Decent books for high school algebra and geometry

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I'm still in high school and looking at majoring in physics in college. I have taken math up to single variable calculus, but I want to go back and relearn algebra and geometry to get a much better understanding of those subjects. I'm considering using the books Algebra by I.M Gelfand and Geometry: A High School Course by Serge Lang. From what I've seen, these books are more focused on actual problems versus just exercises and focus more on proofs than just plugging in numbers. Can anybody else who's read these books give a second opinion or recommend any other good books at the high school level?
 

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  • #2
Ackbach
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A great high school book is Mathematics for the Nonmathematician, by Morris Kline. Don't be fooled by the title - this is the real deal. Everything you need to know is in there.

Other options: Algebra: Structure and Method, Vol. I and II, by Brown, Dolciani, et. al.

Geometry, by Jurgensen, Brown, et. al.

Both of these are Houghton-Mifflin, and have very little fluff in them.

For geometry, if you want a real challenge, work your way through The Bones, which is essentially Euclid's Elements minus all the proofs.
 
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Thanks, I'll definitely look at those books. I started with Gelfand and Lang, and I like what I've seen. I'll probably take a look at The Elements too. Even if it is a little dated, I'm sure I can learn much from it.
 
  • #4
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I would suggest any of the followings:

-Art of Problem Solving series (prealgebra up through calculus). Awesome curriculum.
-The books by Gelfand ... I highly recommend.
-Geometry by Lang and Murrow
-Geometry (books 1 and 2) by Kiselev ... I highly recommend.
-Geometry by Jacobs (1st Ed)
-Basic Mathematics by Serge Lang
-Principles of Mathematics by Allendoerfer and Oakley ... this would be a good review plus lots of new/theoretical stuff
-The SMSG books from the "new math" period. You can find these online in pdf.
-Sharipov has some great (free) books ... I highly recommend them.

If you want some more advanced stuff:

-Geometry Revisited by Coxeter
-Geometric Transformations series by Yaglom
-Introduction to Inequalities by Bellman
-Calculus by Spivak or Apostol
-Get going with some linear algebra (Strang, Apostol, or Sharipov)
 
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I've heard of all of these except for Sharipov. I'll take a look at that, especially since it's free. I've got Kiselev, and more of Gelfand and Lang, so I'll definitely go through those after I finish the books I'm reading now. I guess I better get to studying.
 
  • #6
mathwonk
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In recent years, I have enjoyed reading parts of Euclid's Elements, in the Green Lion edition, and Euler's Elements of Algebra. I have heard good things about Gelfand, but have not seen it. Kiselev is a Russian classic.
 
  • #7
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I remember looking at Euler's book a couple of years ago. It has very interesting results in it that I didn't see anywhere else. I'll read it again after I have a stronger base in algebra. Gelfand's Algebra seems better suited for a second run through of the course. It's pretty skimpy on exposition, but most of the material is contained in the problems, some of which are pretty difficult. It's helped me see the general principle behind many concepts and develop a coherence between them, which is something I couldn't get with my standard textbooks. Other interesting books, both from the early 1900s, are Elementary Algebra and Higher Algebra both by Hall and Knight. (Both are free)
 

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