CS Profs Debate Role of Math In CS Education 583
theodp writes "Worried that his love-hate relationship with math might force him to give up the pursuit of computer science, CS student Dean Chen finds comfort from an unlikely source — the postings of CS professors on the SIGSE mailing list. 'I understand that discussing the role of math in CS is one of those religious war type issues,' writes Brad Vander Zanden. 'After 30 years in the field, I still fail to see how calculus and continuous math correlate with one's ability to succeed in many areas of computer science...I have seen many outstanding programmers who struggled with calculus and never really got it.' Dennis Frailey makes a distinction between CS research and applied CS: 'For too long, we have taught computer science as an academic discipline (as though all of our students will go on to get PhDs and then become CS faculty members) even though for most of us, our students are overwhelmingly seeking careers in which they apply computer science.' Frailey adds that part of the problem may be that some CS Profs — math gods that they may be — are ill-equipped to teach CS in a non-mathematical manner: 'Let's be honest about another aspect of the problem — what can the faculty teach? For a variety of reasons, a typical CS faculty consists mainly of individuals who specialize in CS as a discipline, often with strong mathematical backgrounds. How many of them could teach a good course in cloud computing or multi-core systems or software engineering or any of the many other topics that the graduates will find useful when they graduate? Are such courses always relegated to instructors or adjuncts or other non-tenure-track faculty?' So, how does this jibe with Slashdotters' experience?"
Do you want computer science, or engineering? (Score:5, Interesting)
Re:Do you want computer science, or engineering? (Score:5, Insightful)
Which is really the way it should be broken out. Computer Science should be about the math, theories, and algorithms that make up computation, and computer software engineering should be more about building applications. Sort of like how traditional engineering relates to physics.
Re:Do you want computer science, or engineering? (Score:5, Funny)
Thanks a lot. Like there weren't already enough religious warriors at this party.
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Sadly, there is almost nothing that will be learned in 4 years of college that used that couldn't be taught in 10 minutes of skimming through a "best practices" document that isn't already done in the software packages one would be using for work. It's mainly being used as a litmus test to see if people are trainable. Which is sad. It's got no more meaning than a paper MCSE, but takes
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Sadly, there is almost nothing that will be learned in 4 years of college that used that couldn't be taught in 10 minutes of skimming through a "best practices" document
Given that EVERY student taking science should be made to take basic calculus. In fact in the UK basic (polynomial) calculus used to be
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No, he was saying that at the very least, everyone should have basic levels of education in certain things, and that these things include essentials (e.g. basic math such as calculus, core English literature such as Shakespeare etc).
I would in fact add a few more to the list -- basic chemistry, including physical, organic, and inorganic; basic physics, including mechanics, electromagnetism, quantum mechanics; engineering drawing; at least conversational skills in one non-native language; introduction to mus
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That's one of the points of a bachelors. It isn't a vocational degree.
It is now. Or, rather, it's the new HS Diploma. It no longer guarantees you entry into the middle class. Companies won't take a chance on you because they like you or think you'd "fit in" to their culture if you have a Bachelors. Once, this was, in fact, the case: a BA or BS gained you entry into the corporate world without any questions of specific skills: the employer would train you as needed.
That era is over. There are more college educated people than there are jobs we would consider providing the basi
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What people refer to as "CS math" would have brought science to its knees if scientists payed any serious attention.
CS math requires:
Engineering Math I (Calculus)
Engineering Math II (calc 2)
Discrete Math
And linear algebra or differential equations.
Math for a full-on engineering degree requires:
Engineering Math I (Calculus)
Engineering Math II (calc 2)
Engineering Math III (Even more calculus!)
Diff EQ
Applied Engineering Math
One more math class for full-on engineering than CS. Do you really think that someone making it through two semesters of engineering calculus, discrete math and Dif EQ is completely inadequate?
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If you make it real Software Engineering, meaning it is taught by the Department of Engineering and has the opportunity for p. eng. accreditation, students will end up having to take MORE math (at my university it's something like Lin Alg. I-II, Calculus I-III, ODEs, PDEs, Applied Probability and Applied Stats) just to satisfy their general requirements.
I'm also unclear on exactly what part of CS doesn't require math, applied or not. What kind of programs are you going to write without a strong mathematical
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The software engineering part doesn't need (continuous) math.
Testing, process, management, analysis, design, coding, requirements gathering are all fairly math free.
Sure there are some domains that require continuous math, but there are a hell of a lot of other domains that don't.
Re:Do you want computer science, or engineering? (Score:4, Interesting)
Calculus was where I was introduced to the concept of limits, which is the core of Big O notation.
I really wish some of the people writing the code I now have to maintain understood Big O notation...
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Logic is not mathematics, and legions of mathematicians will tell you this. Mathematical reasoning uses logical reasoning. Models of logics use mathematics. However, logic systems are not mathematics systems. Any part of mathematics is what we'd call a theory in logic.
And implementation does not require only first-order logic. At its core, at least if we are talking computer programs, the reasoning required is a variant of modal logic. If we are talking hardware, there are all sorts of logic that could be u
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And that's why Soviet superiority in computer science helped them to win the Cold War!
Re:Do you want computer science, or engineering? (Score:4, Informative)
You should look at the current jobs market. All of the good paying jobs require solid mathematics knowledge, especially for anything simulation/visualization related - CFD, aerodynamics, combustion systems, design/simulation of industrial processing equipment (grinders, shredders, slicers), and require OpenGL, CUDA, MPI, OpenMP experience as well.
Those jobs that aren't mathematics related, seem to be more arts based (web design) requiring knowledge of Photoshop, 3Dmax. The remainder seems to be management or customer facing roles.
