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I have to admit, being a hybrid math/csci student, I never understood the place of discrete math in mathematics or computer science. It always seemed like a mi

I have to admit, being a hybrid math/csci student, I never understood the place of discrete math in mathematics or computer science. It always seemed like a mish-mash of different topics I'd studied in algebra->geometry->calc (including mv calc, linear algebra, diff eq, and series and sequences)->real analysis. This article is a bit too brief to properly place it (at least I still don't see it), could someone provide some proper context for discrete mathematics that fits into the mold of the standard maths sequence?

gizmo686 9y ago
It doesn't. In my experience, "Discrete Math" is not offered as a math class, but rather as a computer class. In effect, it is the "math for computer science majors" class.
- dcow 9y ago
  That was not my experience despite it being a requirement for the CS major.
- dagw 9y ago
  At the university I went to both the math and CS departments offered discrete math courses with slightly different focuses.
kccqzy 9y ago
Discrete math in my school is mostly about combinatorics, but also graph theory, trees, and things like that. It doesn’t really fit into the standard math sequence IMO. The standard math sequence is essentially single-variable calculus -> multi-variable calculus -> linear algebra and differential equations -> real analysis. Note that all of the above fields essentially operate on continuous things like the real numbers.
- gh02t 9y ago
  That's not quite true, almost any respectable math program is gonna include a significant amount of material on finite set theory and discrete algebra (though maybe not in the non math major escalator, that usually stops at differential equations). That said, I think there is definitely a place for a "discrete math" course, which focuses on teaching things in a more computer science relevant manner. I also think numerical analysis is a much better choice than real analysis for CS majors, but that's a different topic...
  - fjsolwmv 9y ago
    Of course applied math is much more relevant to CS than pure math. CS is an application of math.
    - billfruit 9y ago
      But most applied maths courses/books focus heavily on ODE/PDE which are rarely of help to CS undergrads.
  - kccqzy 9y ago
    Oh I’m interpreting GP’s mention of standard math sequence as something everyone in math/CS/engineering needs to study, not what math majors specifically need to study.
smadge 9y ago
A survey "Discrete Mathematics" course is definitely a mishmash. But every topic in discrete mathematics is rich enough to study in it's own 4 credit 1 quarter undergraduate course: Set Theory, Combinatorics, Graph Theory, Formal Logic, etc.
JonathonW 9y ago
It's hard to place a particular "context" for discrete math; it really is a hodgepodge of topics, loosely linked because they deal with discrete structures (integers, graphs, logic statements) rather than continuous ones (real/complex numbers). It's particularly relevant to computer science because, in CS, we're dealing with discrete structures almost exclusively. The rise of computers and of CS is both what led to the current interest in discrete math subjects as a research field and what led to the development of university curricula in the topic. So, really, discrete math (as a university course) exists mostly to teach some CS-relevant topics that don't necessarily get much dedicated time in the "standard" algebra->geometry->calc progression, because they're more concerned with continuous phenomena. It's sort of a parallel and independent track from the "standard" math sequence.
- craigching 9y ago
  So all responses thus far have been great, I think the thing I struggled with in HS and into university is trying to place everything and see what the current math leads to. So, responding here, but upvoting those that responded to me at this time because all provided me with insight. Thanks!
  - glockenspielen 9y ago
    Head down the Prof Wildberger rabbit hole if you'd like to explore why we might be able to cast aside chunks of conventional math including real numbers and infinite sets. https://m.youtube.com/channel/UCXl0Zbk8_rvjyLwAR-Xh9pQ https://m.youtube.com/channel/UCXl0Zbk8_rvjyLwAR-Xh9pQ https://njwildberger.com https://njwildberger.com
    - fjsolwmv 9y ago
      Might be? Of course we can. Obviously infinite objects are irrelevant to modeling the real world. They are just a shorthand for adding a bunch of annoying qualifiers to every mathematical statement.
      - 9y ago
saagarjha 9y ago
A common use case is prove correctness or running time of algorithms.
- kqr 9y ago
  Prove running time as in complexity analysis is more analysis than algebra though, right?
  - saagarjha 9y ago
    Depends. There's not a whole lot of analysis you can do on sufficiently complex recursive algorithms.

