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TossFloss
Canada606 Posts
On November 08 2010 10:21 professorjoak wrote:Proofs are real math, the only real math. "Calculus" as you learned it actually isn't. One of the first classes you would do in theoretical math is Analysis where you re-derive the proofs of calculus on non-Euclidean metric spaces and see what still works even when you are operating on an abstract space with no physical interpretation. Continuous applied mathematics is mostly done by engineering departments at a lot of universities nowadays (even though that's what I do). + Show Spoiler +While we're at it, "algebra" means something different than what you think it does too.
That's how they do it in Germany. I really wish we adopted their system, stuff I learned in calculus one, two and three didn't make sense until 3rd year real analysis (which wasn't even mandatory).
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On November 08 2010 10:17 Hizzo wrote:It certainly makes you think logically with regards to solving problems (helps problem solving too I'd say a good bit) but other that that I'm not getting too much out of it. I certainly don't regret it but I don't particularly enjoy it  You guys are absolutely right in regards to direction within the field.
Yes that is what you're supposed to get from it. It trains the brain in resolving problems, long hard logical problems. But that is not for everybody to like it that's for sure (I don't either... well discrete maths were fine for me but harder class were a chore).
On the other hand discrete maths is probably one of the easiest course when it comes to "math courses with proofs", which are what real mathematics are, analysis and linear algebra is another story. Calculus (vectors, matrix products, derivatives, integrals etc) is not matheematics, it's its application, and most of it can be done with matlab anyway in real life whereas developing new tools takes another knowledge..
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~Practical science~ whiteknighting squad reporting in to rescue Hizzo.
Honestly, these basic courses are dumbed down heavily to make it possible for everyone to pass without any real effort. They are *not real* math.
I do agree that 'real' was a bit too provocative, perhaps 'useful'? That said, it seems like a good degree of math people here are confusing 'real' with 'pure'.
What a comp sci. person finds useful in math differs from what a mathematician finds useful. Frankly, this should be obvious, yet the math people keep asserting that proofs (a very specific subset of proofs, at that) are universally a critical aspect of problem-solving skills. Why? Because it sounds nice?
An example for my own field--do I really need to understand the derivation of vibrational wave/energy functions from 'first principles' to interpret the results of kinetic isotope experiments? (The answer is no. Sometimes proofs don't really matter.)
I wouldn't expect premeds to seriously have a deep understanding of organic reaction mechanisms, even though
[They] are like push-ups for the mind. The ability to understand and competently apply [patterns of knowledge], [Occam's razor], [basic chemical principles] and general problem solving depends on the same portions of your brain as mathematical proofs. And those skills separate the boys from the men.
Heh, wonder where we've seen that before.
Yes that is what you're supposed to get from it. It trains the brain in resolving problems, long hard logical problems. But that is not for everybody to like it that's for sure (I don't either... well discrete maths were fine for me but harder class were a chore).
The ability to manipulate questions into more readily solved forms is a useful skill toi have. But most of the time there's more relevant ways to develop these skills than a specific sort of proof derivation.
I am __ years old. Compared to Penn State University, I possess superior insight on how CS education should be taught because of the following reasons: .....
You first.
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Obligatory inflammatory statement: no one ever got a science Nobel for proving an equation.
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On November 08 2010 15:28 bbq ftw wrote:
Obligatory inflammatory statement: no one ever got a science Nobel for proving an equation.
They do get Abel's Prizes and Fields Medals 
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On November 08 2010 15:30 Entropic wrote:Show nested quote +On November 08 2010 15:28 bbq ftw wrote:
Obligatory inflammatory statement: no one ever got a science Nobel for proving an equation. They do get Abel's Prizes and Fields Medals
I am pretty sure the Abel Prizes are geared toward the more practical elements of mathematics, which sort of proves my (admittedly unfairly phrased) point.
Feel free to slap me if I'm wrong though.