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Really? I don't know where you are looking, but I don't see the situation you describe at all, not now or ever before. By far the most jobs in software development (you describe a lot of other, perhaps related fields) are about implementing business logic. And I don't mean business logic on the 'quant' level, but rather on the mundane, daily process level. These do not require any substantial knowledge of maths, except to reach a very high level of expertise. Before you say these jobs don't pay as good, tak
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In fact, I would say that there are three separate (but related) categories in computing --
1. Computer Engineering -- this would be akin to any other field of engineering. You learn about microprocessors, VLSI, DSP, and other elements, not dissimilar from EE or ECE. Lots of practical, engineering considerations should be involved.
2a. Theoretical Computer Science -- this, to your point, should be about theoretical computer science, complexity, discrete math, topology, graph theory, and other aspects of "real
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At the same time, it turns out that many math wizards are horrible programmers.
In many ways, I feel you could substitute "programming" with "composing music" in your hierarchy and still be making roughly the same argument; there is a well known overlap between mathematical and musical talent, music can certainly be "reduced to" mathematics. And yet, a math professor rarely turns out as good music as a musician and there is really no general assumption going that the best musicians are also math wizards.
Unfo
Do you want a university or a trade school? (Score:5, Insightful)
I think a better question is: Do these professors think their college should be an institution of higher learning or a trade school? (Disclaimer: I got a PhD from a top-20 university.)
Let me make a few points:
First, while it's true that numerical math is not used in many CS areas, discrete math is. Logic, set operations, and the like are used pervasively in CS. And learning numerical math is a core breadth area that instills mental discipline. Quite frankly, if math is not your strong point, then you should consider moving out of CS.
Second, the role of a university CS undergraduate curriculum is not to teach "cloud computing or multi-core systems or software engineering". It's to teach core CS topics. It's like like suggesting that a mechanical engineering student should be taught how to fix the engine of a Ford Mustang or that an electrical engineering student should be taught how to install video cards into a PC.
Let me make this clear: Any "hot topic" CS subject you teach in a university will be outdated in a few years, quite possibly between the student's freshman and senior year. This includes "cloud computing" and "multi-core systems". Back in my day, the hot topics du jour were ATM networking and grid computing, but fortunately I went to a good university that focused on core topics.
What's the difference, you ask? Here are you go:
Hot topic: cloud computing
Core CS topics: distributed systems, distributed algorithms, operating systems
Hot topic: programming in C#
Core CS topic: programming language structure, compilers, automata theory
Hot topic: multi-core systems
Core CS topic: computer architecture (x86, for example), instruction sets, digital systems
Hot topic: writing video games
Core CS topics: graphics, linear algebra, digital image processing
Learning math and these CS core topics allows students to learn new skills in the future. Case-in-point: Recently I have been working in a new area: machine learning algorithms (SVMs, bayesian inferencing, etc.). The importance of this area has grown in the Google-era and was not widely regarded when I was an undergraduate. My fundamental knowledge in mathematics is serving me well right now.
Finally, the professors quoted in the article are from U. of Tennessee and SMU, which are like 4th-tier universities. So don't take their word too seriously.
Re:Do you want a university or a trade school? (Score:5, Informative)
"It's like like suggesting that a mechanical engineering student should be taught how to fix the engine of a Ford Mustang or that an electrical engineering student should be taught how to install video cards into a PC."
No, it's not like that at all, because a mechanical engineer (or most of them anyway) are not going to be working on cars for a living, and electrical engineers are not going to be installing video cards for a living. But CS students are going to be doing mundane programming for a living.
The problem is that teaching practical, career programming is probably what a Software Engineering program should do. But that is a relatively new degree, and many colleges and universities still rely on Computer Science programs to (supposedly) teach those skills. But for the most part they do not.
It's all very well and good to say CS is one thing, engineering is another... but until academia fully catches up with that concept, many who intend to go into programming as a career are getting the short end of the stick.
And no, despite your derogatory comment, Software Engineering is not suitable material for a trade school, any more than Electrical Engineering is.
Re:Do you want a university or a trade school? (Score:5, Insightful)
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You're missing the point. All of the "Core CS Topics" you mentioned in your lists can be learned (deeply and completely) without having a graduate-level understanding of calculus. Basic algebra and boolean logic pretty much covers it, when combined with CS specifics like understanding algorithmic complexity, etc. The divide is between those that write new fundamental algorithms and need the heavy math to do the research, and those that merely engineer with, implement, and use the wide array of readily av
Re:Do you want a university or a trade school? (Score:4, Insightful)
Finally, the professors quoted in the article are from U. of Tennessee and SMU, which are like 4th-tier universities. So don't take their word too seriously.
This comes off as a snobby, ad-hominem cheap shot. You made some strong points in the rest of your comment and I didn't see the need for it. In the interest of full disclosure -- I hold a master's degree (CS) from a top 20 University; working on the PhD.
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Graphics is only part of video games (Score:4, Insightful)
Hot topic: writing video games
Core CS topics: graphics, linear algebra, digital image processing
FWIW. Graphics is only part of video game development. Most of the time the graphics is largely "outsourced" by licensing a graphics engine. Other parts of game development are in the areas of artificial intelligence, networking, databases, human/computer interaction, etc. Hovering over everything is data structures and design/analysis of algorithms, this is where so many things go wrong. Toss in a good understanding of architecture and compilers. The core CS topics necessary for developing a modern AAA game is pretty comprehensive.
