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