gizmo686 9y ago

It doesn't. In my experience, "Discrete Math" is not offered as a math class, but rather as a computer class. In effect, it is the "math for computer science majors" class.

dcow 9y ago
That was not my experience despite it being a requirement for the CS major.
dagw 9y ago
At the university I went to both the math and CS departments offered discrete math courses with slightly different focuses.

kccqzy 9y ago

Discrete math in my school is mostly about combinatorics, but also graph theory, trees, and things like that. It doesn’t really fit into the standard math sequence IMO. The standard math sequence is essentially single-variable calculus -> multi-variable calculus -> linear algebra and differential equations -> real analysis. Note that all of the above fields essentially operate on continuous things like the real numbers.

gh02t 9y ago
That's not quite true, almost any respectable math program is gonna include a significant amount of material on finite set theory and discrete algebra (though maybe not in the non math major escalator, that usually stops at differential equations). That said, I think there is definitely a place for a "discrete math" course, which focuses on teaching things in a more computer science relevant manner. I also think numerical analysis is a much better choice than real analysis for CS majors, but that's a different topic...
- fjsolwmv 9y ago
  Of course applied math is much more relevant to CS than pure math. CS is an application of math.
  - billfruit 9y ago
    But most applied maths courses/books focus heavily on ODE/PDE which are rarely of help to CS undergrads.
- kccqzy 9y ago
  Oh I’m interpreting GP’s mention of standard math sequence as something everyone in math/CS/engineering needs to study, not what math majors specifically need to study.

smadge 9y ago

A survey "Discrete Mathematics" course is definitely a mishmash. But every topic in discrete mathematics is rich enough to study in it's own 4 credit 1 quarter undergraduate course: Set Theory, Combinatorics, Graph Theory, Formal Logic, etc.

JonathonW 9y ago

It's hard to place a particular "context" for discrete math; it really is a hodgepodge of topics, loosely linked because they deal with discrete structures (integers, graphs, logic statements) rather than continuous ones (real/complex numbers). It's particularly relevant to computer science because, in CS, we're dealing with discrete structures almost exclusively. The rise of computers and of CS is both what led to the current interest in discrete math subjects as a research field and what led to the development of university curricula in the topic. So, really, discrete math (as a university course) exists mostly to teach some CS-relevant topics that don't necessarily get much dedicated time in the "standard" algebra->geometry->calc progression, because they're more concerned with continuous phenomena. It's sort of a parallel and independent track from the "standard" math sequence.

craigching 9y ago
So all responses thus far have been great, I think the thing I struggled with in HS and into university is trying to place everything and see what the current math leads to. So, responding here, but upvoting those that responded to me at this time because all provided me with insight. Thanks!
- glockenspielen 9y ago
  Head down the Prof Wildberger rabbit hole if you'd like to explore why we might be able to cast aside chunks of conventional math including real numbers and infinite sets. https://m.youtube.com/channel/UCXl0Zbk8_rvjyLwAR-Xh9pQ https://m.youtube.com/channel/UCXl0Zbk8_rvjyLwAR-Xh9pQ https://njwildberger.com https://njwildberger.com
  - fjsolwmv 9y ago
    Might be? Of course we can. Obviously infinite objects are irrelevant to modeling the real world. They are just a shorthand for adding a bunch of annoying qualifiers to every mathematical statement.
    - 9y ago

saagarjha 9y ago

A common use case is prove correctness or running time of algorithms.

kqr 9y ago
Prove running time as in complexity analysis is more analysis than algebra though, right?
- saagarjha 9y ago
  Depends. There's not a whole lot of analysis you can do on sufficiently complex recursive algorithms.