Many aspiring to work in game development limit their chances to do so by focusing only on the graphics. Just as many interested in computer programming limit their opportunities by avoiding the advanced math. I will admit that in many of my jobs I did not need the math, however to my surprise I've had job opportunities that did require having had the advanced math classes. Not that I was doing much of the math myself but I needed to understand and communicate with the actual mathematicians. I've had to dig out those textbooks from that "extra" second year of math to implement some algorithms.
Hah! (Score:3)
First, while it's true that numerical math is not used in many CS areas, discrete math is. Logic, set operations, and the like are used pervasively in CS. And learning numerical math is a core breadth area that instills mental discipline. Quite frankly, if math is not your strong point, then you should consider moving out of CS.
Are you kidding?
I was in a PhD program in Electrical Engineering at a top-10 university [not trying to start a pissing contest here]. Quite frankly, I had a much better opinion of CS until I started taking a lot of graduate-level CS courses there.
Saying CS people do a lot of math is like saying a bank teller or cashier does math all day.
I found undergrad and graduate CS students alike would go running for the hills as soon as someone said the words 'integral' or 'derivative' . Random processes and statisti
Re:Hah! (Score:4, Insightful)
Even the industry-standard 'SPEC' CPU benchmarks use the wrong type of averaging which leads to incorrect results -- in some cases a faster computer (which completes all benchmarks faster than a slower computer) can have a *worse* score than the slower computer.
This comment is incomprehensible, on several levels.
No one who works seriously with benchmarks thinks there's any correct form of averaging that diminishes salt consumption. Benchmarking is inherently a high salt diet. Low sodium, high sucrose benchmarks are known as pie charts.
There is one form of averaging I dislike more than most: Apple Pie charts, the primary ingredient of which is a carefully selected Photoshop filter whose slices precisely match a particular CPU's scheduling slots, and never denominated in performance/dollar. We know how fundamentally accurate that benchmark was from all the suicides reported among professional Photoshoppers when Apple switched to Intel (none that I can recall).
Are you trying to imply that the SPEC averaging method has the property that there exits machines x,y such that for all benchmark disciplines b: time[x,b] < time[y,b] yet SPEC[x] > SPEC[y]? That would violate some deep ordering relations, which I've never seen short of fraud.
If you were implying that sum{b} time[x,b] < sum{b} time [y,b] yet SPEC[x] > SPEC[y], and this is somehow prima facie illegitimate, you need to repeat some stats courses. If machine x scores times (20,45) and machine y scores times (31,31) the arithmetic mean and harmonic mean achieve different rankings. Which mean is the wrong mean? You'll be seeking a course which covers the covariance of principle components, one of several reasons why you can't normalize benchmark disciplines to unit weight over measured scores without the copious addition of salt.
I'd love to have seen published the processor heat map after running the Apple Pie benchmark suite. That little red spot is the AltiVec unit, which never gets a break. It takes more than a "correct type of averaging" to ensure fair benchmark coverage.
A good benchmark is one where I look at the numbers and go "that's why I thought, the (pre-Intel) Apple sucks" and the guy beside me goes "yeah, that's what I thought, AltiVec rocks" and we're both right because we filtered our needs and budgets through the numbers presented.
From a purist perspective, I happen to think than on any CPU ever made, it's inexcusable that time to reverse the bit order of a 64-bit integer is greater than the time to increment a 64-bit integer (whose ripple carry unit subsumes every possible path length, making it's implementation a superset of bit reversal propagation paths).
I think of that comparison as benchmarking down to the bare wires. Every CPU I can recall fails this basic test all the way back to the SC/MP. Is symmetry of no importance in computer science? It makes me wonder about CS education altogether.
And don't get me started on popcnt. Not counting either? For shame.
Re:Do you want a university or a trade school? (Score:4, Insightful)
I am so tired of people saying, "Well you have to have math because you have to have logic." Logic is separate from math, and math is largely concerned with inductive logic...You know, the kind you never use in CS? In all the math I've had in my life, the only kind that had deductive proofs of the sort that resemble programming logic, was 10th grade geometry. I started CS via Cognitive Science, which is largely Philosophy. I had more, and more relevant, logic courses in Philosophy than in CS or math, and it gave me a huge edge in programming over my math-centric peers.
I've been in the field for 15 years, and I've never used a single thing from advanced math. I used some pre-calculus once, to figure out how much air conditioner I needed for a server room. I had to take 3 semesters of physics too. What the hell was that about? At the same time, I only had a single course in network theory, and it was obscenely general, with LANs mashed up together with the sort of latency issues you'd only run into if you were networking satellites.
I agree as far as teaching theory...That's all I was ever taught, and it's served me well. But advanced math isn't useful for the vast majority of CS majors.
Re:Do you want a university or a trade school? (Score:5, Insightful)
With a slightly different spin, it used to be the case that a liberal arts education prepared you for many things precisely because it taught you how to think for yourself in several different areas. Find a job in an area you are not an expert in? You will have the skills necessary to learn it. This is completely beyond the ken of most HR departments in companies. Brain-dead companies who think schools are cookie cutters, you must have the right bumps and curves to fit into their industrial machine. And the result is stagnant companies whose Business School Product running them figure their best way to retire early is to ship the company to China and pad out that retirement package.
In concert with this are several social trends. Schools of Education which focus on making Johnny/Sally feel "empowered" with ill-deserved self-esteem rather than taught. Parents who think Johnny/Sally go to school to free them for their two-career lifestyle. Parents who cannot turn off the damn TV and mind-numbing video games since it keeps the little bastards occupied rather than taking an active interest in their education while they are at home. A Hollywood which glorifies the dumb-ass but lovable schmuck who can get a laugh, rap his/her way via a hip-hop philosophy that says get yer ya-yas NOW, forget about actually working for an intellectual attainment that will make you a step above your peers. There's a commercial for a furniture company in my area which uses a rock song with the refrain "I want it all, I want it now, usw". That's the anthem we've taught our kids, you deserve to have it all, right now, no hard work, no paying your dues, you can get it just by demanding it.
