EPTI don't understand all this talk about "not liking proofs" :/
Discrete Math is bullshit - Page 4
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Geiko
France2024 Posts
I don't understand all this talk about "not liking proofs" :/ | ||
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billy5000
United States865 Posts
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 | ||
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Cocojack
United States22 Posts
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. | ||
]343[
United States10328 Posts
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. | ||
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hns
Germany609 Posts
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. | ||
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opsayo
591 Posts
i'm sure being an undergrad though you know better than your professors | ||
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Disposition1989
Canada270 Posts
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BottleAbuser
Korea (South)1888 Posts
"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? | ||
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TG Manny
United States325 Posts
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. | ||
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TylerThaCreator
United States906 Posts
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? | ||
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unichan
United States4223 Posts
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 | ||
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hai2u
688 Posts
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TylerThaCreator
United States906 Posts
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 | ||
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Kalingingsong
Canada633 Posts
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corumjhaelen
France6884 Posts
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. | ||
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IowaEngineer
2 Posts
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... | ||
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ymir233
United States8275 Posts
Engineers use algorithms, mathematicians actually find out new relations via proofs. | ||
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Vestrel
Canada271 Posts
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 >> | ||
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darkcloud8282
Canada776 Posts
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SerpentFlame
418 Posts
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. | ||
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