I know basic geometry and algebra, I know trigonometry but I don't understand it, I'm willing to learn math but 95% of books are not suited for my knowledge (they are too advanced). What are some good books I can read? I especially like reading proofs and problems whit sigma (series ). Sorry for my bad spelling.

I need advice for learning math:

  • Where to start?

  • How?

Your story would help too.

P.S. I like some educational channels.


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    $\begingroup$ Serge Lang's "Basic Math" is pretty good smile.amazon.com/Basic-Mathematics-Serge-Lang/dp/0387967877/… $\endgroup$ – Gregory Grant May 12 '15 at 16:13
  • $\begingroup$ @GregoryGrant Nice link--but the fact that the book is by Serge Lang makes me a little wary...haha $\endgroup$ – Daniel W. Farlow May 12 '15 at 16:20
  • $\begingroup$ @MagicMan I agree, I would never suggest his book Algebra, or his analysis books. But he pulled it off in this one, take a look at the preview on amazon, the table of contents is there and some sample pages. Plus look at the reviews. $\endgroup$ – Gregory Grant May 12 '15 at 16:21
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    $\begingroup$ @GregoryGrant I just checked this: the book also has answers/solutions to nearly every problem in the back of the book, something oddly not mentioned in the table of contents. That's a pretty major oversight in my opinion, but something OP should know--that book looks like a particularly good resource now given the source (Serge Lange), arrangement of content, and full solutions to check work. Bravo for mentioning this book, Gregory! $\endgroup$ – Daniel W. Farlow May 12 '15 at 17:00
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    $\begingroup$ @GregoryGrant I completely agree. I find it to be quite impressive that he was able to write a book like that, going to back to "first principles," more or less, and able to restrain himself from commenting on deep algebra or the like. I've heard stories about Lang going on mini-vacations and writing entire books on them (can't remember the reference). He was a pretty prolific writer to be sure. Usually some pretty heady exposition but this does look like a rather remarkable exception. $\endgroup$ – Daniel W. Farlow May 12 '15 at 17:06

For problem solving first course you can read
Solving Mathematical Problems A Personal Perspective-Terence Tao

For learning counting ways you can read Niven's classic book
Mathematics of Choice How to Count Without Counting-Ivan Niven

For reading elementary calculus you can read
A Course of Pure Mathematics-G. H. Hardy

For number theory I highly recommand you the book
An Introduction to the Theory of Numbers-G. H. Hardy,E. M. Right

Another good book in number theory is
Topics in the Theory of Numbers-Paul Erdos,Janos Suranyi

  • The Enjoyment of Mathematics, by Hans Rademacher and Otto Toeplitz;

  • What Is Mathematics?, by Richard Courant and Herbert Robbins;

  • All books written by George Pólya;

  • All books written by Ivan Niven. (P.S. his introductory calculus textbook is very instructive and pleasant to read)


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