Any Computer Science majors/workers?

[theotherguy]

I think it depends on what you mean by calculus. The theory of calculus (real analysis) is much deeper than what you said. In a course like that all major theorems are proved and you're often asked, for example, not to integrate a particular function, but to show rather that a class of functions, say continuous functions, on a closed and bounded interval is Riemann integrable. This needs rigorous justification without any handwaving.

.

Now this is true. I have many friends who are completely baffled by taking Analysis (proving calculus), and my discrete math teacher forbade us to use anything from calculus because it would be too difficult to prove.

What I mean is, typical calculus classes have the form of "integrate this" or "find this volume" or "find the convergence/divergence of this particular sum", whereas once you get to discrete math, proofs and broader concepts are required.

I guess my view is muddied by the fact that my university lumps discrete math and elementary proofs/mathematical theory into one class that is a pre-requisite for Analysis (the equivalent class plus calculus).

 

[Ennui]

I'm a History major, but only because I absolutely refuse to take the math required for the Computer Science major. Chances are I'll end up working in CS anyway, since I currently know java, HTML, XML, and css, and I'm learning jscript, PHP and python. C++ is up next, hopefully by the time I graduate I'll be set.

My career choice is game development, thus the mod work I've been doing, but to start with I'll probably be working as a web developer.

 

[Sam]

Silence. Maths students are frequently the best students.
And I do humanities for chrissakes.

We don't take kindly to your types around here.

 

[AKIRA]

And to think that many linear algebra courses don't teach linear algebra but rather the application of matrix theory, where the focus is put on computation and formulas. I don't blame you for considering it to be hell. It is often boring and tedious number crunching. If the focus of your class was not on linear operators on finite-dimensional vector spaces then I'd say it wasn't a proper linear algebra class. I hope you'll reconsider.

We were taught matrices, invertables etc..many theorms about matrices. Then we got into 2D-3D vector spaces then we were taught about complex numbers later. It wasn't THAT hard it was just that the T.A.'s that marked our assignments/tests were EXTREMELY anal about everything and docked a lot of pointless marks off.

 

[Vigilante]

It's not an easy major at all but it's probably worth it.

 

[phantomdesign]

They say the proof is in the pudding (ewww), so what I'll say is I got a math degree at the age of 20, while sleeping through my classes. I taught a stereotypical highschool football player on stereoids how to program a TI-89, and I've tutored 3 people, about 4 hours each, and they went from understanding little of college algebra to getting A's on the final. We can argue the minute points all day/night, but the evidence remains the same.

I think by following these three "guidelines" you would come away from a mathematical "concept" with only a superficial understanding of it. You've not included the question of why it is, which is of far greater importance. There also needs to be motivation for the concept. There are many non-trivial theorems proved in a subject all the time, however not all of them are essential knowledge that give you significant insight into that subject or even good mathematical "tools" useful in proving other non-trivial theorems in that subject. This motivation should help explain how a "concept" relates to other "concepts" and hopefully make you eager to understand it.

Also, I'm not so sure that someone who is studying computer science should have their ability and knowledge of the subject gauged by whether or not they can program a Pac-Man game. Programming is a modest-sized portion of computer science, but by no means is it more important or intellectually engaging than its other portions.

What do you mean by "why it is" and these "motivational" things you talk about are distractions only confuse, frustrate, slow the learning process, and motivate people to hate math. (Some proofs are essential & part of advanced math, but that's a different subject.) My case-point about the packman game relates to simple logic.

I disagree. It should be:

1) What is this particular problem about?
2) What formula can I use to represent this mathematically?
3) Why is it represented this way?
4) How can I prove it?
5) What does this say about this mathematical concept in general?
6) How can I use this to solve other problems?

ie.

