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Books for self-learning Mathematics

  1. Mar 19, 2012 #1
    First of all, let me just say hello to the community here, as I am new and this is my first post (hopefully of many).

    Now on to business. Recently I have been reading a book by Silvanus Thompson called Calculus Made Easy. Now, I took Calculus in my junior year of H.S (I am a senior now) but it was the teacher's first time teaching the subject, and the assigned text was too convoluted to read. (In fact the only times I opened it were to do H.W assignments.) In either case, I did not care enough about the class to self-study by some other means and was somehow able to pass.

    A year later I have come to realize my ignorance in even the most basic concepts in calculus and decided to try and self-learn it. Calculus Made Easy was pretty much a godsend, as it explained all of the conceptual ideas in an easy and readable format. Some of the ideas in the book, such as the explanation of the derivative in terms of "little bits of x and y" (i.e dx and dy) and the derivation of the exponential series blew my mind. Now, you might laugh at me but it was really the first time that calculus was more than "plug and chug" to me.

    But I digress. The point of this story and this post is this question: Are there any other books out there like Calculus Made Easy? Books that clarify the arcane mysteries of the mathematical world in a simple, easy to understand, mathematical jargon free speech. Now while I would like to pursue Calculus a bit further, I am equally open to other branches of mathematics. What I would especially like is some sort of progression. (e.g Trigonometry comes before Calculus and Algebra before Trigonometry).

    In the end though it doesn't matter, I am willing to read any book on any topic so long as it is as simple and enlightening as Calculus Made Easy has been.
  2. jcsd
  3. Mar 20, 2012 #2

    In my opinion, if you want to continue studying mathematics (in college for example) then you shouldn't use books of the type " x made easy" or "x for dummies".

    Try the real stuff. It WILL NOT be easy at first, but it will make you stronger in mathematics. Any learning process is painful, and if it ain't, then it's not a proper learning process.

    I think anyone is capable of self-learning Calculus from Stewart's[\b] book. If you find its too difficult, then try "Precalculus" also by Stewart. Don't buy it, any science library has it.

    Good luck!
    Last edited: Mar 20, 2012
  4. Mar 20, 2012 #3
    How about some Spivak?

    Also, get some linear algebra done!
    Linear Algebra is an incredibly pretty subject, makes calculus look like a contraption sellotaped together imo :3
  5. Mar 20, 2012 #4
    If he is asking for a "student-friendly" book I don't think Spivak is a good choice, it's a difficult book for a self-learner.

    For Linear Algebra he could use Larson's. I very much agree in that it is a pretty subject. The best of Linear Algebra is that you don't need any basis at all for learning it besides the very basic arithmetics
  6. Mar 20, 2012 #5
    I don't think there ARE any good books for self-learning rigorous calculus/analysisy type stuff sadly..
    I managed to self learn from it well enough though
  7. Mar 20, 2012 #6


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    Try the book "Practical analysis in one variable" by Estep. It's meant to be easy and rigorous. It's easier than Spivak, but it does cover some theory.
  8. Mar 20, 2012 #7
    Thanks for the quick and numerous reply's. I will look into Esteps book and I have actually taken a look at Spivak. I found the explanations to be mostly intuitive and understandable, but the questions seem to be where the real learning takes place and I am afraid I am not quite up to the challenge (yet).

    I also agree with Alpha Floor in that difficulty usually equates to better understanding but I just want a text that doesn't have to much techinical jargon (though perhaps that may be asking to much). I will however look into Stewart's book.

    Thanks again guys
  9. Mar 20, 2012 #8
    I'd like to second Stewart's books on calculus and precalculus. His books also contain tons of interesting exercises to test if you've actually understood all of it - definitely recommended.
  10. Mar 20, 2012 #9
    I was looking at some of Stewart's Calculus books and now am confused on which one to get. There is: Early Transcendental, Concepts and Contexts, and then just Calculus, also does the edition matter? I'm looking to get 5th edition (its the only one my library has).
  11. Mar 20, 2012 #10
    Don't bother about the edition, in fact, the earlier the better (in my opinion). Newer editions have too much "eye-candy", colours, pictures... it looks rather like a comic book for 4-years old instead of a mathematics text

    As for the book itself, between "early trascendentals" and "calculus" the only difference is that the second one includes a chapter on inverse functions (inverse exponential, inverse trigonometric functions etc)

    Concepts and contexts must be how they call the new "precalculus"...

    EDIT: I've checked, and seems to be a sort of theory backup

    Just get the classical "Calculus", the shorter the name, the better :)
    Last edited: Mar 20, 2012
  12. Mar 20, 2012 #11
    I recommend Early Transcendentals. There's not much difference between that one and the 'normal' Calculus book, but I've got this one (6E) and can vouch for its usefulness. I don't know Concepts and Contexts. Personally, I haven't seen much of a difference between 6E and 7E, although I suspect many errors have been fixed (with so many examples, I suspect it's impossible not to make quite a few of them). I recommend getting the newest edition if you can, but there's no harm in getting a 6E, either - the concepts stay the same, and if something seems out of place you can always google it.
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