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A good book for beginners/novices at mathematics?

  1. Sep 5, 2012 #1
    Hello everyone!

    As the title of this thread possibly suggests to you, I'm not very skilled with mathematics. I would like to say I don't blame my teachers, I'm not insinuating that by any means. What I'm hoping to find is a book that can teach me "from the ground up" (the basics to calculus, if at all possible!) on mathematics. I have difficulties with my college textbooks (college algebra specifically) primarily because I believe I don't understand the underlying principles. Hopefully, if I can learn from said book, I hope to go back to college someday and pursue a science/math related major given that I have at least a basic understanding of math principles. Would anyone be so kind as to post a few titles? I would greatly appreciate it!
  2. jcsd
  3. Sep 5, 2012 #2
    Hey if you don't mind watching videos khanacademy.com is an amazing resource. It covers a ton of mathematical topics and even has review exercises you can play around with.
  4. Sep 5, 2012 #3
    Khanacademy isn't really that good. Do NOT use it as a primary resource and do NOT use it as replacement of a textbook. It is good as a secondary resource though.

    Some good introductory books are "Basic Mathematics" by Serge Lang, "Algebra" by Israel Gelfand and "Elements of Algebra" by Leonard Euler. These writers actually were professional mathematicians and you can see that. They don't focus on silly high school exercises, but rather try to convey why things are true and what the general "philosophy" of mathematics is.

    The texts are not easy however, but do try to read them. And be sure to make all or most of the exercises. It is only by exercises that you can learn.

    Last edited by a moderator: May 6, 2017
  5. Sep 6, 2012 #4


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    It is worth noting that since the Euler is long out of copyright it is quite easy to find via archive.org or google books copies of the Hewlett 3rd ed which is what is for sale at Amazon - although it is also wonderful to note that if one buys through the Amazon link then physicsforums gets a cut of the action.
  6. Sep 6, 2012 #5
    Oh, you're right. I didn't think of that. Here is a link where you can download the book: http://archive.org/details/elementsofalgebr00euleuoft
  7. Sep 6, 2012 #6
    Salman Khan is a good lecturer and his fame is well-deserved. His videos are a nice starting point. The AoPS has their own youtube videos geared toward mathematically-gifted children. Try watching the "MATHCOUNTS minis" series.

    Euler's Elements are just as long and boring as his Calculus volumes. If you have a historical slant (like I do) the books might be fun. Otherwise, I'd avoid them. If you wish, you can read his a lot of his work (translated and typsetted) at typsettedhttp://www.17centurymaths.com/. (Note: It's a work in progress.)

    Gel'fand is a far better choice for an algebra text because it is concise, modern, well-motivated, and has several challenging problems. William Chen's lecture notes are also great, and filled with plenty of problems.

    Of cours
  8. Sep 7, 2012 #7


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    boring? euler? it seems this is a subjective opinion, not shared by all. It is the mathematical depth and clarity of euler that appeals to me, not the history, although his examples, say about country girls exchanging cheeses for eggs, and officers commanding horsemen and foot soldiers paid in florins, are charming.

    of course it was only claimed that euler's algebra is as boring as his calculus, which may be indeed true, i.e. this is consistent with the likely probability that neither is boring at all. The other side of this tautology would be to praise SAXON'S algebra as being every bit as good as his geometry book.

    Since sincere opinions do differ, the lesson here for the OP is of course that he must choose the books to please himself.
  9. Sep 7, 2012 #8
    For really basic stuff like that, you might try JUMP math.


    It only covers grades 1-8. However, if you have trouble with college algebra, that suggests that you might have gaps in your previous background that are making it more difficult, so it might be worth a look. I think the trig/precalc students that I taught would have something to gain from JUMP math and that is one level above college algebra.

    Also if you can find/afford a good tutor, that can make a huge difference.
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