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If the whole of math were represented by the surface of the planet, "discrete math" would be more than half of it. Calculus (i.e. differentiation/integration o

If the whole of math were represented by the surface of the planet, "discrete math" would be more than half of it. Calculus (i.e. differentiation/integration on the reals) on the other hand, would be a city. Perhaps a very populated city, but just one. It's a shame that match curriculum for non-math-majors is an all-roads-lead-to-calculus affair. I think we scare a lot of potentially talented people away from math with that approach.

cperciva 5y ago
"Calculus" is just the most accessible corner of the broader field of Analysis. And a lot of "discrete" mathematics ends up drawing upon analysis (especially complex analysis) as you delve deeper.
garmaine 5y ago
I'm not sure why you think that? Basically all of physics, chemistry, and other physical sciences is calculus. Calculus is the mathematics of rates of change, and basically all physical science is the study of change. Discrete math is very important to computer science. But in the rest of the world, calculus (and differential equations) dominate.
- 123pie123 5y ago
  Double integration - brings not very nice memories back of my hand aching from writing upto 5 pages of workings out
  - __MatrixMan__ 5y ago
    It was especially bad in quantum mechanics where they made us do it the hard way (using calculus) before showing us the easy way (using noncommutative algebra).
- __MatrixMan__ 5y ago
  Maybe we're having a definition difference. My understanding of the term "discrete math" is that it refers to any math whose characters aren't part of a continuum. Anything to do with numbers besides the reals. Anything to to with finite sets. Anything to do with groups, rings, polynomials, trees, graphs, ordinals, lattices, compass-straightedge-constructions, polygons, knots, categories, sheaves, topological spaces, vector spaces, and anything to do with oddities like map coloring or plane tiling, and a lot else too. It's a course in "everything else" for students that are being pigeonholed into a mathematical specialization by the fact that it's been fashionable to use real numbers to describe the world since Newton.
  - smus 5y ago
    Have you studied math? No mathematician would call algebraic topology discrete math, nor for that matter almost anything else on that list.
    - __MatrixMan__ 5y ago
      Yes, I have a degree in it. I'd have to ask around but I know a few algebraic topologists and I'd bet that if pressed to describe their work as more-continuous or more-discrete they'd first tell you that this is a silly way to classify subfields in math and then they'd says it's probably more on the discrete side since it's all about categorizing topological spaces based on whether they have certain discrete properties: - separable - countable - metric - compact Sure the spaces themselves might be continuous, but topology is for telling those spaces apart based on where and how continuity fails. It's a discretization of things formerly suspected to be the the same.
      - smus 5y ago
        I mean the notion of compactness is inspired pretty clearly from the continuum. I also have a degree in pure math and disagree strongly with your characterization of topology, which is literally defined up to homeomorphism which is itself defined by it's continuity. Arguably the whole point of topology is characterized by that which is preserved by continuous deformation, which clearly is inspired by more continuous math. I think you are using incredibly strong language and in a misguided way.
        __MatrixMan__ 5y ago
        Yeah, I think you're right. There's something about real analysis that makes me uncomfortable. I've been struggling for years to put my finger on it. Whatever it is, topology doesn't have it. I had mistakenly decided that it was an overappreciation of continuity, but I think it must be something else.
        5y ago
kevin_thibedeau 5y ago
All of the advanced technology you use on a daily basis depends on calculus for it to be designed and fabricated.
- __MatrixMan__ 5y ago
  I didn't say it wasn't useful, just that it's not representative of mathematics as a whole.
WoahNoun 5y ago
Well this isn't true at all. I'm shocked anyone would upvote this nonsense.
- __MatrixMan__ 5y ago
  How about we play a game where you make a list of mathematical objects which are continuous, and I make a list of ones that aren't. I'll start with sets and you can start with the real numbers, and we'll see whose list is longer. To a certain degree the whole game is nonsense, there's a countable infinity of axioms and a countable infinity of theorems that follow therefrom, so we're never going to get anywhere rigorous with this, but just like it's not unreasonable to say that there are more multiples of 2 than there are of 2000, I think it's fair to say that continuity games on the reals represents a relatively small share when compared to mathematics in general.

