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Discrete Math is bullshit - Page 4

Blogs > Hizzo
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Geiko
Profile Blog Joined June 2010
France1939 Posts
February 17 2012 00:37 GMT
#61
Ok, can somebody help me clear things up ? In the USA, you guys actually do maths without proving anything ?

I don't understand all this talk about "not liking proofs" :/
geiko.813 (EU)
billy5000
Profile Blog Joined December 2010
United States865 Posts
February 17 2012 01:02 GMT
#62
^pretty much. the only time i had to prove stuff was in geometry in high school. we don't even have to prove stuff in cal3 and linear algebra in college. the profs show them in class (like how a formula is derived), but unless you're an aspiring math major you just do practice problems and you're good to go.

i'm taking discrete math this semester, and i think it's one of the most interesting classes i've taken. i feel like i'm in a philosophy class which uses math to explore logic. even if you're not particularly interested in this class, i don't see why anyone should complain. it's an easy class that covers a broad range of topics (assuming you at least do some of the exercises). in fact, they're much related to each other. However, the only hard part was to stop reasoning in everyday english, which may be frustrating to some people
Tiger got to hunt, bird got to fly; Man got to sit and wonder, 'Why, why, why?' Tiger got to sleep, bird got to land; Man got to tell himself he understand. Vonnegut
Cocojack
Profile Joined November 2008
United States22 Posts
February 17 2012 01:10 GMT
#63
Not liking proofs is a pretty...human behavior? In America, we don't usually do proofs till high school (geometry proofs, maybe epsilon-delta proofs in calc) or college (discrete math, foundations of algebra), so when students get there, they usually don't feel comfortable right away (not to mention the confusion from all the symbols that students have never seen before). That being said, a calculus class will usually show the proofs for all the theorems that are used, but students aren't normally expected to come up with them themselves, unless they're that easy.

In my experience, the reason people hate the kinds of "obvious" proofs in discrete math is because we haven't seperated what's "obvious" to us, based on intuition, and what's "obvious" in math. Plus, there's a significance to knowing that once something is proven, it's proven forever. Then we can forever use it to prove bigger, more complicated things. Hopefully keeping that in the back of one's head will make it slightly more bearable.

And sometimes they make you prove obvious things as an exercise to see if you know the syntax. It sounds stupid, since we're proud of our logic, but it's no worse than any other inane task a random class will throw at you.
"No comment." -Anonymous
]343[
Profile Blog Joined May 2008
United States10328 Posts
February 17 2012 05:49 GMT
#64
On February 17 2012 09:37 Geiko wrote:
Ok, can somebody help me clear things up ? In the USA, you guys actually do maths without proving anything ?

I don't understand all this talk about "not liking proofs" :/


So there are a few reasons why Americans (who aren't majoring in math) don't really like proofs:

- American secondary education does not emphasize rigor or proofwriting (as has been stated). Many Americans are introduced to proofwriting when they do "two-column proofs" in geometry... which essentially means "write down every single little step."
- Related: In a lot of intro-level math classes (especially those which aren't for math majors), "proofs" tend to be "show, with painstaking rigor, this obvious fact." Non-math majors taking intro classes aren't expected to do any actually difficult problems, so they're often forced to rigorously show a relatively easy result whose proof is uninteresting.
- Proofs are pretty hard to write, because they force you to actually understand what you're doing without handwaving. That's bad if you're not that interested in the material / problem (and is related to the above point).

But there are probably good reasons why Americans don't teach proofs in high school. Many of the teachers aren't well-trained in rigor, and it's disgustingly hard to grade a poorly-written proof as opposed to a numerical answer. When kids write things like "\sqrt{x+1} + \sqrt{x-1} is slightly less than 2\sqrt{x}, so if x = y^2, then \lfloor \sqrt{x+1} + \sqrt{x-1} \rfloor = 2y-1" (where x is a positive integer) you just want to tear your hair out... T__T

I'm all for teaching rigor and proof-writing earlier, but that's only if a) teachers are properly trained and willing to grade proofs and b) the students aren't bored to death by the inanity of the problems they're given.
Writer
hns
Profile Joined January 2010
Germany609 Posts
Last Edited: 2012-02-17 07:57:46
February 17 2012 07:47 GMT
#65
Oh man thanks everyone, I was opening this topic right when my next door colleague came to the office who happens to be a member of the discrete math group here in the math department. Ee-han timing.