It is amazing any kid makes it through the hurdles adults put in their place to actually learn to think for themselves. Science competitions are petering out because parents are too stupid to demand achievement because, G-d forbid, Johnny/Sally might fail. Johnny thinks his ticket to success is the NBA and NFL because he's never been taught statistics and what that says about his odds for coming out on top...presuming he gets no career-ending injury.
So when I hear comments to the effect of computer science "students" do not need math, I'm horrified we are bringing up a generation of intellectually sclerotic brats who will never be competent to go up against the kids China, Taiwan, Korea, Japan, usw, are generating.
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I hold an undergraduate in electrical engineering and
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There's no reason it can't, but won't be efficient. You might as well ask why someone can't learn to herd sheep, operate a loom, and design/predict the next season's clothing fashions. Someone can do all those things, and they're all related, and yet I kind of doubt that someone who learns to predict fashions is also going to be good at herd-- hey waitaminute, maybe they are really are the same-- no, the weaving skills don't fit into this conjecture at all.
Simple Solution (Score:5, Insightful)
Re:Simple Solution (Score:4, Informative)
Um, the prof was saying calculus and continuous math have little to do with CS. Discrete math, etc, is always going to be a big part of CS/algorithms.
Re:Simple Solution (Score:4, Insightful)
Um, the prof was saying calculus and continuous math have little to do with CS.
And he couldn't be more wrong, IMO. Knowing only discrete math, or only continuous math, can be as bad as being blind or deaf; it may arbitrarily limit the abilities of otherwise smart people, resulting in worse solutions, or none at all, to many problems. For example, factorials of large numbers can be approximated much faster using continuous functions. And since calculus pops up everywhere in the real world, anyone doing real world simulation (like graphics and physics) may need it! In fact, I believe one should be familiar with as broad a field of math as possible; for instance, abstract algebra and geometry are both very useful.
Math is very stable knowledge that can be applied to all kinds of problems and may speed up the learning of new concepts. Industry related things usually aren't that stable: It simply makes more sense to learn proper theory and then specialize as needed for the problems at hand. Moreover, teaching such unstable things in universities is borderline idiotic, since they may no longer be relevant after graduation!
Re:Simple Solution (Score:5, Insightful)
Yeah, exactly - CS needs some very specific kinds of math, and instead of organizing the curriculum around it, universities teach a "jack of all trades" mathematical toolkit that's not especially useful.
For example: in order to get my CS degree, I had to take a statistics course that used calculus. However, according to the school curriculum, this statistics course mostly covered continuous, classical statistics - not the discrete, Bayesian statistics which are so incredibly useful in computer science (why do you think your inbox isn't full of spam? Discrete Bayesian statistics). The only reason why we covered Bayesian statistics at all is because the professor was a Bayesian statistician, and he shoe-horned it into the class.
Another example: I had to take the first calculus series, which was comprised of introductory calculus topics; I also had to take the first quarter of the second calculus series, which was advanced calculus. However, I found out from other students who took the rest of the second calculus series that the later courses covered mathematical topics that are ridiculously useful for computer vision and computer graphics - I believe they covered things like convolution and calculating the curl of a vector field.
Basically, computer science uses a lot of discrete math, and a lot of vector/matrix math. Universities don't have a lot of general education courses that teach discrete math or vector/matrix math. This means that CS students have to slog through a lot of continuous mathematics that is, quite frequently, not very useful, and not necessary to learn the discrete stuff - when they could instead be learning mathematics that would be very useful.
Re:Simple Solution (Score:4, Interesting)
For example: in order to get my CS degree, I had to take a statistics course that used calculus.
Given that calculus-based statistics is pretty important to CS (eg, software metrics, big "O" stuff, writing programs that use statistics, etc), how is this relevant to your complaint?
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In my CS degree I took a "Discrete Mathematics" course. There was also a "Linear Algebra" course that covered matrices and vectors. I also took several other mathematics classes that covered calculus, statistics, etc. Basically, courses over the real and complex numbers. Ignoring calculus is basically throwing out almost all of mathematics that has happened since Newton. Any formulas you use will just be the algebraic results of applying calculus to find them. While it's possible to just use mathemati
Everything we do is maths (Score:2)
It's everywhere. Unfortunately, it seems that the overwhelming majority of those who are taught it are almost universally unable to see where it can and should be applied.
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It's everywhere. Unfortunately, it seems that the overwhelming majority of those who are taught it are almost universally unable to see where it can and should be applied.
Perhaps there is some truth to that, but the history of the last 20 years of CS education has suggested that far too much time is spent teaching maths that have virtually no applicability to life beyond degree.
There are computer fields where math education is critical, such as high end graphics, image manipulation, audio codecs, etc. But for the bulk of software engineers, programmers, network techs, sys-admins, and developers higher maths and calculus is totally unnecessary, simply NEVER used in real life
It's not the math ... (Score:3, Funny)
We need some grammar nazis in the admissions offices.
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Or, we need to realize that people arn't perfect, and that peopel like you could benefit from etiquete lessons and probably a dose of Paxil to help take the edge of the OCD.
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You may try to write off this guy as anal. However, if you mix up your grammar on the job, I'll see you as a moron. Therefore, I'll give you the crappy assignments. Sorry, that is just the way it is. How can I trust you with a computer language when you can't even master the one you grew up with?