1) This problem is asking me how many ways I can shuffle a deck using some algorithm which breaks the deck into two smaller decks A and B, and then rearranges them.
2) It looks like a binomial distribution that can be represented by pascal's triangle.
3) It is represented this way because of combinatoric laws X and Y.
4) I can think about this problem as representing the deck as a string of 1's and 0's for A and B, and selecting a random string of 1's and 0's to uniquely identify an arrangement.
5) Binomial distributions can arise from randomly selecting two different options.
6) Whenever I see options that are either off or on, or A or B, I should try first to represent it as a string of 1's and 0's, and then think about they ways I could be over or undercounting it.

I also think discrete math is much harder than calculus.

In calculus, the questions they ask you have very obvious underlying mathematical concepts and formulas. Once you understand the problem, you just plug in the variables into the formula and get the answer. In discrete math, its not immediately apparent how you can solve a particular problem, and often, the formula you generate to solve it is totally unique to that problem. You have to prove that your formula is correct and that it will work in all variations of the problem to get it right.

Such complexity is unnecessary, once you cut out all the fluff, combining two concepts to solve a "unique" problem isn't much more complex than playing with wooden blocks of different shapes. Discrete math isn't really any more complex than calculus, just different. Once I cut through the fluff and got my cheat-sheet, it was smooth-sailing.

 

[As She Moves]

They say the proof is in the pudding (ewww), so what I'll say is I got a math degree at the age of 20, while sleeping through my classes. I taught a stereotypical highschool football player on stereoids how to program a TI-89, and I've tutored 3 people, about 4 hours each, and they went from understanding little of college algebra to getting A's on the final. We can argue the minute points all day/night, but the evidence remains the same.

You're basing this off the premise that the typical calculus and college algebra classes test for a good understanding of math. How could this possibly be the case when the foundations of both are almost completely ignored? Also, don't think that A's in those classes mean you know the subject. If all you're going for is the grade then that's a separate matter from understanding a mathematical concept, as you put it. Just know that you'd fail any upper division courses in math (i.e. the ones requiring you to justify what you think, say and write) with that attitude.

What do you mean by "why it is" and these "motivational" things you talk about are distractions only confuse, frustrate, slow the learning process, and motivate people to hate math. (Some proofs are essential & part of advanced math, but that's a different subject.) My case-point about the packman game relates to simple logic.

How would knowing the explanation for why something is confuse someone? The whole point of wanting to know this is to clarify it. The topics in elementary math are no less provable than those in advanced math. Again, we're talking about understanding a mathematical concept. You don't do that by simply accepting the concept as being true, no questions asked.

Such complexity is unnecessary, once you cut out all the fluff, combining two concepts to solve a "unique" problem isn't much more complex than playing with wooden blocks of different shapes. Discrete math isn't really any more complex than calculus, just different. Once I cut through the fluff and got my cheat-sheet, it was smooth-sailing.

Cheat-sheet? Uh, huh. Now you're just admitting you don't understand math.

 

[AKIRA]

cheat sheets are pretty good. You spend all this time cramming everything you possibly can on the sheet then in the end you don't use more than half of it because you spent so much time writing shit out that it stuck with you.

...at least that's what happens with me. I understand math somewhat but I am just naturally not that good at it lol. I'm more of a networking kind of guy which is why I switched out of comp sci. Anyway, I hope you choose the right path for yourself deathmaster

 

[Pesmerga]

I always understood that the true nature of math wasn't in what teachers taught you in school, but just the understanding that numbers are arbitrary creations that are built around logic. If you understood the fundamentals of mathematics, you could theoretically figure out the whole of geometry, trig, and calculus.

Of course this is a highly inefficient way to learn math.

 

[Sulkdodds]

Certainly "it doesn't matter whether you understand as long as you get the grade, let alone joy in the subject" does not seem a fantastic approach to any study.

 

[phantomdesign]

You're basing this off the premise that the typical calculus and college algebra classes test for a good understanding of math. How could this possibly be the case when the foundations of both are almost completely ignored? Also, don't think that A's in those classes mean you know the subject. If all you're going for is the grade then that's a separate matter from understanding a mathematical concept, as you put it

I'm not basing X of premixe Y.

