Discrete math is important because the universe is discrete. Continuous math is an approximation that sometimes, but not always, is rather convenient.<p>Once I wrapped my mind around this, I started to understand something. Manifolds are just graphs with many vertices. Fourier analysis studies the eigen-decomposition of the laplacian on a graph, and is used to solve heat, wave and dispersion equations. Stokes theorem (which in a discrete setting amounts to matrix associativity) is a self-evident fact. Most of applied math is thus reduced to a few lines of octave code.<p>Only when you lose discreteness or compactness things start to get nasty. But this is just a flaw in our current definition of real numbers.
> <i>Many students, especially bright and motivated students, find algebra, geometry, and even calculus dull and uninspiring</i><p>That was me. I grew up believing I hated math. Struggled all the way through middle & high school to AP calc and just found it incredibly boring and tedious. Ended up opting out of doing engineering/science in undergrad because I just couldn't stand doing all the math.<p>Long story short, years later ended up going back to school for CS and took discrete math as one of my first courses, and remember being blown away by how cool it was. All this time thinking I hated math!<p>Hard to say exactly what the difference is. Partially I think my brain just groks discrete concepts more easily.<p>But also the class had a heavy emphasis on proofs, which I think was really important. At a certain level this type of problem-solving can start to resemble philosophy. Chugging through a proof, figuring out just the right way to construct it and slapping a triumphant "Q.E.D." at the end is an empowering experience, especially the first time. There's a world of difference between "you throw a ball, solve for its velocity at time x" and "prove that there must be a ball" (I'm embellishing of course). It's a difference between obtaining an answer for a specific instance of a situation, and shedding light on some fundamental/universal property of the world. To me that feels profound in a sense, which makes it exciting.<p>Proofs don't belong solely to the domain of discrete math, of course, so this probably isn't as much a testament to the subject as it is to the general problem-solving approach. It would be nice if students could get exposed to this a bit earlier, I think there are many folks like myself who would realize that they can love math too.
Even if we don't teach a single day of number theory, I think we can all agree that modern society would be better if everybody had to have a semester of basic probability or statistics as part of their education.
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?
> Prominent math competitions such as MATHCOUNTS (at the middle school level) and the American Mathematics Competitions (at the high school level) feature discrete math questions as a significant portion of their contests. On harder high school contests, such as the AIME, the quantity of discrete math is even larger.<p>As someone who participated in these contests, this isn't the entire story. Competitions such as these all require numerical answers, and as such skew <i>extremely</i> heavily towards counting and probability (as in, there's no other discrete math topics but these two). It's only when you get into proof based contents that the real meat of discrete math, namely recurrence, cardinality, graphs, etc. start showing up.
The vast majority of people who learn calculus in school will never model a changing system in their life again.<p>The vast majority who didn't take statistics courses in college will still try to use the limited understanding they have of statistics to assess statistical claims or draw conclusions from reported figures. The vast majority of people who never took discrete mathematics courses will still face problems of figuring out the difference of combinations and permutations at some points in their life.<p>I love calculus and I'm very happy I know it but I would be lying if I said it even approaches the importance of discrete mathematics and statistics in today's world.
I love discrete math, it seems so much cleaner in general. I wish there were more reformulations of calculus, other numerical methods into discrete maths.<p>I think Knuth’s concrete mathematics might have been an attempt at this, but I’ve never found time to dig into it in depth. Perhaps I should try again...
Symbolic logic / truth tables is the single most useful subject I have ever taken wrt programming. It provides an intuitive understanding of conditionals so they can be expressed simply and clearly.
Attention parents of "mathy" kids: A bit off topic, but I just want to put in a testimonial for AoPS online math classes. My daughter used it as the spine of her middle/high-school math education. Great program. Check it out.
I wish I had paid more attention to or had a better instructor for my discrete mathematics course, I find many of the topics covered in it extremely fascinating now, years later. :(
Highly agree. As a current high school student, I've gone out of my way to study discrete math. Though I found calculus interesting, it's not particularly applicable to any part of CS except for a few concepts. OTOH, DM is incredibly useful for practically everything, which is what led me to seek it out.