Edit: Just to add that: Here in Germany, we usually don't do proofs in high school as well. However, our introductionary courses at the university are proof-heavy and there're always proofs as some exercises (also for the non-math majors who have to take math courses like mechanical or electrical engineering or whatever); however, in most cases, you're not supposed to give proofs in exams if you're not taking an exam for math majors. Still, in the first courses, we try to make it very clear to the students that higher mathematics is very different from the stuff they did at high school; so it's fine that they haven't seen rigorous proofs yet and we don't expect them to have, still, we expect them to learn and adapt to the "new" math.
ZerO, Action, Neo.G_Soulkey & FlaSh fanboy~~
opsayo
Profile Blog Joined July 2008
591 Posts
February 17 2012 10:50 GMT
#66
"real math" involves proofs

i'm sure being an undergrad though you know better than your professors
Disposition1989
Profile Blog Joined March 2011
Canada270 Posts
February 17 2012 15:15 GMT
#67
canada isnt much different either. we dont see a real proof til first year of university and even then its pretty basic. the further you go, the more it goes from diddling with functions/vectors/matrices to proving why you can use these methods. by fourth year, youre lucky to see a test less than 80% proofs. maybe slightly different in financial maths but pure maths its all you get. you find out whether you truly like math or not : )
BottleAbuser
Profile Blog Joined December 2007
Korea (South)1888 Posts
Last Edited: 2012-02-17 15:37:22
February 17 2012 15:34 GMT
#68
Don't like it? Don't take it... I, on the other hand, have been finding discrete math to be very useful. It is, as you noted, "useful" for algorithms. Like, you know, how computers decide how to route your post to the server. Or how to control the DB connections that keep the forum up.

"God, this arithmetic shit is so useless! How often am I adding the numbers 829 and 492 together in real life? I can't see how this is useful at all, other than maybe for algebra."

Oh, and higher maths is mostly useless irl. Mathematicians have nothing to do with all their pretty numbers, so they start putting in colors and calling it art. See what I did there?
Compilers are like boyfriends, you miss a period and they go crazy on you.
TG Manny
Profile Blog Joined September 2011
United States325 Posts
February 17 2012 15:35 GMT
#69
At first, I was like...what is this I don't even...

Then reading up on it, it just sounds more and more like you're frustrated with the thought process and when it is applicable rather than the theories themselves. You know, good subject/bad professor type stuff that can sour a student's attitude.

Real mathematics are everywhere in physics, engineering, and CS. Maybe my collective curriculum is different, but my maths/physics force a derivation of an equation before letting us use it (unless the derivation is beyond the capability of the student, ala Physics 1 students who are also calc 1 students, they cannot derive velocity of a particle when given an acceleration BECAUSE there has been little/no exposure to the integration process). An example was to prove that a point in space which I see is 2 meters long is truly infinite meters long (as it is a black hole). I couldn't whip out the equation related to optical relativity, but had to setup a proof and experiment to say what was true before stating the same equation and how it is a true relation of the area.

Maybe I see it in a much different light because of personal interests and experiences, but discrete mathematics are fundamental to doing a lot of math on the computer level.
Singularity is at hand...
TylerThaCreator
Profile Blog Joined May 2011
United States906 Posts
Last Edited: 2012-02-17 15:59:13
February 17 2012 15:57 GMT
#70
currently in 2nd year of studying cs undergrad as my major and I too share the pain of useless ass discrete structures/math. all the math majors are in this topic jumping down the not-so-mathematically gifted's collective throat and I really don't understand why. I did fine in my other math related courses, but these classes are just really dense and have 0 use compared to literally any other cs class...

I made it through 1 semester of discrete without doing any proofs and it wasn't too terrible, still rough getting through it. but this 2nd semester is getting completely ridiculous with complicated probability concepts that go way over my entire (aside from very few classmates) class's heads. There is seriously no link to any computer science at this point. just a math class disguised as a cs requirement and a cs class

when I say useless I mean literally all we do is probability, demorgans bullshit etc. How is any of this applicable to anything meaningful?
aka SethN
unichan
Profile Blog Joined March 2011
United States4223 Posts
February 17 2012 16:07 GMT
#71
I'm taking it right now, but it's really computer science based as the teacher is a computer science teacher, and it's pretty cool :>
Also I'm in high school so yeah. Our multivariable calc class and diffeqs was more numbers and less proofs than the actual university class I think, but we still did a lot of proof stuff, like green's stokes etc
I'm actually liking it so far, but those combinations/permutations are still so confusing/frustrating! haha
:)
hai2u
Profile Joined September 2011
688 Posts
February 17 2012 16:28 GMT
#72
discrete math is pretty important for CS. You will need it if you want to do well in some other CS courses down the line.
TylerThaCreator
Profile Blog Joined May 2011
United States906 Posts
February 17 2012 16:30 GMT
#73
On February 18 2012 01:28 hai2u wrote:
discrete math is pretty important for CS. You will need it if you want to do well in some other CS courses down the line.