Re:It's not the math ... (Score:5, Insightful)
Let's eat grandpa!
Grammar: it saves lives.
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I had to help my uncle Jack off a horse.
Re:It's not the math ... (Score:5, Insightful)
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Look at the way we invented the number zero [anl.gov]. There's no ready analog in the natural world. We can point out the first, second, third, ... apples in a row, but not the zeroeth one, and say "that is apple number zero".
It's one reason we don't use roman numerals for math - no zero (they wrote nullus instead) - and w
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There's no ready analog (to zero) in the natural world.
None?
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I read your as half jest, half serious, but on a serious note: I find that good (and great) programmers are also very clear writers in English.
I think there's a strong correlation between the skills needed to decompose a problem, structure a solution, and find appropriate and understandable (to other programmers and one's self later) constructs in order to write a good program and the same skills in making an argument or mastering a complex t
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A space elevator for the moon would only require the same tensile strength as kevlar, and one for Mars would be doable at the limits of current technology if it weren't for Phobos getting in the way every 8 hours..
So the best way to get an Earth space elevator (or anything else) is to get your materials from the moon, fro
linear algebra (Score:2)
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All the schools I've ever been to require students to take calc 1 & 2 in order to get to linear algebra. Plus, you don't typically see series and sequences until calc 3, and those are probably the most useful portion of calculus for programmers. You don't see it until then because they typically want you to have an understanding of what exactly it is that you're doing.
Differential equations is probably not a bad thing to have under the belt either, depending upon what exactly it is that you're wanting t
Re:linear algebra (Score:4, Insightful)
Re:linear algebra (Score:5, Insightful)
There is always going to be the some aspect of CS that's beyond your grasp, no matter what you take.
As someone who just graduated from a 4-year CS program and is about to get an MS in CS, and as someone who is a paid researcher on a major CS research grant, let me say this: CS is much broader than most people think.
Anyone who says that CS is just about the theory of computation has a very narrow view of CS. There's a sort of bullshit 'purity' argument that anything else should be put into another category like programming or computer engineering.
Some topics are easy to categorize. Design methodologies? Software engineering. CPU design? Computer engineering.
But then there are topics that defy classification. Is compiler design a CS topic, or is it CE? It's probably both. Is static verification a CS topic or a SWE topic? Both.
And then there are topics that obviously belong (at least partially) in CS but often have very little to do with computational theory. Computer vision, natural language processing, network theory, and quite a bit more.
If you limit CS to just algorithms and the theory of computation, students get a very limited view of what's out there. I would argue that students should have a good idea of how real computer systems work, how operating systems are designed, how network systems communicate, and how software is designed and built. None of these topics fit neatly and entirely under the "CS" banner, but that doesn't mean that they aren't important and it doesn't mean that there is not legitimate and ongoing research in those fields.
There is no getting away from the fact that most need to be able to write code after graduating from a CS program. Even in the academic community, most positions involve quite a bit of coding. There are a very few positions where academics can focus on the theory all day long. For most projects, though, publishable results depends on producing a working system, and that means writing code.
Some Math is Good (Score:5, Interesting)
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I don't know about calculus but doing formal proofs.
Thank you.
As someone who went through a very "theoretical" CS program at a top 20, I am certain I was forced to spend WAY too much time doing calculus instead of exploring other areas of math. The core tenets of it are very important, but putting everyone through class after class of multi-var blah blah is just a waste of time. Most students didn't get a chance to take analysis or anything that would teach them about WHY the shit works or what the theory or point of it was. We just had to do course after
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(*) The Euler Summation Formula [wikipedia.org] converts a sum into an approximate integral, or an integral into an approximate sum.
oh, this again.... (Score:3)
There is nothing distinguishing about any of the examples noted; nor worth any study. I don't deny that the mathematics::programming link of overstressed.
Seems the problems are more rooted in basic experience. Many arts understand that imitate comes before create; despite the whining of the student/apprentices. While programming isn't quite an Art, its practice is close enough to deserve a different approach from the basic sciences.
Certainly the root of all evil is falling into the buzz-trap where studying and instance of a technology (java, cloud computing, multi-core(wtf?)) takes the place of learning something worthwhile, like planning, design, debugging.
bah, get off my lawn.
CS is mathematics (Score:3)
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Most people wouldn't hire a mechanical engineer to do machine and tool making, or a civil engineer to dig holes, unless he was also so qualified. One alternative is for universities to have separate tracts for applied programmers and students who are more interested in the theoretical end of CS.
Sidetracking a little, I just read a rant (allegedly) from a late Japanese engineer specializing in nuclear facilities who died in 1990s. He complained that the engineers who drew the designs were oblivious to the mistakes the technicians would make on the ground -- loose screws, poorly fitted parts, etc. that would lead to nuclear disasters like the one Japan might be having now.
And I believe this is what would happen if "CS" people simply designed systems and left the implementation to "programmers". And
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So people want CS to be more useful without changing to anything else (like the name), since companies demand CS, even if that's not what best fits their needs.
Split it (Score:2)
Perhaps I went to the wrong university, but my computer science degree was more like a software engineering degree anyway. The vast majority of my teachers were not math prodigies. I actually did both math and computer science and whenever I tried to link the two I got blank stares from my computer science professors, although my math professors could give me wonderful insights even though that wasn't their field of study.
