Can I take Abstract Algebra as a High School Student?

[Desafino]

I've read up a little bit about Abstract Algebra and it seems like a really interesting subject. A university near me will offer an intro class in it next semester. Trouble is, the university requires Calc III as a prerequisite for the course. I'm taking AP Calc right now at school, but it doesn't look like there's any calculus in the Algebra course. Is the prerequisite simply to ensure that people enrolling have some mathematical aptitude rather than necessary to understanding the material --(I'm a smart kid with a near-perfect SAT score so I think I can probably pick up the material?)

 

[Number Nine]

Introductory algebra almost certainly won't involve anything resembling multivariable or vector calculus unless they happen to cover something unusually specialized. You'll study the basic properties of sets, functions and relations before going on to study algebraic structures. The requirement is almost certainly, as you say, to ensure some level of comfort with advanced mathematics. If you're interested in learning a but of algebra but can't take the course, Gilbert's Elements of Modern Algebra is a fantastic introduction to the subject and to proofs in general. Be aware that the subject is nothing like any mathematics you've ever encountered before.

 

[qspeechc]

The best thing to do is to talk to the person giving the course. E-mail them and ask if you can set up a time to discuss this, or ask them in the e-mail what you want to know. Otherwise get a hold of the secretary.

 

[AlephZero]

Thereis no reason why you need calc III to start on abstract algebra. Quite likely the university course includes some "advanced" examples of algebraic structures that need Calc III to understand them, but that isn't the core part of the subject.

At high school level, I suggest you start by studying groups. There are good examples of groups that don't involve any math concepts beyond integer arithmetic, geometric operations like reflections and rotations, permutations of lists of objects, etc. Then move on to rings, fields, and vector spaces - at which point you WILL come across examples of algebraic structures where the elements of the structure are functions, and you will need calc III to understand what the operations on the elements mean.

 

[Vanadium 50]

We also don't know if linear algebra gets its own course or if it's covered in Calc III, which would be a good reason to teach it before Abstract.

 

[deluks917]

No you don't need anything from multi-variable calculus. You might need the basics of Linear Algebra. I think you should take the class. These notes are good if you want a fast basic intro to LA: http://tutorial.math.lamar.edu/Classes/LinAlg/LinAlg.aspx