What are the differences between precalculus and analytical geometry?

Question

In highschool, I've taken Algebra, Algebra 2, Advanced Mathematics, Analytical Geometry and College Algebra. Now I'm taking Precalculus at a community college, and I've found that this and every other math I've taken above are the same (with the exception of increased difficulty as I progressed from one to the next). Am I delusional, or are they really just the same math with different names?

Answer 1

Analytical geometry per se focuses (no pun intended) on the conic sections. However, if you took an entire class on analytic geometry, chances are that you also delved into some other, somewhat related fields. Typical pre-calculus courses start with exponentials, logarithms, and move on through trigonometry, analytic geometry, and some basic calculus concepts such as differentiation and antiderivatives. In most cases, the courses would have a fair degree of overlap.

Answer 2

Hi Joe,

As a veteran of all of these classes, my own opinion is that analytic geometry is a subject best studied in conjunction with vectors and vector calculus. Why so? Because many of the arcane manipulations you see (or at least that I saw) in analytic geometry in high school can be avoided altogether by using calculus. With calculus, everything falls into place. This isn't true when studying analytic geometry independently of calculus.

"Pre-calculus" at the university I went to was considered college algebra. As far as I know, analytic geometry was not taught independently of calculus at my university. Of course, we had analytic geometry in high school for some reason, and it was a royal pain.

It seems to me that your being fed the same stuff under a different name. But to be sure, I would have to examine the evidence.

James :-)

Answer 3

Your not delusional - look at a big calculus book. All sections have equations and start with limits than it's integrate and than it's differentiate. I noticed one day I was intergrating the same equations I had found dirivitives to.

I also saw the authors like to use powers of 2 a lot like 2,4,8,16,32,64,128,256,512,1024......

They just do it to make BS degrees harder to get.