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What is a good book on basic high school math (algebra, geometry, trig etc.)?

I want a book that presents mathematics in a rigorous manner and with emphasis on creativity rather than memorization. If it comes with a lot problems to work on, so much the better (since I want to study it on my own).

Lord_Farin
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ohdmj
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    Hello, welcome to Maths.SE. Please ensure that your question is fully understandable without the title. The title's purpose is to attract people to your question (and to make it easily searchable). Once it has done that, it's job is done. The question should be self-contained -- I've edited it for you. – Lord_Farin Nov 19 '13 at 08:59

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The following books by I. M. Gelfand are interesting:

Algebra

Trigonometry

The Method of Coordinates

Functions and Graphs

There's also this gem by George Birkhoff:

Basic Geometry

They are written so as to build intuition and get a feeling for what's going on behind the scenes. If you are interesting in delving a little deeper than usual high school topics, then I'd suggest these books too:

How to Prove It - Daniel Velleman

How to Think Like a Mathematician - Kevin Houston

'How to Prove It' is an all time favorite everyone. The second is more of a personal recommendation: I discovered it when I entered university and appreciated it very much. I think the informal discussions and insights it gives are valuable.

There are more references but they depend on what is your purpose: competitions, bridging your way into higher abstract mathematics, etc.

Mark Fantini
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In geometry you can start from Kiselev's Geometry then moving on to praslov problems in geometry.

At least this is what I did however praslov only contains problems and can be easily done by someone who has done school geometry well. Just take a look at it.But nothing is better than kiselev : it teaches you the basics from Nothing,is interesting to read and can be self studied easily.

In algebra, Gelfand's algebra might prove good though I haven't done it myself so can't say anything more about it.

Shreya
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