Advanced Algebra or College Algebra?

[BioCore]

I was wondering what the difference was between textbooks or books that teach Algebra at different levels (elementary, intermediate etc.) and College Algebra. Do College Algebra textbooks cover all levels of algebra and more, or is this some advanced new algebra.

P.S. Not referring to linear Algebra, unless if that is what college Algebra is about.

 

[Monocles]

College Algebra just refers to the algebra usually taught in high school. I think the reasons colleges call it "College Algebra" is to distinguish it from "Algebra", which is usually a course math majors take on groups, rings, fields, etc, which is "some advanced new algebra" (though it's not really new). It is often called "Abstract Algebra" as well, or "Modern Algebra".

 

[WarPhalange]

College Algebra I assume would be more advanced than intermediate and all that.

So in beginning you learn things like what a variable is, how to do basic manipulations, etc. I don't even remember what you learn in the 2nd year high school algebra class, but that's pretty much college algebra as far as I can gather.

 

[Saladsamurai]

College algebra, at my school, covers the following:

College Algebra 1

First of a two-course sequence which prepares students for the study of Calculus. A study of advanced topics in algebra including: equations, inequalities, circles, functions, properties of functions, zeros of polynomial functions and complex numbers, graphs of functions including polynomial and rational functions. Conic sections and advanced topics in systems of equations will be included as time permits.

College Algebra 2

Second of a two-course sequence which prepares students for the study of Calculus. Topics include exponential, logarithmic and trigonometric functions, graphs of trigonometric functions, trigonometric identities and equations, inverse trigonometric and applications of trigonometry. Complex numbers, sequences and series, and polar coordinates may be included as time permits.

 

[Nick M]

At my community college we have mathematics classes that range from "Basic Mathematics" (simple addition/subtraction/multiplication/division/fractions) all the way through Multivariate Calculus, Differential Equations, and Linear Algebra (the highest level of math required by most Engineering schools).

My school offers three levels of Algebra, because it's often the most difficult thing for people to learn - especially those who are starting from the beginning. If you did good in high school and simply need an Algebra refresher, take College Algebra. If you think you need a slow approach to learning Algebra with topics introduced at a much more gradual pace, take Introductory or Intermediate Algebra. However, anything below College Algebra at my school is considered remedial, and doesn't earn any credits. If you are planning on Engineering or Physics, usually anything below Calculus I doesn't earn any credits towards your graduation requirements.

When I started back to school for Engineering, I had very strong algebra skills and credits for Calculus I, but I decided to start fresh in Pre-Calculus - and even retook Calculus I. It was a wise decision, as I've now completed Calculus I & II, Linear Algebra, and am registered for Multivariate Calculus this fall (with a 3.9 GPA). Some people make fun of those who are in college taking Algebra or Pre-Calc, but don't let that scare you... you will be much stronger at math having a solid foundation in Algebra, trigonometric and transcendental function modeling. That solid core will carry over into your other classes too. Most people in my Physics classes had a difficult time modeling functions for sinusoidal data, and spent 3-4x as long as I did generating functions with the proper phase, amplitudes, etc. It's little things like this that make learning challenging material that much easier.

Start where you feel comfortable, and don't be ashamed if you take extra time. Better to take extra time and have an intimate understanding of the material than to be just another yahoo who forces their way through with a C and struggles with material throughout the rest of their schooling.

 

[symbolipoint]

Nick M, most of what you say (post #5) is truthful or reliable. College courses of Algebra will have Introductory and Intermediate Algebras, which are remedial courses of NO college level credit. College Algebra, Elementary Functions, Pre-Calculus(College Algebra plus Trigonometry), and Trigonometry are all college level courses, NON-remedial.

In contrast to what you say, many students find any or all of the courses of Introductory, Intermediate, or College Algebras to be difficult. Yet, still, as you say, students should never try to over-step their level of skill and knowledge in a course which is too hard for them. The course called College Algebra usually contains topics beyond the Intermediate course, and so the new content is difficult for students studying these topics the first and sometimes second time. College Algebra presents zeros and graphs of polynomial functions, exponential & logarithmic functions and their graphs, and a strong but intuitive introduction to limits, and sequences & series; and some such courses if time permits, also present inductive proofs, some linear algebra, and a few pieces from counting principles, probability, and statistics. With all of these topics included in College Algebra, the intermediate level seems easy by comparison.

 

[BioCore]

Thanks a lot for the post Nick M. I was wondering what textbook you guys would recommend? I found this one at my school "College Algebra and trigonometry" by "Steven J. Bryant". It is a pretty old textbook from the 70's although it looks really good because it constantly provides proofs for every theorem and then examples right after to strengthen the understanding.

Now I am still not sure if I should continue with it though or if there is some other better textbook out there currently being used. If you guys have some suggestions I wouldn't mind trying them out.