Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Why Discrete Math Is Important

artofproblemsolving.com

Post reply on HN
Print view View original

91–100 of 127 posts

Re: Why Discrete Math Is Important

#91

Post by jacobolus »

bootsz wrote: post #61

> Many students, especially bright and motivated students, find algebra, geometry, and even calculus dull and uninspiring 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. Long story short, years late…

Don't worry, algebra, systems of linear equations, synthetic geometry, analytic geometry, infinite series, differential and integral calculus, etc. can also be made 'cool' and intellectually stimulating. Likewise discrete math can be made dull and lifeless. The difference has much more to do with quality of problems and teaching than with your brain.

Re: Why Discrete Math Is Important

#92

Post by [deleted] »

whatshisface wrote: post #83
bootsz wrote: post #61

> Many students, especially bright and motivated students, find algebra, geometry, and even calculus dull and uninspiring 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. Long story short, years late…

What you're describing is the basic shift between what lower-ed science/math is like and what "real" (college) science/math is like. The problem is that everything they teach in highschool and below needs to have an escape hatch for "what if they have anti-ADHD* but no clue what's going on?" That's why you were able to solve for v without obtaining any knowledge about the universe, and why taking discrete math did wh…

[deleted]

Re: Why Discrete Math Is Important

#93

Post by jacobolus »

gugagore wrote: post #63
enriquto wrote: post #51

Earlier quoted context omitted.

You can also see it in the opposite sense. The continuous models are an ad-hoc, purely mental, construction. When you have to solve a PDE, you actually build a discrete model (using finite elements), and solve the discrete thing. Except in very simple toy problems, you can never "solve" anything using only continuous tools.

Spectral methods, or any methods where you have chosen a basis of continuous functions and are solving for weights produces solutions in the continuous domain. That's not a discrete model.

The grandparent poster might like Chebfun, http://www.chebfun.org

Re: Why Discrete Math Is Important

#94

Post by Verdex_3 »

jumpman500 wrote: post #80
Verdex_3 wrote: post #73

Earlier quoted context omitted.

Not really. You have to find a way to make the math real to your students or else it becomes just another exercise of "what set of words do I need to say in order to make the teacher happy". At least in my experience, most learning seems to be either incidental OR some sort of vestigial residue of the social component of making the system happy.

What? You can make easily make basic statistic and probability about real problems and interesting. Talk about sports. Talk about risks of the stock market and financial planning. Talk about politics/polling. Talk about gambling/poker. Just takes an interesting teacher to make any subject interesting.

Like, I want to believe you that such a thing is easy. But I'm not really convinced by the assertion that it is followed by a non-descriptive blurb. I mean I get what you're saying, "Find what they care about and try to apply statistics to it." However, I don't believe that this process is easy.

Sports is a good example of why I don't think this is easy. What exactly is the point of statistics in sports? Predicting what teams are going to win or what strategies are superior. Most children in school are not interested in sports because they're into strategy or because they're predicting who's going to win. They're interested in it for social reasons. Which team do their parents or friends want to win. Telling everyone at thanksgiving that the family team is going to lose the game will probably not go well for them. And as far as strategy goes ... I thought the statistical analysis of the extra point kick in football indicates that you should never do it. Teams rarely make use of this at the professional level. Also didn't they make a movie about how nobody pays attention to the math in baseball (Moneyball?). Anyway, if adults who have money and fame on the line can't be bothered to care about statistics in sports, then I don't see how children are going to be much different.

Of course that's where you come in. You say it's easy. Personally, I would love to see why you think this because it looks hard to me. I look forward to a more in depth response from you.

Re: Why Discrete Math Is Important

#95

Post by 2sk21 »

dbcurtis wrote: post #84

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.

Fully agree - the whole AoPS range of books and courses are just amazing. Highly recommended for all kids.

Re: Why Discrete Math Is Important

#96

Post by Sean1708 »

dbcurtis wrote: post #82
crimsonalucard wrote: post #76

Earlier quoted context omitted.

>Discrete math is important because the universe is discrete. Continuous math is an approximation that sometimes, but not always, is rather convenient. This is not true. There are "things" in the universe that are discrete (for example: matter). But whether the universe itself is discrete is something we don't know. What is the smallest discrete measurable length in the universe? We don't know.

Would you concede that the Planck length is a good approximation of the smallest measurable length in the universe?

Why would the Planck length be the smallest measurable length in the universe?

Edit: To be more clear: Is there a theoretical reason why the Planck length would approximate the smallest measurable length?

Re: Why Discrete Math Is Important

#97

Post by jdietrich »

Verdex_3 wrote: post #94
jumpman500 wrote: post #80

Earlier quoted context omitted.

What? You can make easily make basic statistic and probability about real problems and interesting. Talk about sports. Talk about risks of the stock market and financial planning. Talk about politics/polling. Talk about gambling/poker. Just takes an interesting teacher to make any subject interesting.

Like, I want to believe you that such a thing is easy. But I'm not really convinced by the assertion that it is followed by a non-descriptive blurb. I mean I get what you're saying, "Find what they care about and try to apply statistics to it." However, I don't believe that this process is easy. Sports is a good example of why I don't think this is easy. What exactly is the point of statistics in sports? Predicting w…

Trick 'em into thinking they aren't learning and they do.

https://www.youtube.com/watch?v=elTCEVAAEfo

Re: Why Discrete Math Is Important

#98

Post by billfruit »

fjsolwmv wrote: post #25
gh02t wrote: post #21

Earlier quoted context omitted.

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 nume…

Of course applied math is much more relevant to CS than pure math. CS is an application of math.

But most applied maths courses/books focus heavily on ODE/PDE which are rarely of help to CS undergrads.

Re: Why Discrete Math Is Important

#99

Post by jeremysalwen »

BeetleB wrote: post #72
gosubpl wrote: post #49

Earlier quoted context omitted.

Nice thing about "continuous" math is that we have so many "standardised" tools in its toolbox, contrasted with "ad-hoc-edness" of discrete math. Hence interesting is solving discrete problems with "continuous" tools - like e.g. http://ac.cs.princeton.edu/home/

>Hence interesting is solving discrete problems with "continuous" tools - like e.g. http://ac.cs.princeton.edu/home/ I'm often interested in the opposite: Solving continuous problems by going to the discrete domain. I'm not a mathematician, but I did enjoy taking math courses and dabbling a little. My personal highlight was when I was struggling for months to solve a continuous variable problem, but then one day I de…

So is this the solution? The probability that all numbers are less than x is equal to x^n. So then you take the derivative of that to get the probability that the maximum us is exactly x. n x^n-1. Then calculate the expected value as integral from 0 to 1 of x n x^n-1 = n/n+1.

Re: Why Discrete Math Is Important

#100

Post by AstralStorm »

dcow wrote: post #47
enriquto wrote: post #29

Discrete math is important because the universe is discrete. Continuous math is an approximation that sometimes, but not always, is rather convenient. 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 (…

I too have a problem with continuous math. However I have to wonder if we didn't have our senses, would our imaginations be discrete or continuous?

Neurons themselves are working on physics at not quite quantum scales, so probably a good model would be timewise continuous stochastic.
Post reply on HN