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Looking for a specific sort of math book

  1. Apr 9, 2008 #1
    I'm looking for a math book that gives all the definitions and explains how every system was derived, starting at addition and subtraction, going up to pre-calculus.

    A bit of background: I dropped out of school to go to work at an early age (first year of high school). I did a lot of self-study and got a job as a computer programmer, which I have been doing now for 10 years. I have picked up quite a bit of math on my own as the years have gone by, but it has always been on a by-need basis. I would find myself in a situation where I need math to solve a specific problem, then I would learn how to solve that kind of problem.

    Needless to say, this has given me a knowledge of math with a lot of holes in it. Recently I have become interested in math, and decided to do self study to get my knowledge up to college/university level, at which point I can join lectures at my own pace while I continue working.

    So, as a first few steps I got book-lists from the local high schools, and bought the relevant ones. I have been working through the problems easily enough but I have sort of come to the conclusion that either books are not "my kind" of books, or they are simply not suited for self-study.

    They are mostly teaching silly "do it like this" rules, without explaining how these things were derived. I'll give you a very elementary example to explain what I mean. It is like they tell you that "+" and "-" equals "-", "+" and "+" is "+", and "-" and "-" is "+". Fair enough, but to understand WHY this works, you need to be shown a line going from negative something, through 0, and into the positive, and then do arithmetic on that line.

    I have this feeling that the books I have are not suited for self-study, because it is expected that the teacher should fill in all and do all the explaining of why the methods work.

    So, I am looking for a book that clearly explains how they got from A to B, preferably starting as low as arithmetic, explaining the laws of commutativity and so on, then building on this to get all the way up to precalculus.

    I have never seen a math text that actually mentions the laws of associativity when explaining how to solve equations, but it is the core reason why, say, you have to change the signs of an expression when you dissolve a subtracted parenthesis.

    I can work out a lot of these problems for myself, I was almost able to go from Ax^2 + Bx + c to the general formula, but I want a book that proves every operation I am doing, both mathematically and with examples and text.

    I am looking for deeper knowledge of what I am doing. I guess I am looking for a book that can spell out the WHY of every operation for me. Preferably with a lot of examples and excersises to work though :) Is that asking a lot?

    So, given my history, and what I think I want, what book(s) would you recommend?

    Edit: I guess Euler's Elements of Algebra is the exact sort of book I am talking about, though it deals only with a specific area and is somewhat old (It might make develop some out-dated notation?).

    Last edited: Apr 9, 2008
  2. jcsd
  3. Apr 10, 2008 #2
  4. Apr 11, 2008 #3
    Thanks a lot Daverz, I'll check it out and add it to my next shipping of books.

  5. Apr 11, 2008 #4
    An excellent book to work from by yourself is Engineering Mathematics Through Applications. It gives online complete solutions to all the problems in the book.
  6. May 24, 2008 #5


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    i would try euler if i were you.
  7. May 29, 2008 #6
    This algebra book has also gotten good reviews and I've just ordered it. I have a kid who's been struggling a bit with algebra and I'm looking at it to see if I can use it to help make clear the whys and wherefores (and therefores!).

    Algebra by I.M. Gelfand, Alexander Shen ISBN #0817636773.

    Amazon has it for about $20. I tried to post the link but evidently I'm too new a poster to be allowed to do that.
  8. May 29, 2008 #7


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    Last edited by a moderator: May 3, 2017
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