I think we're on ths same page here (depending on your definition of foundations). Foundations being ignored confused me about calculus initially. It's like "do this method here" and then "now that we see X, we use Y method." F*** vague methods, what the hell is dX/dY, what is it useful for, and how I use it mathematically?

Just know that you'd fail any upper division courses in math (i.e. the ones requiring you to justify what you think, say and write) with that attitude.

*cough* I HAVE A MATH DEGREE.

I got A's in those courses & I liked those courses. The great thing about those courses is you're allowed to find and use more efficient logical forms to solve problems.

How would knowing the explanation for why something is confuse someone? The whole point of wanting to know this is to clarify it. The topics in elementary math are no less provable than those in advanced math. Again, we're talking about understanding a mathematical concept. You don't do that by simply accepting the concept as being true, no questions asked.

I never said "Explaining X confuses people." I'm just promoting a more simplified explanation (which includes "What is X?"). Modern teaching methods fail by either doing nothing but shoving the method down your throat, or take a look at any math book and look at the 5-10 pages of text for each new lesson . . . THAT is what causes people to lose motivation and be confused.

Cheat-sheet? Uh, huh. Now you're just admitting you don't understand math.

Ummm? what? Lets keep this non personal.

I programmed about 80% of the programmable math concepts in my math and physics classes, which requires a COMPLETE understanding of the concept, usually more indepth than presented in the text.

Regardless, the value of a "cheat sheet" is that you can find the information you're looking for quickly. When you can find relevant information in seconds, it makes relating concepts and understanding how they work much faster. At least for me and anyone I've tutored.

I always understood that the true nature of math wasn't in what teachers taught you in school, but just the understanding that numbers are arbitrary creations that are built around logic. If you understood the fundamentals of mathematics, you could theoretically figure out the whole of geometry, trig, and calculus.

Of course this is a highly inefficient way to learn math.

I agree with everything, but the last statement. I think it's a much more efficient way to teach math.

Ex: Rather than understanding 500 formulas for parenthesis, if you just know what the damn parenthesis are . . . about 85% (more more) of the concepts that follow just make sense.

 

[theotherguy]

I would say that the majority of math classes are taught horribly, miserably wrong, and that AP math classes are even worse.

Most math classes will present you with an idea, and then say something like "Look folks, it ALWAYS works!" and you accept it at face value. Example: "Look children, all numbers are uniquely factorable into primes! It ALWAYS works this way!" But they never say why this is so, and they never go into any depth about it at all.

When they teach you to add and multiply and subtract and divide, they just teach you an algorithm, or a book-keeping method of figuring out how to do it. They don't say WHY the algorithms work the way they do.

AP math classes teach to the test. They give you great shortcuts for finding and solving problems on standardized tests, but utterly fail in getting you to think about the problems for yourself.

Look, all of these methods may work for the vast majority of people, and may get you happily through all of high school math. All the doctors and lawyers in the world would just need a few simple shortcuts to get through math, and our school systems are set up to produce doctors and lawyers. Even engineers only need a limited understanding of algebra and calculus to get by.

But for us theoreticians, these shortcuts and mistakes in the teaching of math have left us scrambling and confused about the subject matter.

Not everyone is a mathematical genius, and not everyone can get a math degree at 20. The rest of us have to struggle through this slog of difficult concepts in a field that we despise.

I hate math. I hate having to prove things, and I hate having to prove things more and more rigorously as problems get more and more complex; but if I had been taught the basics of proofs and algebra long ago, like say kindergarten, I would be much better off.

Really, that's the way math should be taught. You should, of course, learn the basic operations first, but you should learn them in multiple bases, not just base 10. You should have a firm understanding of just what it means to add, subtract, multiply and divide. You should then be taught algebra immediately, perhaps even concurrently to being taught how to do the basic operations. You should then get into discrete math and proofs, and only after that should you be introduced to calculus.

