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Geometry textbook

  1. Jun 23, 2013 #1

    I'm starting university in September and wanted to consolidate my current knowledge.

    I got hold of a nice textbook called 'foundation mathematics' which covers algebra to fairly basic calculus, but was looking for a good one on geometry.

    Can anyone recommend any decent books (or websites) that covers simple mathematics (geometry, algebra, trig, beginning calculus, arithmetic, etc) quite rigorously?

    Last edited: Jun 23, 2013
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  3. Jun 23, 2013 #2


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    The Geometry textbook by bass & others, through Prentice-Hall is an excellent one. It's a high school Geometry textbook.
  4. Jun 24, 2013 #3


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    What does quite rigorously mean? I would suggest a book by Lang, Coxeter, or Courant. The geometry book Geometry: A Comprehensive Course by Dan Pedoe while not perfect is a good overview at a low price. For arithmetic do you mean something like A Course in Arithmetic by J-P. Serre or more like 2/3-3/5=1/15?

    If you like older books many are free online like
    The new complete system of arithmetic, composed for the use of the citizens of the United States by Nicolas Pike
    Algebra: An Elementary Text-Book for the Higher Classes of Secondary Schools and for Colleges by George Chrystal
    Elements by Euclid
    Last edited: Jun 24, 2013
  5. Jun 24, 2013 #4
    Why are you recommending Serre for a guy who is still in high school?? Why do you possibly think this is a good recommendation?
  6. Jun 24, 2013 #5


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    ^It does not say still in high school in the OP. I did not recommend it, I asked for clarification. I have know high school students who have read it, they were unusual.
  7. Jun 24, 2013 #6
    He says this:

    And he's currently reading a book on basic algebra. And he wants recommendations for websites of things like trig. And you honestly think he wants something on the level of Serre's course in arithmetic? Wow...
  8. Jun 24, 2013 #7


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    I don't "honestly" think anything about the level wanted as it is unclear. Serre was an example of a very high level. The suggested books were more usual. Perhaps a better way to phrase the question is

    OP on a scale of 0-2000 where Math Made Easy: 1st Grade Workbook, Ages 6-7 by Sue Phillips and Sean McArdle is a 25 and Serre is a 1000 what level do you want.

    or even better
    Please provide more details about what you would like in an arithmetic book.
    Last edited: Jun 24, 2013
  9. Jun 24, 2013 #8
    Thanks for the help!

    I need to be a bit clearer. The level that I am at is that I am just starting university, and probably the most advanced stuff I've done is calculus using hyp/inv trig functions, induction, Mclauren series etc. Hopefully that gives an idea of where I am at.

    What I am looking to do is read over simple stuff that I already know, but whilst being aware of where everingthing comes from, proving things etc. As said above I'm mainly looking for a geometry book, and your suggestions look pretty appropriate so thanks :)

    I have found that it can be helpful to look at things like trig again with the perspective that I have now, and this can sort of solidify the connections between topics in my mind.
  10. Jun 24, 2013 #9


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    Are you particularly interested in mathematics or just looking for the basics? For example often a student interested in mathematics will like a trigonometry book with spherical trigonometry, proofs, and some challenging problems for a review. For arithmetic do you just want to review things like fractions, percents, and addition; do you want some outdated methods like long division, compound addition, and taking cube roots by hand; or do you want to learn about prime numbers, congruence, diophantine equations, and proving number facts? Most calculus books have some proofs you can read one with particular emphasis on proofs if you like.
  11. Jun 24, 2013 #10


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  12. Jun 24, 2013 #11
    I'm from the UK so I'm actually doing my degree in Mathematics (we usually just do one subject, rather than the major/minor 'mixed course' US system). What you mention above sounds like the sort of thing I'm after. I want to review what I already know, but with an emphasis on proof.

    Thanks :)
  13. Jun 26, 2013 #12


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    Euclid's elements (Dover books) is a must have if you are interested in the subject. To get a passing grade, get whatever they are teaching.
  14. Jun 30, 2013 #13
    The Four Pillars of Geometry

    by John Stillwell
  15. Jul 4, 2013 #14
    For books that cover a good amount of different subjects:

    Principles of Mathematics - Allendoerfer and Oakley
    Basic Mathematics - Lang

    For geometry in particular:

    Kiselev's Geometry (Books 1 and 2)
    AoPS Geometry
    Jacobs Geometry (1st Edition)
    Euclid's Elements
  16. Jul 4, 2013 #15
    read the Elements by Euclid it will transform you
  17. Jul 5, 2013 #16
    You can use the college algebra class at udacity.com
    For calculus you can use Mit Course Ware.
    Use Khan academy For trigonometry and Geometry.

    What is the full name and the author of the book that you used?
    Last edited: Jul 5, 2013
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