General > RANT
Continuance of the INfinity Proposal
Numsgil:
--- Quote from: abyaly ---I guess you didn't have a good teacher for that stuff, then. It's possible to do quite a bit without using fancy words. In one of my undergrad classes our professor intentionally didn't tell us what most of the things were in order not to distract people from the important things. Eg: "Show that if a1, a2, a3, ... is a number sequence such that for any positive number c there is a natural number N such that if n and m are greater than N, then |an - am| < c, then a1, a2, a3, ... converges." was one of the problems, but in that class we never used the term cauchy sequence. Avoiding new words does tend to make things a big longer, though.
I'm sorry your classes were focused on memorization. That is not a good way to learn the material.
--- End quote ---
It would have helped, but even explained out in words makes it hard to understand. It's like having the Pythagoras theorem explained as "In any right triangle, the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares whose sides are the two legs". You can't just gloss over a sentence like that and understand what it means. You need pictures and notation.
--- Quote from: Peter ---Good teachers can help a lot. Especially in math. This reminds me of a math teacher that, well tried to explain differential equations
He just ignored any questions with, you're supposed to know that or that's not important. He didn't really explain anything but just start writing the whole calculation down. And often it came to mind with him, that he made another mistake, wipes a part away. And starts doing something else he hopes that works. , strange experience that was.
He didn't did it every class that extreme, but it was sure he wasn't a good math-teacher. I'm not sure anyway how he did exactly maybe he did improve. I skipped those classes after a while.
Fact was that most failed math that specific semester, I was then one of the lucky ones that passed it.
That wasn't becouse it was all hard, the classes (math) from him really was confusing.
--- End quote ---
I had a teacher like that for a discrete math class in computer science. I knew most of the material already, but the way he explained things, it sure didn't feel like it
abyaly:
But once you grasp what something means when decompressed from the notation, you can understand any mathematical statement.
Numsgil:
Yeah, most math things are actually pretty easy to understand. The hard part is just presenting the idea in a way that someone can understand it. Pure math hasn't quite gotten as far as basic arithmetic in this regard. English (any human language for that matter) is an ill fit for mathematical ideas, because it's not always clear what's a loaded word (group and set in a mathematic sense mean something very different from English, where they really mean the same thing), and what's just filler to make it grammatically correct. Presenting ideas in a way that's easy to understand isn't easy, of course. I'm not faulting anyone for the current state of affairs.
It's like word problems. I hated word problems in Elementary school because they had to use loaded words for operations. "difference" meant subtraction, "and" means addition, unless you're talking about some other field of math like sets (where it means intersection, which is counter intuitive because addition is a constructive process that makes something bigger, and intersection is a destructive process that makes it smaller <-- an insight in to how my mind works).
I don't have a better solution, though. The set building notation isn't all that much better than raw English, for instance. Upside down A's and backwards E's are just as confusing. It's taken calculus hundreds of years to be as digestible as it is (and it still has a ways to go, I think). So hopefully in hundreds of years they'll figure out better ways of presenting the material that isn't so obtuse.
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