Slashdot Mirror
CS Profs Debate Role of Math In CS Education
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?"
And, for that matter, do you want to learn in the classroom, or in industry?
The World Wide Web is dying. Soon, we shall have only the Internet.
If you don't want math with your computer science, learn computers / networks / shiny jargon at a trade school
I don't know about calculus but doing formal proofs help me in learning programming because they are, in essence, the same thing. In a formal proof, you break down a problem into simple steps and state the authority for each. It is similar to programming. So some math is good.
Don't stop where the ink does.
Before everybody jumps all over him for being wrong and off-topic and all that, I'm going to agree with him. As working programmers, not necessarily CS professors, we manipulate language(s) for living, both formal languages for programs, and natural language for (ick!) documentation and communicating with others on projects. These languages, formal and informal, have both syntactic requirements and expressive requirements. A statement (or function) may compile cleanly and yet read as complete gibberish to a human trying to understand what this piece of code actually does; similarly, an e-mail may read as though it says something useful, yet impart no actual information. We all see examples of these phenomena every day when we write code for a living.
No folly is more costly than the folly of intolerant idealism. - Winston Churchill
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.
Put my fist through my alarm clock with its ding-dong death inside my ear. - The Blackjacks.
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.
Let's eat, grandpa!
Let's eat grandpa!
Grammar: it saves lives.
To the haters: You can't win. If you mod me down, I shall become more powerful than you could possibly imagine
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.
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.
Software engineering and computer science are two entirely different fields. I don't know why they're combined so often.
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.