Overall I enjoyed my m
Physics and CS (Score:2)
Physicists think computer science means numerical calculus, since most of theoretical physics is difficult calculus problems. Perhaps this is why there are so many physicists who write unreadable code.
consider the source (Score:3, Insightful)
Here's my opinion (disclaimer: please don't trust my opinion, a random guy on slashdot, either): basically, if you know math, you will use it. You don't need it; you will still find a way to survive in the software world without knowing math, but math will open many doors for you. Would you really want to be shut out from understanding computer graphics, understanding artificial intelligence, and algorithmic complexity? That's just in computers, if you close your mind to math you'll be closing your mind to understanding the way the physical world works, too. You'll be losing the logical/mental discipline that comes from understanding math. Why would you want to give up all that, and try to live as a code monkey?
It's called computer SCIENCE (Score:3, Insightful)
I have seen many outstanding programmers who struggled with calculus and never really got it.
That's because computer science is not programming. You won't find an outstanding computer scientist who doesn't have a solid mathematical background. The theory of computation and the basis for all we do is entirely based in math, and therefore understanding math is essential and inseparable to understanding computer science.
our students are overwhelmingly seeking careers in which they apply computer science.'
If you're looking to be a vocational institution, by all means, drop the math and train your students to be code monkeys. Yes, train, not teach, because teaching them would consist of providing them with a solid mathematical foundation on which to base their careers.
And it's patently false that applications of computer science do not require math. In my field, robotics, I do a lot of programming, but I do just as much theoretical work to understand the algorithms I'm using, and to develop new ones. Linear algebra, statistics, convex optimization.... these are all mathematical topics I use regularly, and I couldn't function without. Cutting topics like these not only take the Science out of CS, but the true value from the education itself.
Math=not patentable. let's keep the math in but... (Score:2)
Different Definitions (Score:5, Insightful)
I have seen many outstanding programmers who struggled with calculus and never really got it.
The summary is not absolutely clear on who makes this statement, but the article attributes it to "a professor". I don't know where this professor works, but the outstanding programmers I know can all do calculus in their sleep. Not all programmers, or even all good programmers, but the outstanding ones. It isn't about continuous versus discrete, which is a complete and utter red herring, but the ability to think abstractly. Hell the best programmer I know is a pure theoretical mathematician: his code is always beautiful, clear, easy to maintain, and, imporantantly, correct; he's prolific to boot. But he's an outstanding programmer. I know plenty of work-a-day programmers who are not outstanding, and whom I would suspect would have problems with integration by parts.
Based in part on my differing experience, I posit that the quoted professor does not work at a high-end institution where really outstanding programmers are likely to be found. This opinion is bolstered by the observation that discrete mathematics (the Z transform, difference equations, discrete Fourier transforms, and the like) and continuous mathematics really are not that different if taught properly. If an individual can't master continuous and discrete mathematics, then they are not going to be an outstanding programmer, because they can't think sufficiently abstractly.
Outstanding programmers can do system architecture, data structure design, algorithmic development. No one who can design and understand a Fibonacci heap is going to have problems with dx/dt.
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I have seen many outstanding programmers who struggled with calculus and never really got it.
The summary is not absolutely clear on who makes this statement, but the article attributes it to "a professor". I don't know where this professor works, but the outstanding programmers I know can all do calculus in their sleep. Not all programmers, or even all good programmers, but the outstanding ones. .
Well if you phrase things like that I can't argue with that because the definition of a great programmer vs a very good one is subjective and you can always shift the goal posts. However I can say without doubt that there are famous and noteworthy programmers that aren't mathematically inclined, and that many of them would be rusty on Calculus even if they were able to do it very well at some point. I don't consider myself outstanding in the sense you describe, but I do know that while Calculus doesn't scar
Being bad at some Math(s) isn't the end... (Score:2)
...but my degree experience (CS at one university and Software Engineering at another) poor Mathematics skills just makes life more difficult. You will just have to accept that you have to work harder than others who are good at it (if only to overcome your dislike). It is also worth noting that there are different branches of Mathematics and being bad at all of them is different to being bad in only area but fine in others. Further, different courses will place different emphasis on Mathematical content (e
Math utility (Score:2)
I know (as even the summary said) this is a religious/contentious topic, but: For both CS and computer engineering, math as a discipline provides several abstract tools in terms of abstraction, modeling, and discipline, as well as actual concrete skills (for algorithmic analysis, estimations and the like).
But the summary mentions continuous math, and I must say most non-CS programmers will only encounter discrete problems. Unfortunately some problems do require floating point or control of continuous proc
I went for artificial intelligence (Score:5, Interesting)
University through AI had me taking computer courses -- which sounded like fun, since I was a computer guy all my life. It would have taken four years before even getting to an AI course, because of all the math courses along the way. I don't care what you say, when I walk through a room, my brain doesn't do any calculus to avoid walking into the desk. It just doesn't. But AI in CS said "calculus is the fastest way to approximate natural path finding".
So I left, and switched to psychology, where AI is called cognitive modelling.
The first day said "the goal is to model things after natural processes, if it takes ten days for the computer program to walk through the room, but it does so naturally, computers will be faster next year."
The third day of the course was to write a neural network in LISP -- oh, and to also learn LISP from scratch -- to solve a real-world decision-making problem. We had two weeks to complete the assignment.
Neural networks are fun, by the way. And ten years later, when I wrote an on-line ticketing program that needed to choose the best way to apply multiple coupons to multiple purchases (in a self-serve kiosk application), brute-force computation did it in 60 seconds, competent programming did it in 10 seconds, pre-computing did it in too much memory for the device, a neural network did it in 50 milliseconds. My client was very happy -- and never knew.
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The problems I tend to encounter that require advanced computer programming haven't found dynamic programming to be useful. Here's why.
