Place of Analytic geometry in modern undergraduate curriculum

[Bananeen]

Hello.
I am a freshmen student in mathematics at Moscow State University (in Russia) and I'm confused with placing the subject called "analytic geometry" into the system of mathematical knowledge (if you will).

We had an analytic geometry course in fall; now we are having a course in linear algebra and it seems like most of the facts from "analytic geometry" are proved in a much more systematic and easier manner (quote from http://en.wikipedia.org/wiki/Linear_algebra" "Linear algebra has a concrete representation in analytic geometry"). Many of our progressive professors also think that analytic geometry should be eliminated from the curriculum to clear more space for a linear algebra course.

So I'm confused:
1) if analytic geometry is a "concrete representation" of linear algebra, then why is it studied along with calculus (and not along with linear algebra) in US universities? (e.g. textbooks like )

There were, however, interesting parts of the course that were not covered in linear algebra: synthetic high-school-style treatment of beautiful topics like non-Euclidian and projective geometries.
Then
2) why is not there a separate course for such topics in US curricula? As I understand US math majors study 2 basic subjects - real analysis and (abstract+linear) algebra (math 55 at Harvard, 18.100 and 18.700-702 at MIT). Are these geometric topics integrated into one of these courses or they are not considered worth studying for a modern math major?

Thank you

PS. This question is also important for me because it helps a lot to browse through US top universities for textbooks they use and notes. Unfortunately, Russian mathematical school is now in tatters and US textbooks are often significantly better. And since in high school geometry was among my favorite subjects I am particularly concerned about our geometry sequence and want to browse through best geometry syllabi.

 

[g_edgar]

Long ago there were two separate courses, "Calculus" and "Analytic Geometry". Then (perhaps around the 1950s ... ?) they were generally combined into a single course "Calculus with Analytic Geometry". Those courses hope to intersperse the topics so that some analytic geometry can be used in calculus, and some calculus can be used in analytic geometry.

 

[Studiot]

Hello Bananeen and welcome.

I suppose it depends on what was in your analytic geometry syllabus. Much of the work in modern analytic geometry has been directed at computer uses and is not linear although we often try to establish linear approximations for ease of calculation. Mapping surfaces, for instance, is generally non linear. I know some of this is an overlap with projective geometry but it needs to be covered sometime. In the ultimate analytic geometry is about applying algebraic style formulae and processes (including calculus) to our world, regardless of where they come from.

go well