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God I hate this class. Anyone else taking it right now?
I cannot stand proofs. That is all we do, and it's so dumb because I know I'm not going to have to prove why that partially ordered sets cannot have more than one greatest element, or why two odd numbers added together are even outside of this class.
Classes like this piss me off. I cannot see any application of this class outside of algorithms and stuff. I don't even consider it a real class, it just feels like there's so much hand-waving going on - I'd kill to be able to go back to vector calc or any REAL math over this.
/rant
 
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Why do you have to take it then?
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Preach it brother! I've taken a lot of classes/seminars that promise one thing but then go into left field and forget about the original subject altogether. Complain to someone higher up and try to get the class removed for future students.
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discrete math is very very broad... but its a really cool branch of math.
i dunno, are u not good at proofs? generally ppl who are bad at proofs dont like courses like these, and conversely ppl who are good at proofs love the classes.
and discrete math is so applicable, you see it in like everything from combinatorics to probability (ie RVs with discrete distributions, outcomes)
have u taken real analysis or complex analysis? cause discrete math is more useful in the real world, in general, imo
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I feel the same way about psychology. I won't be doing any "conditioning" any time soon, I don't give a fuck if a dog salivates to a bell or footsteps, I don't understand why I have to learn all this nonsense to become a nurse..
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You cannot stand proofs.
You'd kill to do REAL math.
Contradiction. I have just proved you don't know what math is.
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On November 08 2010 09:50 Karliath wrote:
Why do you have to take it then?
Required for Computer Science majors at Penn State.
On November 08 2010 09:53 Oracle wrote:
discrete math is very very broad... but its a really cool branch of math.
i dunno, are u not good at proofs? generally ppl who are bad at proofs dont like courses like these, and conversely ppl who are good at proofs love the classes.
and discrete math is so applicable, you see it in like everything from combinatorics to probability (ie RVs with discrete distributions, outcomes)
have u taken real analysis or complex analysis? cause discrete math is more useful in the real world, in general, imo
I just can't get into it. I mean sure with recurrence, algorithms, probability and cryptography and all of that junk it's applicable, but god it's such a chore for me. I am not good at proofs and things that are super abstract. I was much more of a calculus 1/2/3 (vector) and matrices man.
On November 08 2010 09:52 Emon_ wrote:
Preach it brother! I've taken a lot of classes/seminars that promise one thing but then go into left field and forget about the original subject altogether. Complain to someone higher up and try to get the class removed for future students.
if only 
On November 08 2010 09:57 searcher wrote:
You cannot stand proofs.
You'd kill to do REAL math.
Contradiction. I have just proved you don't know what math is.
Ok let's change "real" to "continuous", will that do it? How about given the set of all mathematics, the definition of the word "real", and two arbitrary elements of your choice that you prove to me that I do not know what real mathematics is using structural induction? Seems like you'd like something sadistic like that.
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Ugh you're in the wrong field if you don't like discrete math.
Also how does someone "hate" proofs... they are instrumental to building up rigorous mathematical knowledge.
I used to be a math major, but I switched to computer science, mostly because i hated continuous math. Real analysis was boring and confusing as hell to me.
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If there was a software engineering degree here I'd have gone after that instead, but alas...
All of the info sessions I've gone to for big companies that have had co-ops and new hires talk to us never make any mention of having to use discrete math on the job, so I cannot say that the field is not for me.
It seems we are opposites. I love continuous math, and almost took differential equations as a gen ed but I couldn't find an appropriate time to squeeze it in. I also took the whole semester vector calc instead of the half semester one that was required
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On November 08 2010 09:54 Elegance wrote:
I feel the same way about psychology. I won't be doing any "conditioning" any time soon, I don't give a fuck if a dog salivates to a bell or footsteps, I don't understand why I have to learn all this nonsense to become a nurse..
If, by the end of studying to become a nurse, you don't understand the applications of what you learn in intro psych, you probably shouldn't be a nurse.
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I'm assuming you're taking it as part of a CS degree, especially given the algorithms reference? I hope you aren't a math major, because pretty much all math classes past calculus are very proof heavy.
Stuff like graph theory and combinatorics is very relevant to algorithms, in which you can also expect to be doing a lot of proofs. I didn't particularly enjoy Discrete or Algorithms - I'm more interested in programming than research - but they're still very important to be exposed to. Algorithms is a very important part of CS regardless of what you're planning to do in it. It's arguably the most important (if not most fun) part even if you're mostly into programming, as a lot of the difficulty in writing many programs is developing a solid algorithm - once that's done almost anyone who knows a language decently could write the actual code.
I'd try to get something out of the class even if it isn't much fun, it will help you later.
