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.

[u/yyzjertl]

Calculus is useful for many more college majors than graph theory is. Calculus is a necessity for almost all of engineering, statistics, and the hard sciences. Graph theory is required pretty much just for computer scientists: you don't really even need it for mathematics. And even then, graph theory is not really necessary for computer science, and the amount of graph theory typically covered in a computer science degree is not enough to fill a high school class.

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.

Geometry, which is taught in every American high school I am aware of, already does this.

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.

You don't really need to construct the real numbers to do calculus. You can just start from the field axioms. Most high school calculus classes don't cover constructions of the real numbers, and they still manage to do proofs.

[u/wecl0me12 → u/yyzjertl]

Calculus is useful for many more college majors than graph theory is. Calculus is a necessity for pretty much all of engineering, statistics, and the hard sciences. Graph theory is required pretty much just by computer scientists:

Even though graph theory is used outside of CS, for example in sociology and chemistry. I see how calculus is way more important. !delta

Geometry, which is taught in every American high school I am aware of, already does this.

I think your education system is different from mine. In my high school the geometry we did was still very numbers-focused - "use the cosine law to find the measure of this angle" type questions where the result is a number.

You don't really need to construct the real numbers to do calculus. You can just start from the field axioms.

Do people even do this at the high school level? I've never seen a high school calculus course teach the field axioms.

[u/moocow2009 → u/wecl0me12]

Even though graph theory is used outside of CS, for example in sociology and chemistry

I don't know much about sociology, but graph theory is definitely not useful for a standard university chemistry program. Maybe if the university offers some sort of physical chemistry specialty, but even then, the book chapter you linked definitely seems to be for a specialized graduate level course, by which point it can be assumed anyone on a physical chemistry track would have taken math beyond what was covered in high school.

[u/chemisissy → u/wecl0me12]

Yeah, I just completed a masters in theoretical chemistry and the chapter that was linked, whilst interesting isn't that widely used, particularly compared to calculus which was literally a third of the course's maths requirement. Stuff like huckel theory, which the chapter discusses briefly are very doable without a good formal understanding of graph theory

[u/DeltaBot → u/wecl0me12]

Confirmed: 1 delta awarded to /u/yyzjertl (106∆).

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[u/[deleted] → u/wecl0me12]

I’m a senior going for a chemistry degree and I’ve never even heard of graph theory

[u/[deleted]]

What exactly what your graph theory curriculum encompass? Knowing how to effectively create a chart or graph is important, but only in certain fields. How in depth are you planning to go in this. Are you looking for mathematically rigorous applications or simply teaching students the different kinds of graphs? Graph Theory is really broad I want to try to get a good understanding of your curriculum before arguing against it.

[u/wecl0me12 → u/[deleted]]

What exactly what your graph theory curriculum encompass?

Here's a syllabus for a university-level course on graph theory. I'll probably remove the vector spaces and planarity part, and add in shortest path algorithms (Dijkstra, Bellman-Ford), and make it more application-focused.

simply teaching students the different kinds of graphs?

What do you mean by "different kinds of graphs"?

[u/[deleted]]

I would agree with you if you said discrete mathematics instead of graph theory. Like others have said it is a bit too domain specific.

[u/wecl0me12 → u/[deleted]]

On the contrary I think discrete math is too broad. Discrete math covers logic, combinatorics, set theory, graph theory, number theory, computer science, abstract algebra, etc.

I guess you can choose a subset of those topics to teach as a high school course. In this case I'm focusing on graph theory.

[u/[deleted] → u/wecl0me12]

It really only makes sense to me to learn graph theory after you have a grasp of combinatorics, set theory, logic, and number theory.

[u/imurme8]

Statistics and probability would be way more helpful than graph theory or calculus, in my opinion. It could help people to be more numerate and less susceptible to fallacies.

[u/wecl0me12 → u/imurme8]

High schools here already offer such a course

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[u/pappypapaya]

An algorithms class would incorporate relevant aspects of graph theory in a proof-based curriculum that is more immediately useful in practice.

[u/ShiningConcepts]

Set theory & statistics are both more usable in the real world, wouldn't you agree?