Dynamic programming winds up being a mathematical technique to a CS problem. Math techniques are notorious -- in my world -- for requiring clearly bounded problem spaces. Specifically where a complex problem is complex because it has many subproblems. In my business world, a problem is complex because it does not have distinct subproblems (overlapping or otherwise). In
The maths are scary! (Score:3)
I used to think that too, until week before last. I'm a literature major who couldn't make it past second semester calculus. Until week before last I never needed to do any math in programming beyond arithmetic.
Then I landed on a project involving OpenGL. There's a heck of a lot of math there, and a lot of math/graphics jargon. What makes it even more frustrating are all the tutorials for beginners that assume you've majored in math and never bother explaining homogeneous coordinates, frustrums, etc. Almost as annoying as they're assuming you already know the syntax to glsl. I am good at geometry, and could write very complicated POVray models, but OpenGL has been kicking my butt due to my lack of linear maths.
The post seems about Calculus only, not all math (Score:2)
My understanding is that CS is effectively a branch of applied mathematics. Therefore, it's puzzling to me how CS can be taught without any math, which is some people want to advocate. However, it does seem strange that a lot of CS programs require their students to study Calculus, differential equations, and other continuous math subjects. Discrete math is a lot more useful in CS. Calculus should probably be taught only up to differentiation and integration (just one semester) and then followed by discrete
Missing the point (Score:2)
The point of teaching math at all, at least past checkbook arithmetic, is to endow students with the ability to think logically. Those who have an aptitude for science and engineering may find more advanced math such as calculus and linear algebra useful for their careers. However, the vast majority of people will never use more than arithmetic "for math's sake". Still, the hope is that those geometry classes taught them how to think carefully, break a problem down into its constituent parts, and solve i
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Applied software engineering programs (Score:5, Insightful)
I started a Bachelor's in computer science and switched to an applied software engineering program. It's much less math, and the average course is far more useful in the real world. All the employers I've talked to so far have said that they prefer hiring out of the applied program because the students are ready to start working and have a broader range of skills.
As many have already pointed out, computer science != programming.
What we need is more schools that offer applied programming programs for those who want to become programmers and not computer scientists. And more students need to learn the differences between them and which one they want.
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Almost every MIS we've hired has turned out to be an idiot who you can't rely on to do something they haven't been explicitly trained for. I only hire CS degrees or Math degrees. I care that my workers are smart and can learn hard things quickly. I have to pay them more but they're worth it.
So I disagree with you. We don't need more applied programs because we have plenty. The fact that someone goes to school for 4 years to learn programming hilarious. Programming is supposed to be a 1 or 2 semester c
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I wouldn't want to fly in a plane built by an engineer that didn't know physics, and I wouldn't want to run software written by a programmer that didn't know computer science. Both are possible, but tend to end badly.
Computer science as an academic discipline (Score:3)
Dennis Frailey makes a distinction between CS research and applied CS: 'For too long, we have taught computer science as an academic discipline (as though all of our students will go on to get PhDs and then become CS faculty members) even though for most of us, our students are overwhelmingly seeking careers in which they apply computer science.'
I get that the extent of math necessary in computer science is an open question and I won't pretend to have an answer to it, but challenging the presence of math, and the academic approach in general, in a university setting bothers me. Of course computer science ought to be taught as an academic discipline in an academic setting. Who cares if students will use it in their careers? The whole point of a university is to study academic disciplines—maybe you intend to apply them and maybe you don't, but either way they are considered worthy of pursuit for their own sake. And that goes not just for computer science (assuming that's your major) but for math, science, and humanities as well.
If you just want to get a job as a programmer without learning all that theoretical stuff, skip the university altogether and just buy a book, or go study at a technical college. Now, you might have a really hard time getting hired without that bachelor's degree, and that does indeed suck, but that's the fault of the labor economy—it's not fair to ask universities to change their philosophy to accommodate corporate culture.
Ah but you are touching on another debate (Score:3)
Most people are job seekers and college is just a hoop to jump through in that pursuit - I've run into plenty of people without passion for their subject of study; they are there for the job they want (influenced by the pay, stability, and misconceptions of what that job will be to them.)
Industry only ever cares about the bottom line; human resources are just another form of resource with some PR risks attached to it-- but otherwise quite removed from humanity. They pressure universities along with their dr
Math is not applicable ... (Score:2)
In most real-world jobs that I've worked in, it's more about being able to shuffle data from one pile to another efficiently, rather than working the math (which is, at best, uncertain). I say this from the background of having a degree in Drama and yet, I still have a decent job as a programmer doing real work (not as a manager, either).
The major problem with switching to applied computer science is figuring out which technologies or sets of technologies are going to be truly useful going forward. It could
Seems to conflate programming and CS (Score:2)
Unfortunately, there are many disciplines within CS that require a math background. I couldn't imagine approaching a graphics class without having taken Linear Algebra, or a class covering formal languages, state machines, and the like, without having gone through Discrete Mathematics. For that matter, Calculus 1 level stuff occasionally comes in helpful with determining the complexity of algorithms, and networking classes routinely apply intro-level calculus in order to calculate numbers like the most effi
time for IT to drop the need BS or MS for level 1 (Score:2)
time for IT jobs to drop the need BS or MS for level 1 jobs what use Calculus on HELP DESK? Desktop support? or IT ADMIN?
and Most CS Educations are poor for IT work anyways trade schools are much better.
http://www.csmonitor.com/USA/Education/2011/0202/Does-everyone-need-a-college-degree-Maybe-not-says-Harvard-study [csmonitor.com]
http://www.networkworld.com/news/2011/022511-it-graduates.html [networkworld.com]
I find my CS staff never use math... (Score:2)
Keep in mind when old-timers like me were in college, CS was about determining how to best utilize the 640 KB of memory you had available. You needed to understand more math than now.
