a quick refresher. Some things I have forgotten, like some of the operations with fractions, but nothing that couldn't be recovered in about a week.

    However, most of the books I was taught with taught by rote memorization of arithmetic algorithms without a deeper understanding of why those algorithms work, which probably explains why I forgot them in the first place. Same goes for early algebra.

    I'm wondering if it wouldn't be easier to start by approaching mathematics as a logical framework, rather than simply a mechanical method for manipulating numbers.

    I could probably wrap my head around elementary set theory and mathematical logic, so I'm wondering if there are any textbooks that teach from that perspective.
  7. Jul 19, 2011 #6


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    I have a set of notes which are posted here on this forum which starts off with basic properties of integer numbers and then derives the proper addition rule for fractions later on. It uses letters as representation of numbers straight away though.
  8. Jul 19, 2011 #7
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