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On November 08 2010 15:28 bbq ftw wrote:~Practical science~ whiteknighting squad reporting in to rescue Hizzo. Show nested quote +Honestly, these basic courses are dumbed down heavily to make it possible for everyone to pass without any real effort. They are *not real* math. I do agree that 'real' was a bit too provocative, perhaps 'useful'? That said, it seems like a good degree of math people here are confusing 'real' with 'pure'. What a comp sci. person finds useful in math differs from what a mathematician finds useful. Frankly, this should be obvious, yet the math people keep asserting that proofs (a very specific subset of proofs, at that) are universally a critical aspect of problem-solving skills. Why? Because it sounds nice? An example for my own field--do I really need to understand the derivation of vibrational wave/energy functions from 'first principles' to interpret the results of kinetic isotope experiments? (The answer is no. Sometimes proofs don't really matter.) I wouldn't expect premeds to seriously have a deep understanding of organic reaction mechanisms, even though Show nested quote +[They] are like push-ups for the mind. The ability to understand and competently apply [patterns of knowledge], [Occam's razor], [basic chemical principles] and general problem solving depends on the same portions of your brain as mathematical proofs. And those skills separate the boys from the men. Heh, wonder where we've seen that before. Show nested quote +Yes that is what you're supposed to get from it. It trains the brain in resolving problems, long hard logical problems. But that is not for everybody to like it that's for sure (I don't either... well discrete maths were fine for me but harder class were a chore). The ability to manipulate questions into more readily solved forms is a useful skill toi have. But most of the time there's more relevant ways to develop these skills than a specific sort of proof derivation. Show nested quote +I am __ years old. Compared to Penn State University, I possess superior insight on how CS education should be taught because of the following reasons: ..... You first. --- Obligatory inflammatory statement: no one ever got a science Nobel for proving an equation.
Nobody ever got a science Nobel without the work of mathematicians.
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I'm not actually sure where you're going with this.
I could just as reasonably note that no one ever got a science Nobel without lab techs. No one ever got a science Nobel without being grammatically literate.
I picked "proving an equation" for a reason. The point is, certain peoples' specific brands of arcane mathematics are, in fact, not the root of all scientific achievements.
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TossFloss
Canada606 Posts
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Higher level CS topics require a solid grasp of mathematical proofs. To name a few: proof of correctness and run/space complexity analysis all look like mathematical proofs - because they are.
I said universally applicable for a reason. A lot of people are conflating skill in a very specific set of mathematical manipulations with skill at problem solving in general. They are two very, very different things. There are also some people, demonstrated by Mr. Hochs, claiming that people are basically retards if they aren't skilled in the former subject. This tends to set off certain whiteknighting alarms in my head.
See:
Yes that is what you're supposed to get from it. It trains the brain in resolving problems, long hard logical problems. But that is not for everybody to like it that's for sure (I don't either... well discrete maths were fine for me but harder class were a chore).
Again, there's a certain universality implicit in that statement. Its its this sort of argument I take issue with.
I'm don't disagree with Penn State University. How does this apply to me?
My guess is that you don't represent PSU anymore than I represent my university (could be wrong though :$).
You used an appeal to authority ("X university does it", it must be correct), I'm merely calling you on it.
There's no Nobel prize in mathematics.
Amazing, people getting recognized for things other than proofs; who could imagine such a thing? I do agree it was an ill-advised comment, it did seem to blend well with all the other people saying pointlessly inflammatory things though.
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TossFloss
Canada606 Posts
@bbq ftw,
I'm done arguing. I have a degree in CS, top marks in a handful of advanced CS courses, discussed the question of curriculum with various professors and graduates in my field, etc. etc. etc. Everyone's welcome to their own opinion. I genuinely hope the OP reconsiders his position; but I'm not wasting any more time on this topic.
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It's no wonder that people are flipping a bitch over the OP's statements. He's basically taking a shit on mathematics with each sentence. But given that it is a rant, let us all try and refrain from shitting all over him and instead discuss why we believe discrete math is such a useful class.
It seems like this discrete math course is much like the course I took when I was in college. It serves the dual purpose of exposing people to proofs as well as teaching them topics in discrete math.
For a CS major, it is abundantly clear that the topics of discrete math (graph theory, combinatorics, etc.) are VERY relevant. I'm not even going to bother arguing about why this is important.