OTOH, I actually think that multiple languages are a must for programmers these days. I - for one - speak/write German and Spanish. I have seven programmers with CS degrees and an additional six analysts with CIS degrees working for me.
then they're software engineers (Score:5, Insightful)
Software engineering and computer science are two entirely different fields. I don't know why they're combined so often.
Real CS people need more continuous math than ever (Score:3)
CS is more about continuous math than ever.
Until the mid-1980s, computer science was mostly about discrete mathematics. Knuth is heavy on combinatorial and clever integer math. Mathematical logic and proof of correctness were big. I went through Stanford CS for a Masters in the mid-1980s, and and never had any class that required serious number-crunching.
But now it's completely different. Graphics, game programming, machine learning, robotics, control, audio and video processing, and even finance all involve heavy number-crunching. Differential equations come up everywhere. Statistics is far more important, and there have been major developments in the theory of statistics. (Much classic statistics assumes you're limited on compute power; that's why "least squares" methods were so popular once. Now there are better techniques, ones much better at handling outliers.) As a result, AI is working much better than it did during the "expert system" and "AI Winter" eras.
Basic calculus is not advanced math. Calculus is just what gets you to entry level so you can learn real math. Real people use this stuff. Last year I took a course at Hacker Dojo on machine learning, taught by a quant from Blackstone Capital using the Stanford course materials. They assumed everyone had a thorough knowledge of calculus. I'm not a "math person", nor an academic, but that's the price of staying active in this industry.
If you just want an "IT" degree, you may not need much math. The math parts will be bought with the package you install and administer. But in that case, you're probably better off getting a degree in business administration with some extra IT courses.
Crappy code is the undoing of Computer Science (Score:3)
I don't know if developing math skills helps with what is mostly a craft such as programming, but I think that encouraging an anti-intellectual atmosphere in the programming community will only lead to an even greater abundance of insultingly crappy code that consumes more effort and causes more frustration than any other factor in the industry.
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I would submit the math requirements are common in the core requirements of any Bachelor of Sciences degree, rather than specific to a Computer Science major.
If you don't want to master basic college-level math to earn a sciences degree, then perhaps you should be lobbying academics to offer a Bachelor of Arts with a Applications Development major instead.
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I guess this is what I'm talking about. I have a B.Sc, I got it years ago, and here you are with your snarky response, judging me, as if I'm too stupid for the math (yes, it's implied with what you said). It's not that I can't learn it, as obviously I did, it's that it wasn't useful. But I guess if it helps validate people like you, it will never change, since it's a big circle-jerk in acadamia.
Less math limits job opportunities (Score:3)
I don't get why I had to learn all the math in university. I agree some math is useful, but I have never in my 10 years working applied any of the advanced stuff, nor found learning it helpful.
And some other grad from your class will tell a completely different story. My first job was pure tech, embedded kernel software. My second job was molecular modeling. If I did not have the math (which I too never expected to use) I would not have been qualified for that job. Also, later when I went to business school I used more advanced math in marketing classes than I ever did in computer science (again, I never expected this).
So basically the CS program is preparing your for more advanced jobs, a wid
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1. Undergrad comp sci is for the fundamentals of comp sci, not the latest marketing buzzwords like "cloud computing";
There is a lot of fundamentals in distributed systems/algorithms/computing. And as far as I understand it, it doesn't depend on any established branch of "mathematics".
Sure, you can always find courses on "cloud computing" that teaches you how to create Amazon EC2 instances, call remote APIs and so on, but there is a lot of difficult things in there, which, I presume from your maths background, probably didn't appreciate.
Nah, you weren't the worst (Score:2)
Is any discussion ever on topic? (Score:4, Insightful)
Computer Science != Being a Programmer (Score:4, Insightful)
I think the distinction between pure "research grade" CS and applied "I want to get a job in the real world" CS is the important thing.
For too long it has seemed as though if you like computers then you should aspire to a CS degree. But as everyone finds out, the stuff you learn in a real in-depth CS program is often not applicable to much in the world of interesting application development. The stuff that IS could just as easily be taught in a more applied way without all the math.
We're supposed to be leveraging "re-use" and not re-inventing algorithms every time, so people should be able to use a library of algorithm objects (or whatever) for pretty much ALL applied programming, at which point all you have to understand is the trade-offs between different available choices and what they do but not necessarily how they do it or especially how to invent a better one.
I think of "real" CS as what you find in Knuth. If you want to publish papers on combinatorial algorithms then you probably want at least a master's in math before you even get started with the computer stuff. You will then aspire to getting a job as a CS professor, or possibly working in a corporate sponsored lab for IBM or maybe Google. But the things this type of scientist does may not be the kinds of things that actually got people excited about computing to begin with.
If what you really want to do is to build cool applications and Change The World(tm) then honestly hardly ANY math is needed, and while more knowledge and a better understanding of the fundamentals of what's going on will always make you better, there might be more effective and efficient things to expend your effort on, especially in cross-discipline areas that interest you and which you would like to work in.
Pure CS is really just pure math, and there are a limited number of applications (and jobs) in such a thing. What really makes computers interesting is their applications, so instead of CS, why not learn applied programming plus an application domain like Biology, Finance, etc. Ask yourself "what problems do I want to solve?" and if computing is going to be a tool to that end and not just an end unto itself, then a pure CS degree is probably a waste of effort.
G.
Re:Computer Science != Being a Programmer (Score:4, Interesting)