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I like graph theory. You draw some shapes, you draw some lines. It's like the kind of things you can do with your crayons. I reckon kids could be introduced to

I like graph theory. You draw some shapes, you draw some lines. It's like the kind of things you can do with your crayons. I reckon kids could be introduced to it earlier in friendlier language.

xcambar 5y ago
Wholeheartedly agree. Graph theory is probably one of the most relatable, accessible theories available. It is a fantastic tool to discover algorithmics, as you can visually apply your thinking. FWIW, I personally wrote my master thesis on small world graphs, (_ie_ Kevin Bacon, 6 degrees, that kind of graphs), building structures to add properties to such graphs, and it is, without a doubt, the best memory of my cursus at the university.
- ffhhj 5y ago
  Can imagine Logo programming lang for graphs.
js8 5y ago
> I reckon kids could be introduced to it earlier in friendlier language. They can be! I remember when I was about 10, I learned about Eulerian paths from a popular math book for kids.
thomasahle 5y ago
I'm pretty sure this is also what draws in a lot of researchers. We're lucky that the theory is also so often useful.
bmm6o 5y ago
Specifically for planarity, it's pretty easy to convince yourself that K5 and K3,3 are minimally non-planar. You don't come out with a rigorous proof but you do get an intuitive feel. With a decent motivating example it's accessible to kids.
adrianN 5y ago
I also like graph theory. I don't think kids should have to learn it. It's much, much less useful than statistics, linear algebra, and calculus in everyday life or most university courses. Math in schools should, imho, be a mixture of mostly "how to lie with statistics" with a little preparation for engineering and science degrees. People need an intuition for statistical reasoning to understand the news and participate in democracies. It's about as important as being able to read complex texts. You need some calculus and linear algebra to understand basic physics. Most other areas of math are primarily interesting to Mathematicians and Computer Scientists.
- jonsen 5y ago
  I aggree that statistics is important, but graphs are of some use in statistics: https://en.m.wikipedia.org/wiki/Graphical_model https://en.m.wikipedia.org/wiki/Graphical_model Can’t find the link now, but I’ve seen a pedagogical framework for learning basic probability by manipulating dynamic graph-“walking”. Absolutely useable with kids.
  - goldenkey 5y ago
    You are probably referring to https://en.wikipedia.org/wiki/Dynamic_Bayesian_network https://en.wikipedia.org/wiki/Dynamic_Bayesian_network
    - jonsen 5y ago
      Found it: https://mathenchant.wordpress.com/2017/08/16/prof-engels-marvelously-improbable-machines/ https://mathenchant.wordpress.com/2017/08/16/prof-engels-mar...
      - goldenkey 5y ago
        Wowzers: https://youtu.be/Ap5NslpYikU https://youtu.be/Ap5NslpYikU Very interesting stuff..Engel's probability abacus.
  - adrianN 5y ago
Agingcoder 5y ago
Yes, I actually had a graph theory session with 6 year olds ! We talked about graphs, graph coloring, eulerian paths, etc all with pencils and paper. It was a 'talk about your job to schoolchildren' day, and I thought they might relate to graphs. It was so successful that all kindergarten teachers in the same school started doing it as well. The unexpected part was the other parents, who looked at the poster the children had made about chromatic numbers complete with examples : quite sadly, they were a lot more scared than their children!
TechBro8615 5y ago
As someone who hated math and was really bad at it since calculus (mostly due to lack of rigor), yes. Once I got to algorithms class, I struggled at first but after a session with my (really excellent) professor, something “clicked”. I really think graph theory and discrete math in general should be taught much earlier. Maybe even before (or alongside) calculus in high school. Calculus isn’t really a legitimate prerequisite in this case.

I like graph theory. You draw some shapes, you draw some lines. It's like the kind of things you can do with your crayons. I reckon kids could be introduced to it earlier in friendlier language.

xcambar 5y ago

Wholeheartedly agree. Graph theory is probably one of the most relatable, accessible theories available. It is a fantastic tool to discover algorithmics, as you can visually apply your thinking. FWIW, I personally wrote my master thesis on small world graphs, (_ie_ Kevin Bacon, 6 degrees, that kind of graphs), building structures to add properties to such graphs, and it is, without a doubt, the best memory of my cursus at the university.

ffhhj 5y ago
Can imagine Logo programming lang for graphs.

js8 5y ago

> I reckon kids could be introduced to it earlier in friendlier language. They can be! I remember when I was about 10, I learned about Eulerian paths from a popular math book for kids.

thomasahle 5y ago

I'm pretty sure this is also what draws in a lot of researchers. We're lucky that the theory is also so often useful.

bmm6o 5y ago

Specifically for planarity, it's pretty easy to convince yourself that K5 and K3,3 are minimally non-planar. You don't come out with a rigorous proof but you do get an intuitive feel. With a decent motivating example it's accessible to kids.

adrianN 5y ago

I also like graph theory. I don't think kids should have to learn it. It's much, much less useful than statistics, linear algebra, and calculus in everyday life or most university courses. Math in schools should, imho, be a mixture of mostly "how to lie with statistics" with a little preparation for engineering and science degrees. People need an intuition for statistical reasoning to understand the news and participate in democracies. It's about as important as being able to read complex texts. You need some calculus and linear algebra to understand basic physics. Most other areas of math are primarily interesting to Mathematicians and Computer Scientists.

jonsen 5y ago
I aggree that statistics is important, but graphs are of some use in statistics: https://en.m.wikipedia.org/wiki/Graphical_model https://en.m.wikipedia.org/wiki/Graphical_model Can’t find the link now, but I’ve seen a pedagogical framework for learning basic probability by manipulating dynamic graph-“walking”. Absolutely useable with kids.
- goldenkey 5y ago
  You are probably referring to https://en.wikipedia.org/wiki/Dynamic_Bayesian_network https://en.wikipedia.org/wiki/Dynamic_Bayesian_network
  - jonsen 5y ago
    Found it: https://mathenchant.wordpress.com/2017/08/16/prof-engels-marvelously-improbable-machines/ https://mathenchant.wordpress.com/2017/08/16/prof-engels-mar...
    - goldenkey 5y ago
      Wowzers: https://youtu.be/Ap5NslpYikU https://youtu.be/Ap5NslpYikU Very interesting stuff..Engel's probability abacus.
- adrianN 5y ago

Agingcoder 5y ago

Yes, I actually had a graph theory session with 6 year olds ! We talked about graphs, graph coloring, eulerian paths, etc all with pencils and paper. It was a 'talk about your job to schoolchildren' day, and I thought they might relate to graphs. It was so successful that all kindergarten teachers in the same school started doing it as well. The unexpected part was the other parents, who looked at the poster the children had made about chromatic numbers complete with examples : quite sadly, they were a lot more scared than their children!

TechBro8615 5y ago

As someone who hated math and was really bad at it since calculus (mostly due to lack of rigor), yes. Once I got to algorithms class, I struggled at first but after a session with my (really excellent) professor, something “clicked”. I really think graph theory and discrete math in general should be taught much earlier. Maybe even before (or alongside) calculus in high school. Calculus isn’t really a legitimate prerequisite in this case.