Can abstract math be understood through concrete examples?

[pivoxa15]

How to go about it? I had abstract algebra in mind.

Is the main thing to do as many solid examples as possible?

So the only way to understand the abstract it is to think concrete then generalise?

 

[mjsd]

what kind of abstract algebra? does that mean Group Theory and Representation theory?

 

[ozymandias]

As Von Neumann once said, you don't understand it, you just get used to it :).

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Assaf
http://www.physicallyincorrect.com/"

 

[pivoxa15]

As Von Neumann once said, you don't understand it, you just get used to it :).

--------
Assaf
http://www.physicallyincorrect.com/"

That's a very nice quote, possibly my favourite in mathematics as it is not only pleasant but useful.

So how do you get used to abstract maths? By constructing as many concrete examples as possible?

 

[pivoxa15]

what kind of abstract algebra? does that mean Group Theory and Representation theory?

I had abstract maths in general on my mind but I am mostly interested in abstract algebra mainly rings and groups at the moment.

 

[HallsofIvy]

The first thing to do is to learn the definitions exactly. In mathematics, to a larger extent than other studies, definitions are "working" definitions- you use the precise words of defintions in proofs or problems.

 

[pivoxa15]

In pure maths I have always known that there are two levels. One is the definition, the second is doing the maths. For the mathematically challenged, they get stuck on the first level especially when it gets more abstract.

What are the steps after the definitions are known well?

 

[JasonRox]

In pure maths I have always known that there are two levels. One is the definition, the second is doing the maths. For the mathematically challenged, they get stuck on the first level especially when it gets more abstract.

What are the steps after the definitions are known well?

You said it. Do some math.

 

[yasiru89]

I defer somewhat, since the best way to understand what is abstract is to adopt a frame of mind suited to it instead of trying to bind it to grounded examples.

Pure mathematics flows my friend in the eternal closure of definition, proposition and proof.

 

[Gib Z]

The easiest way to understand difficult and abstract mathematics is to become Terry Tao or someone of a similar standing. If that is not possible, practice makes perfect.

 

[pivoxa15]

The easiest way to understand difficult and abstract mathematics is to become Terry Tao or someone of a similar standing. If that is not possible, practice makes perfect.

I thought Terry is on the concrete of abstract maths if that makes sense. i.e His speciality is in analysis and combinatorics which may be more concrete then some of the other branches in algebra or topology.

 

[Gib Z]

I meant it more generally, ie Have natural abilities like him. I'm sure he wouldn't have too much trouble grasping most mathematics given some time, even if he hasn't studied it before.