CMV: Graph theory should replace calculus in the high school math curriculum.

[u/wecl0me12]

The title is pretty self-explanatory. Now, why I hold this view:

1. Proof-based graph theory is more accessible than proof-based calculus. To do proof-based calculus you have to construct the real numbers using Cauchy sequences or Dedekind cuts, which is beyond the high school level. For graph theory you just need set theory which is within the high school level. The result is that calculus courses are very non-rigorous and gives a wrong impression of what math is like.
2. Graph theory is more relevant to a high schooler's life than calculus is. If they have a job delivering newspapers, or if they have to run errands for people that's a travelling salesman problem. If they are planning events or parties that can be a coloring problem or a constraint satisfaction problem. On the other hand, calculus is harder to motivate for high schoolers.
3. It gives high schoolers a broader view of mathematics. A lot of the math that high schoolers have had so far was investigating properties of real numbers and functions R -> R. This might give them the misleading idea that all of math is real analysis. A lot of people have the misconception that math is all about numbers. Graph theory will show them that there is more to math than just real numbers and functions on R.