On Sun, 6 Jan 2013, email@example.com wrote: > On Sunday, January 6, 2013 11:46:37 PM UTC-5, 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 pre-algebra, pre-calculus, pre-math, pre-school pre-stuff about? Does it teach anything or is it just various sorts of kindergarten school?