cperciva 5y ago

"Calculus" is just the most accessible corner of the broader field of Analysis. And a lot of "discrete" mathematics ends up drawing upon analysis (especially complex analysis) as you delve deeper.

garmaine 5y ago

I'm not sure why you think that? Basically all of physics, chemistry, and other physical sciences is calculus. Calculus is the mathematics of rates of change, and basically all physical science is the study of change. Discrete math is very important to computer science. But in the rest of the world, calculus (and differential equations) dominate.

123pie123 5y ago
Double integration - brings not very nice memories back of my hand aching from writing upto 5 pages of workings out
- __MatrixMan__ 5y ago
  It was especially bad in quantum mechanics where they made us do it the hard way (using calculus) before showing us the easy way (using noncommutative algebra).
__MatrixMan__ 5y ago
Maybe we're having a definition difference. My understanding of the term "discrete math" is that it refers to any math whose characters aren't part of a continuum. Anything to do with numbers besides the reals. Anything to to with finite sets. Anything to do with groups, rings, polynomials, trees, graphs, ordinals, lattices, compass-straightedge-constructions, polygons, knots, categories, sheaves, topological spaces, vector spaces, and anything to do with oddities like map coloring or plane tiling, and a lot else too. It's a course in "everything else" for students that are being pigeonholed into a mathematical specialization by the fact that it's been fashionable to use real numbers to describe the world since Newton.
- smus 5y ago
  Have you studied math? No mathematician would call algebraic topology discrete math, nor for that matter almost anything else on that list.
  - __MatrixMan__ 5y ago
    Yes, I have a degree in it. I'd have to ask around but I know a few algebraic topologists and I'd bet that if pressed to describe their work as more-continuous or more-discrete they'd first tell you that this is a silly way to classify subfields in math and then they'd says it's probably more on the discrete side since it's all about categorizing topological spaces based on whether they have certain discrete properties: - separable - countable - metric - compact Sure the spaces themselves might be continuous, but topology is for telling those spaces apart based on where and how continuity fails. It's a discretization of things formerly suspected to be the the same.
    - smus 5y ago
      I mean the notion of compactness is inspired pretty clearly from the continuum. I also have a degree in pure math and disagree strongly with your characterization of topology, which is literally defined up to homeomorphism which is itself defined by it's continuity. Arguably the whole point of topology is characterized by that which is preserved by continuous deformation, which clearly is inspired by more continuous math. I think you are using incredibly strong language and in a misguided way.
      - __MatrixMan__ 5y ago
        Yeah, I think you're right. There's something about real analysis that makes me uncomfortable. I've been struggling for years to put my finger on it. Whatever it is, topology doesn't have it. I had mistakenly decided that it was an overappreciation of continuity, but I think it must be something else.
        5y ago

kevin_thibedeau 5y ago

All of the advanced technology you use on a daily basis depends on calculus for it to be designed and fabricated.

__MatrixMan__ 5y ago
I didn't say it wasn't useful, just that it's not representative of mathematics as a whole.

WoahNoun 5y ago

Well this isn't true at all. I'm shocked anyone would upvote this nonsense.

__MatrixMan__ 5y ago
How about we play a game where you make a list of mathematical objects which are continuous, and I make a list of ones that aren't. I'll start with sets and you can start with the real numbers, and we'll see whose list is longer. To a certain degree the whole game is nonsense, there's a countable infinity of axioms and a countable infinity of theorems that follow therefrom, so we're never going to get anywhere rigorous with this, but just like it's not unreasonable to say that there are more multiples of 2 than there are of 2000, I think it's fair to say that continuity games on the reals represents a relatively small share when compared to mathematics in general.