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On November 08 2010 10:02 Hizzo wrote:
If there was a software engineering degree here I'd have gone after that instead, but alas...
All of the info sessions I've gone to for big companies that have had co-ops and new hires talk to us never make any mention of having to use discrete math on the job, so I cannot say that the field is not for me.
It seems we are opposites. I love continuous math.
Well yeah if you just want to do basic programming it's probably not super important to have a vast knowledge of discrete math. However it's still very useful for understanding and developing algorithms. It also underpins most of the "science" part of computer science. Any classes you take that aren't just straight programming or software engineering will probably incorporate it.
I guess the best advice I can give you is either to find an application of it you like (there are a lot of cool areas of computer science), or grimace and bear through the class requirements so you can graduate and do some programming.
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Haha reminds me of my microeconomics class where we do nothing but consumption optimisation problems...
Let's say in the future you go into a job interview, and they ask you for your skills... "Hey, I know how to maximise somebody's utility through 2nd order calculus!" "huh you f**king high??"
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Thanks for the tip. I am trying to salvage something from it - I am more programming than anything as well. I was originally comp eng. because I am a huge hardware enthusiast but man...circuits suck.
On November 08 2010 10:08 5unrise wrote:
Haha reminds me of my microeconomics class where we do nothing but consumption optimisation problems...
Let's say in the future you go into a job interview, and they ask you for your skills... "Hey, I know how to maximise somebody's utility through 2nd order calculus!" "huh you f**king high??"
LOL. I had interviews with IBM and Lockheed Martin recently and it gave me a great deal of hope for the degree, because no question required an answer like that. I mean I had some technical questions but they were all in regards to things that I'd be doing and they wanted to make sure I had an idea of what was up.
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United States24615 Posts
As someone who did a lot of the continuous math (physics major) but none of the discrete, I often feel like I missed out on that and wish I knew it... I see the value of what I wish I knew :/
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On November 08 2010 10:07 Kashll wrote:
I guess the best advice I can give you is either to find an application of it you like (there are a lot of cool areas of computer science), or grimace and bear through the class requirements so you can graduate and do some programming.
This is exactly what I had in mind
On November 08 2010 10:09 micronesia wrote:
As someone who did a lot of the continuous math (physics major) but none of the discrete, I often feel like I missed out on that and wish I knew it... I see the value of what I wish I knew :/
It's too late now but otherwise I'd have offered you my seat.
I the last time I did proofs before this was in high school in some math and god that was a mess. I did well on everything until that part then oh man...not good.
In discrete math I was good until we got to relations. Then everything went downhill (still rolling down said hill).
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Discrete math can be useful depending on the type of computer science you want to get into. As you said it's important in algorithm development, and proofs. There is a whole branch of computer science for which discrete math is one of the more basic building blocks so it's generally a required course for computer science students to get them introduced to such concepts.
I think it's fine to have some courses like these since it introduces students who might now know what particular direction of their degree they want to go into. It's a good basic course to try and get students interested in stuff you wouldn't ever really hear/learn about outside of school.
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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.
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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.
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User was warned for this post
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Isn't developing algorithms an important part of computer science/programming? If so, I don't understand why taking a class that has applications towards algorithms would be a waste of time.
If you're developing an algorithm or code for a company wouldn't it be useful to be able to prove that your algorithm or program is more efficient than the current algorithm or program being implemented?
I also don't think they would bombard you with complicated application problems right off the bat. I find that most courses just give you the basic problems so you get a sense of how it works.
Also, real math classes are actually proof based I believe. But I do agree with you in that I enjoy computational math courses over proof based math courses.
Hopefully there's a higher level course you can take that will make discrete math more useful to you. ^^ It would suck to have taken a course and wasted your money for nothing.
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If we were applying it to algorithms I'd like to do that but we have not touched on it thus far other than that it is an application.
Also when I said "real math" I was not trying to start a debate over what real math actually is, but convey my opinion that I am displeased with how it is going so far.
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I took this class a year ago and it was one of my favorite classes ever. I guess thats what happens when you have a class with Arthur Benjamin =D
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On November 08 2010 10:29 Hizzo wrote:
If we were applying it to algorithms I'd like to do that but we have not touched on it thus far other than that it is an application.
You probably won't touch on it during the Discrete class. Assuming it's like most places, it's a math class taught by the math department, and they tailor it toward their own majors.
You'll touch on the applications of it in Algorithms once you actually get to the Algorithms class, where you'll be expected to have the background from Discrete.