can you be more specific? That's literally what everyone has posted in this topic...but it seems to be limited to cs courses that are continuations of discrete math only
aka SethN
Kalingingsong
Profile Joined September 2009
Canada633 Posts
February 17 2012 16:33 GMT
#74
discrete math is the most frustrating class imo, you can barely hear what the prof is saying most of the time.
Dess.JadeFalcon
corumjhaelen
Profile Blog Joined October 2009
France6884 Posts
February 17 2012 16:47 GMT
#75
I'd venture that a good part of people frustration is precisely because you've never been asked to do proofs before.
Proving so called "obvious stuff" is very important : it helps you familiarise with the concept even better than examples, and as we say in France "Ce qui se conçoit bien s'énonce clairement" (which more or less means that if you really understand something it should be easy to explain).
From what I see those "discrete maths" seem like a very good introduction to quite a few thing in cs, more or less everything with true algorithms in it.
As for a specific example, google pagerank is partially based on the Perron Frobenius Theorem (a linear algebra not totally trivial theorem).
Or during my internship this summer, I worked on the informatic security system of a nuclear reactor, and I was pretty happy to know De Morgan's laws.
Won't add much because I'm not familiar with the american curriculum.
‎numquam se plus agere quam nihil cum ageret, numquam minus solum esse quam cum solus esset
IowaEngineer
Profile Joined February 2012
2 Posts
February 17 2012 18:23 GMT
#76
Wow so many responses. I feel better for it.

I've gotten some other books on doing proofs and they are making up for my professor's shortcommings. Perhaps at the end of the course I will be thankful for all of these new ways of expressing myself. I loved proofs in geometry, and I really think that it will be more fun once we are moving beyond the intro steps. Statistics was hard and used the same language, but it meant something, so it was easier to relate to.

But man it is taking a lot of patience to sit through this part where you're not allowed to skip the most obvious steps...
if the shoe fits, wear it.
ymir233
Profile Blog Joined June 2010
United States8275 Posts
February 17 2012 22:31 GMT
#77
You realize that proving/deriving/generalizing stuff is most of what higher-level math is about...any computer can solve for an integral (that's why we say "reduced to quadratures" right) but no computer could have created Maxwell's Laws or proved Existence-Uniqueness for every given nonlinear continuous differential eqn in a box...without providing a general solution.

Engineers use algorithms, mathematicians actually find out new relations via proofs.
Come motivate me to be cynical about animus at http://infinityandone.blogspot.com/ // Stork proxy gates are beautiful.
Vestrel
Profile Blog Joined December 2010
Canada271 Posts
February 17 2012 22:40 GMT
#78
I'm taking a discrete math course this semester and it's kicking my ass and so much stuff is going over my head. Class average on the first quiz was ~60% and that's supposed to be a high grade. My first instinct is to blame the teacher but it probably wouldn't be right to think that..

I've always been 'ok' at math, never amazing, but I love programming, so I'm considering doing some software engineering program instead of CS >>

darkcloud8282
Profile Joined December 2010
Canada776 Posts
February 17 2012 23:15 GMT
#79
I don't see the point of doing proofs unless you are becoming a mathematician. You will simply use a formula that you are given and someone else has already proven it works.
SerpentFlame
Profile Blog Joined July 2008
415 Posts
Last Edited: 2012-02-18 00:24:30
February 18 2012 00:22 GMT
#80
On February 18 2012 08:15 darkcloud8282 wrote:
I don't see the point of doing proofs unless you are becoming a mathematician. You will simply use a formula that you are given and someone else has already proven it works.

To prove something is to understand. Understanding is everything: for example, in computer science, you absolutely need an understanding of algorithms if you want to be a real problem solver and not just a code monkey. Of course, for engineering and other disciplines, its sometimes enough not to understand why formulas work but just to know that they do.
I Wannabe[WHITE], the very BeSt[HyO], like Yo Hwan EVER Oz.......
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