
Re: What difficulties encountered by beginners in abstract algebra?
Posted:
Jan 7, 2013 4:48 AM


On Sun, 6 Jan 2013, porky_pig_jr@mydeja.com wrote: > On Sunday, January 6, 2013 11:46:37 PM UTC5, Dan Christensen wrote:
> > I am working on some introductory notes for group theory. What > > difficulties are typically encountered by math or science undergrads > > in an introductory course on abstract algebra? > > The same kind of difficulties as moving from Calculus to Analysis. Need > set theory, need some intro to logic and proofs. > What do you mean need an introduction to logic and proofs? I learned logic and proofs during my high school sophomore year in the Euclidean geometry class. Where are they these days?
> In fact, the same difficulties are encountered by those taking the > course of Linear Algebra. With a mindset of Calculus, they don't realize > it's quite a different ball game. No longer "just go ahead, apply some > rules, do some number crunching, get the answer". So they expect to > spend a few minutes right before the class start to do the homework, and > of course they fail. What they must realize: need some time to think and > absorb the problem. I went through all of that.
Learn to think? Don't they learn that in high school? Weird. When I entered college, thinking was taken for granted. Now we have to teach kids to be homo sapiens?
What's all the prealgebra, precalculus, premath, preschool prestuff about? Does it teach anything or is it just various sorts of kindergarten school?