On November 08 2010 10:31 ReketSomething wrote:
I took this class a year ago and it was one of my favorite classes ever. I guess thats what happens when you have a class with Arthur Benjamin =D
Awww Benjamin wasn't teaching it the term I took it at Mudd. /jealous
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Hope you get used to it. Math courses that require a shitton of proofs are not for non-math major people.
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On November 08 2010 09:54 Elegance wrote:
I feel the same way about psychology. I won't be doing any "conditioning" any time soon, I don't give a fuck if a dog salivates to a bell or footsteps, I don't understand why I have to learn all this nonsense to become a nurse..
I reeeaally hope your trolling. If you dont think understanding part of how the brain works is important to a medical field then I dont know what to say... besides psychology is a pretty cool class imo.
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On November 08 2010 10:41 BnK wrote:
Hope you get used to it. Math courses that require a shitton of proofs are not for non-math major people.
I'll try, for my sake.
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Almost every maths course I've done past the 1st year as an undergraduate was basically all rigour and proof. It's certainly not unique to discrete maths. Proofs are what mathematics is about. If you don't like them then I really wouldn't recommend you do any more maths couses.
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On November 08 2010 09:47 Hizzo wrote:
God I hate this class. Anyone else taking it right now?
I cannot stand proofs. That is all we do, and it's so dumb because I know I'm not going to have to prove why that partially ordered sets cannot have more than one greatest element, or why two odd numbers added together are even outside of this class.
Classes like this piss me off. I cannot see any application of this class outside of algorithms and stuff. I don't even consider it a real class, it just feels like there's so much hand-waving going on - I'd kill to be able to go back to vector calc or any REAL math over this.
/rant
almost none of the classes u ever take will you ever actually use the material you learned ever again
the idea is that they are teaching you to read high level material, learn to think in a certain way, analyze certain topics, and be able to understand high level concepts. the skills you get out of higher level math classes will help you grow as a mathematician whether or not you remember the exact derivation of some theorem
calculus is not "true mathematics", as they basically give you an algorithm and you apply it. you can google and teach a monkey to follow a step by step process. you can teach any kid to google a theorem and plug in numbers. that's not real math.
true mathematics doesn't tell you where to go or what to do, its when you step outside the box and use ingenuity to prove things and explore subjects.
do you think all the algorithms you like and enjoy came out of thin air?
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On November 08 2010 10:58 opsayo wrote:Show nested quote +On November 08 2010 09:47 Hizzo wrote:
God I hate this class. Anyone else taking it right now?
I cannot stand proofs. That is all we do, and it's so dumb because I know I'm not going to have to prove why that partially ordered sets cannot have more than one greatest element, or why two odd numbers added together are even outside of this class.
Classes like this piss me off. I cannot see any application of this class outside of algorithms and stuff. I don't even consider it a real class, it just feels like there's so much hand-waving going on - I'd kill to be able to go back to vector calc or any REAL math over this.
/rant almost none of the classes u ever take will you ever actually use the material you learned ever again the idea is that they are teaching you to read high level material, learn to think in a certain way, analyze certain topics, and be able to understand high level concepts. the skills you get out of higher level math classes will help you grow as a mathematician whether or not you remember the exact derivation of some theorem calculus is not "true mathematics", as they basically give you an algorithm and you apply it. you can google and teach a monkey to follow a step by step process. you can teach any kid to google a theorem and plug in numbers. that's not real math. true mathematics doesn't tell you where to go or what to do, its when you step outside the box and use ingenuity to prove things and explore subjects. do you think all the algorithms you like and enjoy came out of thin air?
Don't get ahead of yourself. I never said anything about anything besides not liking the course, saying that it was a lot of hand-waving, that I don't like proofs, and that for my purposes I cannot foresee needing to use anything learned outside of creating algorithms. Also, taking what I said about "real math" and running with it after clarification is cool.
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United States4126 Posts
I had to take this class last semester for a CS major too, except for some reason my professor was pretty awesome and didn't dwell too much on proofs. I have another friend taking it right now with a different professor and they're ONLY doing proofs like you are :/ Sucks that it's what you're doing because the other topics in discrete are a lot more fun and interesting.
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The experience you had was pretty interesting! I wish it were like that.
Proofs are the only things I do not like, I actually had no problems with predicates or anything like that until Strong Induction (mathematical induction is easy). Now with relations things are looking more grim!
This semester all around is poop, haha. Also taking C, however important I know it to be, and I just do not like it! I very much miss C++ and java...come back to me OOP.
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On November 08 2010 11:09 Hizzo wrote:Show nested quote +On November 08 2010 10:58 opsayo wrote:On November 08 2010 09:47 Hizzo wrote:
God I hate this class. Anyone else taking it right now?
