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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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    $\begingroup$ There are many topics in mathematics. Only learning calculus and algebra is not enough in my opinion. $\endgroup$
    – Mc Cheng
    May 9, 2016 at 11:10
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    $\begingroup$ You should try Khan Academy... $\endgroup$ May 9, 2016 at 11:11
  • $\begingroup$ The web has a wealth of lecture notes on algebra and analysis. Just try what you find interesting. $\endgroup$ May 9, 2016 at 11:11
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    $\begingroup$ @user170039 I disagree with this 100%. In fact learning philosophy will be detrimental to learning math. $\endgroup$ May 9, 2016 at 12:03
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    $\begingroup$ Using an "encyclopedia" to learn mathematics sounds boring. $\endgroup$
    – miracle173
    May 9, 2016 at 14:58

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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.

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    $\begingroup$ @user170039 What are you working for the philosophy department ? You want to learn the language of Math not that of Philosophy, they are two TOTALLY different things. Besides philosophy has its head so far up its.... $\endgroup$ May 9, 2016 at 12:14
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    $\begingroup$ @JeanMarie Again I simply disagree, its funny, they guy says he wants to study math and one person tells him he should learn philosophy and another computer science...I recommend he also learns German, French and Russian...first! then with any luck he will never get down to math. (And "surely" who uses the word "surely"?) $\endgroup$ May 9, 2016 at 12:24
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    $\begingroup$ If anyone can find anything of substance in Wittgenstein's book "Philosophy And Mathematics" I'd like to know what it is. $\endgroup$ May 9, 2016 at 13:22
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    $\begingroup$ @DanielWainfleet: Many philosophy students have idols that they cannot let go off. That is often why they keep telling others to worship the same idols. In fact, that is one of the major reasons why "learning philosophy will be detrimental to learning math", because most of it is about parroting idols. The other reason is that most philosophers are completely incompetent in basic logic. For example, Wittgenstein spouted nonsense when he couldn't understand Godel, but till today all his idolizers repeatedly try to find new-fangled ways of twisting all his words in an attempt to save face. $\endgroup$
    – user21820
    Jun 1, 2020 at 7:40
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    $\begingroup$ @user21820 . When the geometer Coxeter was at Oxford and Wittgenstein was a Visiting Professor there, W. asked C. what he thought of his new book. (I d.k. which book that was.) C. replied that he thought it was gibberish. $\endgroup$ Jun 1, 2020 at 22:42
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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.

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Here is what you are searching for (english only): https://www.thegreatcoursesplus.com/category/mathematics

I'm with you on this, text books can be really boring especially with the medial opportunities of today. (Think of ads and the CSI series, why can't a math class be like this :( )

The great courses offers video courses on demand thought by the best teachers they can find and good medial explanation work.

Tipp: Register for the newsletter and wait a week you will get far superior offers

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