What Do Math Majors Wish They Knew Before Graduation?

[jk]

I don't know. I don't see it any differently then a physics class where you are given a lecture and then a separate lab period. The motivation may just be to get it over with, but you end up learning quite a bit. I've always learned more in labs than in lectures - usually against my will! And the work *is* much harder, because you have to think on your feet.

It's likely many students would not like this, especially if they have no real interest in math.

-Dave K

I have had those lab periods too and it is very different. In a Moore class, you are essentially rederiving everything while in a lab you are basically solving problems. The fact that you have no crutches (no textbook, no direct help from the instructor or students) means that you have enormous pressure to work it out yourself. It also means an increase in confidence that what you thought were hard or impossible problems are now within your reach. Sometimes it takes 2 or 3 tries at the board to get it right so it might mean that you finish a proof days later. You don't necessarily have to "think on your feet" because some of the material takes time. You also learn to refine your arguments and present it in the clearest fashion because you have the time in between classes to work on it.
There are people who do not like it. Some prefer very structured classes and do not like the open ended nature of it. Some have no interest in working so hard...they just want to get their grade and be done with it. But if you have an interest in learning mathematics, you should give it a try if you have a chance.

 

[dkotschessaa]

Well, I'm not sure such a thing is happening where I am, but I'll keep an eye out.

I am very happy though that a professor has invited me to study with him during a summer session where he will be mostly bored teaching a precalculus summer course, but available all day, so he wants to do something. I am stoked.

 

[dkotschessaa]

Any more adds to the original post would be cool, if anybody has any ideas. I'd love to see this as the "corollary" to mathwonk's thread. (I dream big, you see).

It's kind of a "if I knew then what I know now" sort of thing.

-Dave K

 

[20Tauri]

I am very happy though that a professor has invited me to study with him during a summer session where he will be mostly bored teaching a precalculus summer course, but available all day, so he wants to do something. I am stoked.

That sounds fantastic. I wish I had professors who wanted me to spend the summer hanging out and doing math.

 

[dkotschessaa]

Question RE: Analysis

I know inevitably I will take Analysis, and it will likely be the most difficult course in my major. What are the things I can do now as I go along to make sure I'm prepared by the time I get there?

Is it the "abstract-ness" of the course that makes it difficult? Or is it not having a solid grasp of calculus? Fortunately we have a course devoted to abstract mathematics, which so far is my favorite course. I do think I am pretty inclined towards abstract math above "calculation" type courses, which is good news.

-Dave K

 

[homeomorphic]

Is it the "abstract-ness" of the course that makes it difficult? Or is it not having a solid grasp of calculus?

I think people who get that far usually have a sufficient grasp of calculus, and part of what you gain from the class will be a deeper mastery of it, so that's part of what the class is for, rather than something you have to have coming into it. I'm not sure it's the abstractness, although that is part of it. The difficulty is conceptual and in the fact that you have to do serious proofs.

 

[ZombieFeynman]

I took Abstract Algebra and Analysis using the moore method. The pace is slower, but i find it to be a far better method for upper divisional proof based classes.

 

[dkotschessaa]

I took Abstract Algebra and Analysis using the moore method. The pace is slower, but i find it to be a far better method for upper divisional proof based classes.

Cool, but I doubt we have anything like that. I'd love it though.

-Dave K

 

[dustbin]

I took Abstract Algebra and Analysis using the moore method. The pace is slower, but i find it to be a far better method for upper divisional proof based classes.

Can I ask where this was at?

 

[dkotschessaa]

Can I ask where this was at?

GooglePedia(A word I just made up) actually had an answer for this one:

http://en.wikipedia.org/wiki/Moore_method#Current_usage_of_the_Moore_Method

 

[dkotschessaa]

"When a flaw appeared in a 'proof' everyone would patiently wait for the student at the board to 'patch it up.' If he could not, he would sit down. Moore would then ask the next student to try or if he thought the difficulty encountered was sufficiently interesting, he would save that theorem until next time and go on to the next unproved theorem (starting again at the bottom of the class)." (Jones 1977)

It sounds kind of wonderful and terrifying at the same time.

-Dave K