I cannot stand proofs. That is all we do, and it's so dumb because I know I'm not going to have to prove why that partially ordered sets cannot have more than one greatest element, or why two odd numbers added together are even outside of this class.
Classes like this piss me off. I cannot see any application of this class outside of algorithms and stuff. I don't even consider it a real class, it just feels like there's so much hand-waving going on - I'd kill to be able to go back to vector calc or any REAL math over this.
/rant almost none of the classes u ever take will you ever actually use the material you learned ever again the idea is that they are teaching you to read high level material, learn to think in a certain way, analyze certain topics, and be able to understand high level concepts. the skills you get out of higher level math classes will help you grow as a mathematician whether or not you remember the exact derivation of some theorem calculus is not "true mathematics", as they basically give you an algorithm and you apply it. you can google and teach a monkey to follow a step by step process. you can teach any kid to google a theorem and plug in numbers. that's not real math. true mathematics doesn't tell you where to go or what to do, its when you step outside the box and use ingenuity to prove things and explore subjects. do you think all the algorithms you like and enjoy came out of thin air? Don't get ahead of yourself. I never said anything about anything besides not liking the course, saying that it was a lot of hand-waving, that I don't like proofs, and that for my purposes I cannot foresee needing to use anything learned outside of creating algorithms. Also, taking what I said about "real math" and running with it after clarification is cool.
I don't get it. You say that the class is proof-based and then go on stating that there is a lot of hand-waving? That's a contradiction right there. If the class is proof-based it means it is rigorous and there is no room for hand-waving... Proofs do not allow for hand-waving or they are not proofs...
It seems like you just simply don't like maths. Maths is proof-based. Every single rigorous maths course will be proof-based.
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I have some very conflicting views, so I may sound a little harsh at times, and I am by no means qualified enough to have any real say (4th year Math/CS major at UCB), but here goes.
I'm pretty sure that for 90% of people, they say the same thing for Algebra. It's not needed for their profession, and it seems like a bunch of handwaving. That doesn't stop it from being important. If you ever want to go deeper into CS, then you're going to be dealing with almost all math. Almost everything you learned is built from the mathematics that you abhor.
I think you're opinion of math may come from your previous education. What you learned in high school is based upon a formulated approach designed not for the real world, but for academia itself. To me, learning math is like learning logic. It's about problem solving. The theorems and equations that you learn are the tools that you are given. However, people put too much on these theorems and equations, rather than the process. For example, what use is the quadratic equation in the real world? When will you be doing a calculation and stop to say "Now I can use the quadratic equation," when you have a computer right there, or when you can use much simpler methods to find the answer. How about if I tell you to do 28*32? People start to pull out their pen and paper, when it should take about 5 seconds to say 896 (difference of squares). They learn (a-b)(a+b) = a^2-b^2, but they never learn what it is. They just know "When I get a problem of this form, I can do this and that," without knowing what the true intention behind the problem is.
In your discrete mathematics class, you probably have to approach a bunch of different kinds of problems, each one requiring a different approach. You might be going through propositional logic, combinatorics, induction, etc. The most important part of the class isn't learning exactly all of DeMorgan's laws by heart, or know the formula for Baye's Rule. It's knowing when and where they are applicable, and being able to maneuver through them. Personally, I have a lot of friends that come to me with "math" questions on topics that I have only seen once or twice. However, the vast majority of these "math" problems from non-math courses are straight forward equation manipulation, or simplifying equations, and all it really takes is a strong foundation and wikipedia to answer these questions once you get the hang of it.
EDIT: I hate C. I think it's a great language if you know what you're doing, but something with it just doesn't quite click with me.
EDIT2: Just remembered I have this bookmarked if you're interested: http://www.maa.org/devlin/LockhartsLament.pdf
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Aotearoa39261 Posts
Go study engineering - that's "real" math according to your definition.
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Lol... Plexa's right... if you're looking for direct applications to real world stuff. Math isn't the best place to search.
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i just think you're confused as to what "real" math is, versus what you enjoy doing
when it comes to programming, in the "real world" i am 100% sure anything you've programmed thus far will have no application to your future job either.
the general consensus seems to be:
you: "i hate this math class, i wish math classes (or at least this one) wasn't like this
us: "get used to it, thats what math is"
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It seems our op is having a rude awakening from his bubbly days of baby calculus, baby differential equations, and baby linear algebra and he is NOT pleased! 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.
User was temp banned for this post.
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This is a great read, thank you for posting it.
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TossFloss
Canada606 Posts
On November 08 2010 09:47 Hizzo wrote:
God I hate this class. Anyone else taking it right now?
