Oddly enough I never really used any of these while studying CS. Now that I'm in bioinformatics, some of the stuff is commonly used, particularly Bayes' theorem and information theory.
Equations True Computer Science Geeks Should (at Least Pretend to) Know
61–70 of 100 posts
Re: Equations True Computer Science Geeks Should (at Least Pretend to) Know
#62I would prefer to see the Cook-Levin theorem in place of the pumping lemma.
Re: Equations True Computer Science Geeks Should (at Least Pretend to) Know
#63Earlier quoted context omitted.
I disagree. Programming is math. Highly advanced math, in fact. It's just a different type of math. And the 11 equations in the OP's article just barely touches on what CS is about. There is far more to it than that.
No. Programming is logic , and logic is a superset of math. What you need to make good programs isn't some obscure, arcane language that the few who actually understand it (mathematicians) assert to be the universal answer to everything, yet refuse to make it more accessible (when it could be), what you need is logical thinking and the ability to think in abstractions. Yes, studying math will teach you this, because…
Do you have an example of mathematics that could be made more accessible but hasn't been?
Re: Equations True Computer Science Geeks Should (at Least Pretend to) Know
#64Earlier quoted context omitted.
I had to actually double check if the author was from the US or not, since in some places it was just so incomprehensible. I agree the applications were glossed over or skipped, but that is probably the most interesting aspect of the equations as well. Without practical information, the article is sorely missing true sustenance.
This effect is often true for people whose native language is math :-) But to be fair most disciplines have their own jargon, math happens to have its own keyboard too.
Most other disciplines don't try to force their jargon onto other fields though. Math often does.
Also, I'd generally say that almost all jargon is bad. A quote that's frequently attributed to Einstein says that "If you cannot explain something in simple terms, you do not have adequately understood it". Math and science in general should take this to heart, because I feel that many people have forgotten this or never really understood it in the first place.
Re: Equations True Computer Science Geeks Should (at Least Pretend to) Know
#65Earlier quoted context omitted.
No. Programming is logic , and logic is a superset of math. What you need to make good programs isn't some obscure, arcane language that the few who actually understand it (mathematicians) assert to be the universal answer to everything, yet refuse to make it more accessible (when it could be), what you need is logical thinking and the ability to think in abstractions. Yes, studying math will teach you this, because…
Do you have an example of mathematics that could be made more accessible but hasn't been?
A more recent example I've come across are n-dimensional spaces. I realized that most people have problems to make sense of the concept behind that because they've been stuck in thinking mathematically.
I think of points in an n-dimensional space as objects holding n different types of information, which is a practical approach, and has lit a candle for some other people I explained it to this way as well.
For example, images are often stored as 4 dimensional structures, with the dimensions representing height, width, depth and color value. Every point in that structure is a pixel of the image. You can easily expand this to any number of dimensions, and it still makes sense - you're just adding information (eg, add a fifth dimension for time, and you've got yourself a sequence of images - a simple video).
My beef with the way math is often approached is that on the one hand, it's asserted that math is the universal solution to all problems - including practical ones - but on the other hand, more often than not math is removed so far from reality that it's nearly impossible to make any practical use of it.
Re: Equations True Computer Science Geeks Should (at Least Pretend to) Know
#66Earlier quoted context omitted.
I disagree. Programming is math. Highly advanced math, in fact. It's just a different type of math. And the 11 equations in the OP's article just barely touches on what CS is about. There is far more to it than that.
No. Programming is logic , and logic is a superset of math. What you need to make good programs isn't some obscure, arcane language that the few who actually understand it (mathematicians) assert to be the universal answer to everything, yet refuse to make it more accessible (when it could be), what you need is logical thinking and the ability to think in abstractions. Yes, studying math will teach you this, because…
Why do you claim logic is a superset of math? My understanding of Gödel's incompleteness theorems is they show you can't reduce arithmetic to a consistent & complete logic.
Re: Equations True Computer Science Geeks Should (at Least Pretend to) Know
#67Nope.
Re: Equations True Computer Science Geeks Should (at Least Pretend to) Know
#68Earlier quoted context omitted.
Do you have an example of mathematics that could be made more accessible but hasn't been?
A more recent example I've come across are n-dimensional spaces. I realized that most people have problems to make sense of the concept behind that because they've been stuck in thinking mathematically. I think of points in an n-dimensional space as objects holding n different types of information, which is a practical approach, and has lit a candle for some other people I explained it to this way as well. For exampl…
I don't think any mathematician will assert that math is a practical subject or the universal solution.
In math, we just define n-dimensional Euclidean space, but no implication is made about the physical world.
Re: Equations True Computer Science Geeks Should (at Least Pretend to) Know
#69Earlier quoted context omitted.
At two jobs now I've had a conversation with talented comp sci grads and we all agreed 99% of programming is drudgery and the 1% that requires you to turn off your music and sit in dead silence is rare and still not as challenging as comp sci syllabuses (syllabi?) would suggest. An unfortunate side-effect is that many people who could have become highly productive mid-level programmers are scared off because they don…
I disagree. Programming is math. Highly advanced math, in fact. It's just a different type of math. And the 11 equations in the OP's article just barely touches on what CS is about. There is far more to it than that.
For many years, computers sucked at math. In many cases the job of a programmer was not to make the computer do complicated math, but to come up with clever ways to get out of doing complicated math.
That's not really true anymore, now that so many technologies from gaming to communications rely on concepts and algorithms from higher mathematics. While I'm skeptical about the importance of the particular equations on the author's list, I don't think it's reasonable any longer for software devs to plead ignorance (your humble correspondent included).
Re: Equations True Computer Science Geeks Should (at Least Pretend to) Know
#70Earlier quoted context omitted.
Do you have an example of mathematics that could be made more accessible but hasn't been?
A more recent example I've come across are n-dimensional spaces. I realized that most people have problems to make sense of the concept behind that because they've been stuck in thinking mathematically. I think of points in an n-dimensional space as objects holding n different types of information, which is a practical approach, and has lit a candle for some other people I explained it to this way as well. For exampl…
That's totally the standard way that all mathematicians think about n-dimensional spaces.
I've never heard a mathematician claim math is the universal solution to all problems... sounds like you had a bad high school experience. Do you need a math-hug? :)