With regards to proofs: if you are going to construct an algorithm, how are you going to prove correctness to yourself, if not to other people? The proofs that you are doing now may seem silly and pointless, but they are meant to help show you a more rigorous way of thinking. I do think that applying this kind of rigorous thought process will help you become a better problem solver.
Also, I occasionally get those moments of enlightenment where I realize how something really works. I love those moments.
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I'd like to point out that I'm an electrical engineer (so I've taken and seen many of the concrete applications of math, including basic transforms and convolution and other basic properties), work in software engineering (thus have experience in ICS and developing and testing algorithms) and have a math minor (and have taken several upper level rigorous proof based math courses).
As someone whose field of work in fact deals with purely the application side of mathematics, I say that I have learned a great deal and have a huge advantage on those I work with because of my math background. The inherent understanding involved with taking on even a mathematics minor is huge, and being purely application based is fine, but in my opinion, not as capable as someone who has enough experience dealing with proofs and the backbone of the theorems and algorithms we apply.
I don't know what bbq ftw's point is, the best I could understand is that he's saying mathematics didn't create everything - which I don't think anyone will argue against. It sure did create a lot, however, and is the most pure science field you can partake in. He's obviously admitting that learning to construct and read proofs develops your intelligence, he just mentions that "there must be a better way."
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To be honest Id rather take Discrete Math over all these calculus courses. But... what do I really know Im only a 1st year CS major. 
edit: I took discrete math in high school instead of pre-cal.
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Prooving stuff? whaaat? Like, who wants to make sure an algorithm won't crash before actually running it on billion of $ worth problems?
Seriously, I understand many people hate discrete maths/proofs. But we sure do need people doing that.
edit: I realize my post is a bit short. I work in a field where we use discrete maths/proove stuff before running our algorithms. One example is energy use optimization: you cannot really afford "on the field" experiments, that may cost a LOT, so you need to do some theoretical work beforehand.
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I'm taking Discrete Mathematics for a CS degree and I don't really understand the application either... Like, we talked a little bit about RSA encryption and once about quicksort time complexity, but that's it. I'm pretty sure our professor doesn't know anything about computers, either (he was our linear algebra professor as well, but I'm pretty sure he teaches mostly random mathematical theory courses). The proofs don't really bother me since pretty much all of my classes even remotely related to math are just proofs, but I just don't understand how this class is related to CS... By the way, what university do you go to? And how is this not "real" math?
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I joined just to vent about this topic, so I hope that's a good enough reason to 'bump' the post.
I'm taking an intro discrete mathematics and I'm so full of venom about it right now, I feel like dark clouds are coming out of my eyes. Here we go:
I don't like proving something that is obvious, like De Morgans or the distributive law. I am required to write more and more painfully obvious steps like here's something from the homework:
prove that if x is an element of complement-A intersection complement-B, then it is not an element of A.
!!!?!?!? Isn't that already given?
1.) x is an element of complement-A intersection complement-B
2.) x is an element of complement-A and an element of complement-B by definition of intersection
3.) x is an element of complement-A by 2
4.) x is not an element of A by definition of complement
OMG when will it end?
Not allowed to skip over that! Why???
It goes on and on, points taken off for the slightest use of your own mind without explicitly stating what you were doing.
Prove that if the sky is above you, then the sky is up
Prove that if you are a person, then you are not not a person.
Prove that if you are wasting your time then you are not having a good time in discrete mathematics
...I've got real programs to write. I've got money to make. What the F is all this dilly dally???
I don't mind a proof that accomplishes something, and puzzling it out is fun sometimes but this course is causing me a lot of suffering.
That's all.
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lol wat the last guy posted was !#$@#$in hilarius!!!!
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As someone who delved deep into the realms of pure mathematics, particularly in groups, algebraic number theory and topology
I can only say if you don't like this, you should avoid maths in uni
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Take a single 3d Graphics course, and you will cry yourself to sleep wishing you paid more attention to Discrete Math.
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eff, i'm taking discrete math right now since i'm minoring in computer science. sooo annoying. doing counting right now (probably of getting a flush if u choose 5 cards out of a 52 card deck, etc) and i already know it's going to lead to my downfall
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EPT
