Graph Theory: Pure or Applied?

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Discussion Overview

The discussion revolves around the classification of graph theory as either a pure or applied subject. Participants explore the nature of graph theory, its theoretical foundations, and its practical applications, considering both perspectives in the context of mathematical study.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant suggests that graph theory is both theoretical and applied, emphasizing the importance of a theoretical background while allowing for experimentation with graphs and their properties.
  • Another participant argues for the classification of graph theory as primarily pure, recalling their experience focused on proving properties of graphs.
  • A different viewpoint proposes that graph theory should be classified along a concrete/abstract axis, highlighting its abstract aspects while also noting its visualizable elements.
  • This participant also mentions the relative independence of graph theory from other branches of mathematics, suggesting that beginners can engage with it without extensive mathematical knowledge.

Areas of Agreement / Disagreement

Participants express differing opinions on whether graph theory is primarily pure or applied, indicating that multiple competing views remain without a consensus.

Contextual Notes

Some limitations in the discussion include varying interpretations of what constitutes 'pure' versus 'applied' mathematics and the potential ambiguity in defining the concrete/abstract classification.

andlook
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Hi

Is graph theory a more pure or applied subject?

I thought it was pure but now I am confusing myself because it has so many applications.

Thanks
 
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It is both a theoretical and applied subject. You will decide how you'll use it. You can construct proofs and/or you can experiment with numerous graphs, their properties and their application. but a theoretical background is a must
 
I'd say pure. When I took graph theory, it was all about proving stuff about graphs (which is far from easy!).
 
I have dabbled in it both for fascination of 'pure' aspects and for some applications.

Would it be useful to classify it not by, or not only by, the pure/applied axis but along the concrete/abstract axis. It no doubt has abstract aspects, but it is often about perfectly 'concretely' visualisable things, whether they are useful or not and they always might be - a bit like 2 and 3D Euclidean geometry. Is that not one nice thing about it - for some of us?

Is not another nice aspect that it is relatively independent of other branches of mathematics, so a beginner can go quite far without a vast mathematical background?
 

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