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Math for seven-year-olds

jdh.hamkins.org

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Re: Math for seven-year-olds

#4

Post by vanderZwan »

> Next, we considered Eulerian paths and circuits, where one traces through all the edges of a graph without lifting one’s pencil and without retracing any edge more than once. We started off with some easy examples, but then considered more difficult cases.

Wait, there's math devoted to that? I used to do that as a kid for fun!

Re: Math for seven-year-olds

#5

Post by aidos »

Great project. Strangely enough I was thinking about going through something similar just yesterday (to teach my work mate about graphs).

My daughter isn't even 3 yet so this would still be a little beyond her. Not by much though, given how approachable it has been made.

I've downloaded the kit for later in life.

Re: Math for seven-year-olds

#6

Post by aidos »

vanderZwan wrote: post #4

> Next, we considered Eulerian paths and circuits, where one traces through all the edges of a graph without lifting one’s pencil and without retracing any edge more than once. We started off with some easy examples, but then considered more difficult cases. Wait, there's math devoted to that? I used to do that as a kid for fun!

Ha! There's a whole branch of math dedicated to variations on it (http://en.wikipedia.org/wiki/Graph_theory).

Re: Math for seven-year-olds

#7

Post by crasshopper »

aidos wrote: post #6
vanderZwan wrote: post #4

> Next, we considered Eulerian paths and circuits, where one traces through all the edges of a graph without lifting one’s pencil and without retracing any edge more than once. We started off with some easy examples, but then considered more difficult cases. Wait, there's math devoted to that? I used to do that as a kid for fun!

Ha! There's a whole branch of math dedicated to variations on it ( http://en.wikipedia.org/wiki/Graph_theory ).

For graph colouring I think the right WP link is Ramsey theory.

Also not sure graphs are a "branch" of mathematics, that would be like saying polygons are a "branch" of mathematics. (Branches would be like CA, AT, DG, ... as in http://arxiv.org/list/math/recent.) I see graphs as just a common object that relates to a variety of mathematical areas.

Re: Math for seven-year-olds

#8

Post by ColinWright »

crasshopper wrote: post #7
aidos wrote: post #6

Earlier quoted context omitted.

Ha! There's a whole branch of math dedicated to variations on it ( http://en.wikipedia.org/wiki/Graph_theory ).

For graph colouring I think the right WP link is Ramsey theory. Also not sure graphs are a "branch" of mathematics, that would be like saying polygons are a "branch" of mathematics. (Branches would be like CA, AT, DG, ... as in http://arxiv.org/list/math/recent. ) I see graphs as just a common object that relates to a variety of mathematical areas.

  > For graph colouring I think the right WP link
  > is Ramsey theory.
That turns out not to be the case: Ramsey theory is an area of Graph Theory that overlaps with, but neither subsumes, nor is subsumed by, questions related to coloring graphs.

  > Also not sure graphs are a "branch" of mathematics, ...
It may be the case that you are unsure, but my PhD is in Graph Theory, specifically, and I can assume you that it is a recognized area of mathematics.

  > I see graphs as just a common object that relates
  > to a variety of mathematical areas.
Similarly groups, topological spaces, sets, etc. Math is built on abstraction - the idea is to find commonality, extract it, then study it in its own right. Then anything you prove there applies to everything it came from. Graph Theory is like that, and it is its own subject within math.
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