I cannot stand proofs. That is all we do, and it's so dumb because I know I'm not going to have to prove why that partially ordered sets cannot have more than one greatest element, or why two odd numbers added together are even outside of this class.
Classes like this piss me off. I cannot see any application of this class outside of algorithms and stuff. I don't even consider it a real class, it just feels like there's so much hand-waving going on - I'd kill to be able to go back to vector calc or any REAL math over this.
/rant
Fortunately, your university administration can make up for your lack of vision. Mathematical proofs are like push-ups for the mind. The ability to understand and competently apply algorithms, complexity, data structures and general problem solving depends on the same portions of your brain as mathematical proofs. And those skills separate the boys from the men.
As a public service, please complete the following:
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: .....
I normally don't rail on people like this. But I hope you will realize the arrogance of what you've wrote.
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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.
---
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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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" :/
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^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
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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.
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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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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.
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"real math" involves proofs
i'm sure being an undergrad though you know better than your professors
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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 : )
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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?
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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.
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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?
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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
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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.
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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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discrete math is the most frustrating class imo, you can barely hear what the prof is saying most of the time.
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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.
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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...
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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.
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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 >>
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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.
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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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On February 18 2012 09:22 SerpentFlame wrote:Show nested quote +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.
But the proofs done in these classes have literally 0 relation to algorithms and their derivations. That's the problem that me and my fellow discrete-sufferers are dealing with.
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On February 18 2012 00:57 TylerThaCreator wrote:
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?
Wait, your math classes are directly linked to cs? I study cs 2nd year in Germany and as the math faculties (which are really good at our university, among the best in germany even) manage all the lectures we rarely get any direct applications or links to cs at all in most of the lectures. Pretty much all of it is just the logic and the proofs behind the math and often just an abstract view on the applied math that you would see if you had to solve a problem in science or in an exercise. Our calculus/mathematical analysis lecture had no link to cs at all if I recall correctly, and half of the exam were proofs about cauchy convergency, continuity and stuff like that, we were really grateful about any task where you could actually "calculate" something like an integral, a convergency radius or an induction proof without thinking too much about it.
In contrast to that our discrete math lecture was really refreshing and I personally thought most of it was applicable, so I'm pretty baffled how much hate it gets here. Graph theory is as close as it can get to algorithms&data structures, combinatorics is always helpful pretty much everywhere and our lecture also had a good portion of information about algebraic structures like fields, rings, groups etc., also modulo calculation rules and the math behind it, which is used a lot in programming. The basic logical structures with de morgan's rules etc. are also pretty important if you look at how the logic of a computer is built. I don't see how it should be useless for cs.
Of course it wasn't super exciting and I think math lectures are dull in general, but besides numerical analysis it was one of my favourite math lectures. Numerical analysis was the only lecture that had a ton of applications presented for us in the lecture, so most of our class liked it more than the other math lectures.
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On February 18 2012 09:55 TylerThaCreator wrote:Show nested quote +On February 18 2012 09:22 SerpentFlame wrote: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. But the proofs done in these classes have literally 0 relation to algorithms and their derivations. That's the problem that me and my fellow discrete-sufferers are dealing with.
What exactly are you doing? Your earlier post only mentioned "probability stuff" do you mean basic probability counting methods or proving theorems about probability spaces?
Discrete math is stuff like graphs, etc, which should be quite relatable to cs.
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The "problem" with discrete math in US CS curriculum is that the math is actually very basic stuff, but CS people who aren't also studying math aren't trained for mathematical rigor. So the things that we're asked to prove seem intuitive, we just want to wave our hands -- but the point of the class is to show how something that may border on intuition, or perhaps is too complicated to intuitively derive, might be proven.
What you end up with is a smorgasbord of intro probability, logic, combinatorics, number theory, and who knows what else. In retrospect (I have a degree :p), this is probably for the best. CS students need to be familiar with these things to be capable, and probably will need to take deeper math classes as is appropriate for their specialization, but there just isn't enough time in a 4-year course to double an engineering degree with a math degree (not unless you work your ass off, anyway).
The short of it is, if you take real math classes, then classes like this become a joke. But there isn't enough time in your day to be meditating on obscure math proofs when your time is better spent in lab.
As for relevance, it's all relevant introductory material depending on where you end up. Understanding RSA & number theory is damn important if you go into computer security, and beyond that you need to learn abstract algebra (that wasn't in Swordfish ).
Pedantic proofs are no fun. But there will come a time when you're working on a problem and something that seems obvious isn't working, and you have no choice but to break it down into definite terms. Whether you write it out formally or solve it in your head, at some point you need to decide if something you do not already know is true or false.
I think structural induction is pretty cool when it is useful.
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