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I am aged 62 and have lost all skill in mathematics. I would like to learn basic to advanced (primary school > university) math. What books explain such a vast variety of subjects or the following?

  1. Algebra

  2. Geometry

  3. Trigonometry

  4. Calculus

  5. Linear Algebra

  6. Analytic Geometry

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    $\begingroup$ Have you considered taking courses at a nearby university in these subjects? If you aren't interested in earning any credits or a degree, you could probably even do it for free by asking the instructors if they would mind if you sit in on (i.e., "audit") their classes. You wouldn't be officially registered, so you won't have to pay for tuition, but you would get the exposure you are looking for. $\endgroup$ – layman May 31 '15 at 21:07
  • $\begingroup$ My suggestion is Bruce E. Meserve, Fundamental Concepts of Algebra. He covers a range of topics including sets, arithmetic, polynomials, plane geometry and others. Aside from those basics, there's a nice discussion of compass and straightedge constructions that I personally enjoyed. What you'll find missing is the entirety of calculus; the author focuses on algebraic topics. $\endgroup$ – GPerez May 31 '15 at 21:16
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    $\begingroup$ Possible duplicate of Recommend books for learning math from elementary school? $\endgroup$ – Greek - Area 51 Proposal May 28 '18 at 3:55
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Not a book, but I would strongly recommend KhanAcademy if you don't mind staring at a computer for long periods of time. It has great videos, exercises, instantaneous feedback and gives you hints as you work through problems, if you need them, but still want to work through the problem.

The range of topics is from elementary math to university math, and you can navigate using the world of math maps or select missions to work through. As a teacher I recommend it to my students all the time, and as a student, I use it to reinforce concepts I struggle with when going through my university courses.

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  • $\begingroup$ I know KA but I would rather prefer a book, thanks. $\endgroup$ – Jesus Christ May 31 '15 at 21:38
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In general, Schaum's books are very suited for self study. Here is for example a book that contains quite a bit:

http://www.amazon.co.uk/Schaums-Outline-College-Mathematics-Edition/dp/0071626476

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Most high level books will not be able to contain all that information, because of how dense most of those topics are. However, if you are looking for a challenging read, the best text book I have ever read was Theodore Shifrins' Multivariable Mathematics. It contains a wide variety of things that you have posted, but in their most advanced form. It does not talk about the simple mappings you would talk about in a first year calculus course, but rather about mappings from R^N to R^M. It has a great introduction to linear algebra and some analytic geometry as far as some of the imagery and later integrals go.

I am uncertain as to how much skill it is you have lost over the years. If the above book seems too challenging, Stewarts' Calculus books are a great place to start. Many universities use this book as the introduction for most calculus courses. It will not, however teach you much linear algebra as Shifrins' book will, but it does in fact have everything else you were looking for.

Hope I could help.There is a lot more I could suggest, but I don't want to make this answer too dense and boring to read. Here are some links.

http://www.amazon.ca/Multivariable-Mathematics-Algebra-Calculus-Manifolds/dp/047152638X

http://www.stewartcalculus.com/

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