 

[Pesmerga]

Certainly "it doesn't matter whether you understand as long as you get the grade, let alone joy in the subject" does not seem a fantastic approach to any study.

I think of educational establishments as speed limit signs. There are the majority who reluctantly follow the limit within 10-15 mph, the few idiots who fall behind and slow down traffic for the rest, and then the sport cars who ignore the limit and just burn jet fuel to get to their destination.

I think it's important to have speed limits as a sort of benchmark, instead of relying on the sport cars to set impossible and unsafe standards.

 

[Ennui]

I hate math. I hate having to prove things, and I hate having to prove things more and more rigorously as problems get more and more complex; but if I had been taught the basics of proofs and algebra long ago, like say kindergarten, I would be much better off.

Really, that's the way math should be taught. You should, of course, learn the basic operations first, but you should learn them in multiple bases, not just base 10. You should have a firm understanding of just what it means to add, subtract, multiply and divide. You should then be taught algebra immediately, perhaps even concurrently to being taught how to do the basic operations. You should then get into discrete math and proofs, and only after that should you be introduced to calculus.

Wut? First off, I'd like to see you teach a 5 year old algebra. I tutor elementary schoolers, mostly 3rd or 4th graders, several years older than that, and I've spent entire tutoring sessions trying to figure out how to get an 8 year old to understand how to read a non-digital clock.

Second, why would we learn to perform operations in anything other than base 10 unless we were all planning on being either mathematicians or CS people? Base 2/hex are the only other essentials for the most part anyway, and once you understand how Base X works you can do pretty much all of them. We standardize with base 10 for a reason.

 

[AKIRA]

Wut? First off, I'd like to see you teach a 5 year old algebra. I tutor elementary schoolers, mostly 3rd or 4th graders, several years older than that, and I've spent entire tutoring sessions trying to figure out how to get an 8 year old to understand how to read a non-digital clock.

Second, why would we learn to perform operations in anything other than base 10 unless we were all planning on being either mathematicians or CS people? Base 2/hex are the only other essentials for the most part anyway, and once you understand how Base X works you can do pretty much all of them. We standardize with base 10 for a reason.

this is in north america where most kids aren't taught well from a young age. Hey, i'm one of them, maybe that's why i'm not that great at math. Look at the education system in europe, most of those kids are taught algebra in like grade 4 or 5. I didn't see algebra until grade 7!!

Look at China...those kids are taught like everything from age 5 and the majority of those kids are geniouses compared to us.

Now, i'm not saying every north american kid is dumb, but the whole education system here needs a lot of tweaking.

 

[Qhartb]

Well, this thread has drifted quite a bit, but I'll say that I majored in CS and work in the industry. I'm on the software team at a hardware company.

Also, I enjoy rigorous math courses. I'm not sure how I wish math were taught at a young age -- teaching more conceptually would give a deeper understanding to the students who can follow, but runs the risk making it harder for some to learn basic mathematical skills that they may have gotten through memorizing algorithms and tables. We may end up with better accountants and worse clerks.

 

[Ennui]

this is in north america where most kids aren't taught well from a young age. Hey, i'm one of them, maybe that's why i'm not that great at math. Look at the education system in europe, most of those kids are taught algebra in like grade 4 or 5. I didn't see algebra until grade 7!!

Look at China...those kids are taught like everything from age 5 and the majority of those kids are geniouses compared to us.

Now, i'm not saying every north american kid is dumb, but the whole education system here needs a lot of tweaking.

I don't know if using China is a good example though. They have better average test scores but Chinese schoolchildren also spend quite a lot more time in school and doing schoolwork out of school than North American children. Not to mention the extreme cultural differences.

I do agree that our education system here is flawed, but the solution to that is in the teaching methods, not necessarily what we teach or in what order. And I agree with Qhartb's second paragraph there.