Analytic geometry - textbook

  • #1
Hello! I'm looking for a good analytic geometry textbook. I'm studying circumferences and sphere and I'm using the book Analytic Geometry: A vector approach from Wexler but I find this book quite bad. I want some suggestions!

Thank you.
 

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  • #2
mathwonk
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i am puzzled how to answer this because has ever asked me for a book of analytic geometry before. maybe a good old calculus book back when it was called calculus and analytic geometry, maybe an old version of george b thomas' Calculus and analytic geometry.

gee, its still called that recently,

https://www.amazon.com/dp/0201531747/?tag=pfamazon01-20&tag=pfamazon01-20

or maybe the last part of the excellent book, Principles of Mathematics, by Allendoerfer and Oakley.

https://www.amazon.com/dp/B001CD9834/?tag=pfamazon01-20
 
  • #3
Here, in Brazil, we have analytic geometry in college (I'm studying physics). Well, I'll try to find this book. Thank you for your help.
 
  • #5
mathwonk
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Since this topic has almost disappeared from the US math curriculum, I really didn't know what it consisted of. Nonetheless it seem the books I suggested do cover it.

It seems to be a study of elementary Euclidean geometry from the standpoint advocated by Descartes, namely coordinate geometry. So one introduces coordinates and then studies the same objects that could have been studied without them, namely circles and ellipses, parabolas, and hyperbolas, as well as their presentation as conic sections.

One also studies to some degree changes of coordinates, e.g. polar coordinates, and representations of the same basic quadratic curves via polar coordinates.


As described in the introduction to the chapter in Allendoerfer and Oakley: analytic geometry consists of taking equations and finding the graphs of those equations in the coordinate plane, and conversely, taking curves in the plane and writing equations to describe them. Oh of course one also discusses lines and line segments.

Almost the only book i found on amazon devoted exclusively to this topic was the one below from 1918, but it is a topic that would probably benefit students today. It just gets left out as part of the general, but unfortunate, move away from geometry in the US.

https://www.amazon.com/dp/B004QO9RGE/?tag=pfamazon01-20
 
  • #6
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I might not be very helpful,but here is another book with a similar title to the one you said you are using:
https://www.amazon.com/dp/0486404528/?tag=pfamazon01-20&tag=pfamazon01-20
I'm sorry I haven't read it either, but it is also cheap, with very good reviews. However, it looks like you need to know some linear algebra to read the book, which you may or may not know.
 
  • #7
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At my university, the Analytic Geometry is kind of an "Intro to linear algebra" course... What mathwonk said is covered but with a linear algebra approach, so that when the student gets to the "real" Linear Algebra course (based on Friedberg or Hoffman), he has some familiarity with the concepts...
 
  • #9
phinds
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About 50 years ago, I studied Analytic Geometry using a Schaum's Outline book on exactly (and exclusively) that topic. It was terrific, and even this much later, you can still find it on-line (it's the 1958 edition, as I recall). More recent editions, I'm not so sure about.
 
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  • #10
Petek
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I also taught myself Analytic Geometry from the Schaum's book about 50 years ago. I still have it! The copyright is 1950.
 
  • #11
mathwonk
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alissca123, are you at UNAM? I am interested in whether one cvan still buy copies of the monografias del instituto de matematicas? I can't find them on the web anymore.
 
  • #12
Yes! I've found the Analytic Geometry (Schaum's Outline) pdf! Thanks for all the answers!
 
  • #14
mathwonk
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yes. number #13 (1983), abelian integrals, by my friend george kempf, is a great treatment of the topic of jacobians and the riemann singularities theorem that cannot be beat.

I have two copies actually myself, but it is a shame it is not available more widely. there are other nice titles as well. did you know my friend sevin recillas? or xavier and carlos gomez mont?

i apologize for diverting the thread.
 
  • #15
mathwonk, it's ok don't worry! Unfortunately the book Analytic Geometry (Schaum's Outline) is too simple, it won't help at all :(
 
  • #16
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I thought I found a book that pretty closely matches what you want:

I might not be very helpful,but here is another book with a similar title to the one you said you are using:
https://www.amazon.com/dp/0486404528/?tag=pfamazon01-20&tag=pfamazon01-20
I'm sorry I haven't read it either, but it is also cheap, with very good reviews. However, it looks like you need to know some linear algebra to read the book, which you may or may not know.
In fact, here are some others:
https://www.amazon.com/dp/0486466728/?tag=pfamazon01-20&tag=pfamazon01-20
https://www.amazon.com/dp/0486481603/?tag=pfamazon01-20&tag=pfamazon01-20
 
  • #17
qspeechc, is it possible to find these books online? If yes, can you send me the download link?
 
  • #18
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yes. number #13 (1983), abelian integrals, by my friend george kempf, is a great treatment of the topic of jacobians and the riemann singularities theorem that cannot be beat.

I have two copies actually myself, but it is a shame it is not available more widely. there are other nice titles as well. did you know my friend sevin recillas? or xavier and carlos gomez mont?

i apologize for diverting the thread.
Only by name, they are pretty famous around here (except Carlos, i've never heard of him)...
I think they replaced the Monografías with these ones... Aportaciones Matemáticas... http://texedores.matem.unam.mx/publ...ion=com_remository&Itemid=57&func=select&id=9
 
  • #19
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qspeechc, is it possible to find these books online? If yes, can you send me the download link?
It doesn't seem any of the books are legally available for free download. You can look at a bit of Hausner here:
http://books.google.co.za/books?id=...=gbs_selected_pages&cad=3#v=onepage&q&f=false

I can't find anything on the other two, except some very short reviews of Robinson:
This concise undergraduate-level text explores the relationship between algebra and geometry. Topics include determinants and linear equations, matrices, linear transformations, projective geometry, geometry on the sphere, and much more. An elementary course in plane geometry is the sole requirement, and answers to the exercises appear at the end. 1962 edition.
from amazon.com, and from google books:
This brief undergraduate-level text by a prominent Cambridge-educated mathematician explores the relationship between algebra and geometry. It is the result of several years of teaching and of learning from discussion with students the most effective methods. An elementary course in plane geometry is the sole requirement, and answers to the exercises appear at the end. 1962 edition"

I would think the first place you would look is the library, not necessarily for these books, but for books related to your course. When I was a student, a few years ago, you could even search for and loan books from nearby universities, so you can try that too.

For Hausner and Schuster there are used copies on amazon.com for less than $5, and Robinson for less than $8.

Sorry, that's all the help I can give.
 

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