At school, I was very good at mathematics, but now I'm 40 years old and I think I have forgotten almost everything I have learnt. I want to study again mathematics because I'm very interested on it.
How can I learn it? Is there any book or encyclopedia to learn it (calculus and algebra)?
I don't want to learn on school's books because I'm sure I'm going to get bored with them.
What are your recommendations?
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Introduction To Geometry by Donald Coxeter. Great fun, doesn't need to be read linearly. No pre-requisites. If you thought there wasn't much to geometry in 2 dimensions..... For calculus, if you don't have a clear grasp of the logical foundations of the real number system, you will be lost. Perhaps someone else can recommend some modern texts that cover this.
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As someone who naturally gravitates towards self-study (even in the formal classroom setting), the first thing you MUST understand is that you are in for a grueling (but ultimately very satisfying) marathon and NOT a sprint, no matter where you start. My experience is that self-study (well, really all learning) is not suited for the linear dogma of the educational orthodoxy. Understanding comes in waves and often has a way of eluding the rigid schedules of classroom based education. Even when I first took calculus, I understood very little of it until about two weeks after the course was over. At first, the mind is so overwhelmed by the minutae of a new intellectual endeavor that one cannot see the forest for the trees but once one has become comfortable with the language/notation/main results of a given field the insight tends to come in waves and often when one least expects it.
Be warned that you have to be incredibly stubborn and disciplined to self-study mathematics. It takes a certain measure of ruthlessness towards oneself to make meaningful progress. I would also recommend investing in MuPad or Mathematica but not so you can avoid computation (it is a necessary evil) but so that you can ensure that your computation is correct. It is also fun to play around with and I cannot overstate the value of "playing around" with ideas. This site is also a valuable resource with a great many sharp minds who truly love mathematics and will gladly assist you so long as you put forth the necessary effort.
As for where to start, I recommend linear algebra followed by calculus/analysis but you would probably be advised to brush up on your basic algebra (it comes back faster than you'd expect). If it were me, I'd stray away from the more esoteric fields that some have suggested and build up a solid foundation. Linear Algebra Done Right by Sheldon Axler is a quality text, though you might consider supplementing it with a more computationally based text like Strang to get the hang of the basic operations, especially if it your first time around the block.
Great question, I wish you the best of luck. Here is a different suggestion, of course its just that, another idea. Dont start with algebra/calculus its so standard and tied up with school/university curricula. Instead learn some different areas of mathematics that dont require background and are more conceptual. Good examples are Combinatorics, including graph theory, very beautiful ideas here, requiring no background, but youll be solving propblems and learning yo think mathematically. Other possibilities are Set theory, Logic, Euclidian Geometry, Projective Geometry and of course elementary number theory.