I had to take 2 semesters of calculus to get my Business Degree in MIS. I have worked 5 years and never used it. I never use Calculus, Geomerty, or Trig on the job. The only math I use at work is basic Algebra and arithmetic. I expect the same can be said of a lot of professions (Computer Scientist, Biologist, Economist,…). Why then, do so many of these college majors require Calculus?
It’s interesting that you cite those three majors: Comp. Sci, Biology, and Economics. From personal experience I can point out that calculus is extremely useful in both Computer Science and especially Economics (don’t know about biology, though). In Economics calculus is used to evaluate statistics and extrapolate data which would otherwise be completely opaque to the observer; calculus is VERY useful for advanced statistics and probability. Computer Science requires knowledge of calculus because both Microelectronic Engineering (the design of computer chips) and Electrical Engineering are calculus intensive, and it wouldn’t make sense to isolate Comp Sci from its brethren. Many programmers are also required to design applications that perform complex mathematical operations, for which knowledge of calc. would be an obvious advantage.
Many majors require it because calculus is an ingenious way of understanding the world around us, even if it isn’t “practical” in your life routine. Many engineers never use anything more advanced than Calculus I on a day to day basis, but that doesn’t mean they should be ignorant of Differential Equations.
In Business, where numbers and statistics are prevelant, calculus could be a very formidable tool for some people.
While I would say calculus would be important to the Computer Scientist, that’s not what most people who get their comp sci degrees go on to become. Like me, they go on to become programmers. From my own experiences, learning calculus was not time well spent. I’ve forgotten almost all of it now, simply because I’ve never had call to use it.
In some areas, you would wind up using it (if you were given a job that had a lot of math in it). The problem is that “computer programming” is another one of those terms that is too all-encompassing. There are really quite a few domains of work that programmers could wind up in. It’s like getting a degree in “science”.
I realize I’m not in that class of programmer that would need calculus - and I feel fine and dandy that I’m not.
I think Calc is almost becoming like Latin. It’s a holdover of a classic liberal arts/science education from the olden times, but is not very relevant in the modern, professional work world. I think Calc is mainly used by PhD’s doing research/teaching, and simply is not used much by the rest of us with Bachelor degrees.
Sure, but do we want to pass Calculus along as “something for smarter people than us to do”?
I would disagree with likening Calc to Latin. Calculus is more important than ever in the technology that surrounds us. If you don’t feel that calculus was time well spent, then hey, who am I to argue? It wasn’t exactly a rockin’ time for me either. But if we’re talking about certification in a specific field, such as computer science, then certain requirements are made. I would agree that dividing comp sci into different fields might clear things up, such as a non-calc version called “Application Engineering.” Or something.
What I’m fighting here is the loss of an intellectual commodity. If no one sees the value of calc, it will get lost and forgotten(the ole’ use it or lose it axiom). Don’t trust our thinking to the “PhD’s.” They’re normal people like you and me.
The same argument could be (and has been) made for Latin being very relevant. Latin can be key to the understanding of language and figuring out words and phrases that you don’t already know. And who doesn’t need to be skilled in language?
You have to draw a line somewhere (especially when other people are telling you which classes you have to pay them to teach you). Of course, everybody has their own idea of which ones are the “important” classes. That’s why it takes so long to get a technical degree (or others - I’m just more familiar with the technical ones).
Calculus is right at the treshold of advanced mathematics, and I think it’s a good thing it’s taught in college; it’s not the formulas you’re gonna remember, but the method, and that kind of mental discipline and problem-solving is going to help you throughout any profession.
I took graduate particle physics classes, and I can tell you, as a result, no programming problem scares me.
The underlying mathmatical basis of just about any technical discipline you can name relies on calculus. (Yes, including biology. There are many, many biological processes which are best described using differential equations.) The OP mentioned that he only uses algebra and arithmetic at work. Well, I would be willing to bet that many of the algebraic formulas he uses were derived by using calculus.
Here’s an example. What’s the area of a circle which has a radius R? Simple: PIR^2. But how do we know its PIR^2? Trial and error? No. It is derived using calculus. The area of a circle is rdrd(theta) integrated over all angles from theta = 0 to 2PI and all radiuses from r=0 to r=R. When you solve the integral, you come up with the familiar formula PIR^2.
But here’s the thing. These days, most of the calculus has already been done for you. As a mechanical engineer, if I want to know the stress in a loaded beam, I can just look up the algebraic formula in a book. I don’t really NEED to know the calculus behind the formula; I can get by without it. But all I’d be doing is getting by. If there was a loading condition that wasn’t in the book, I’d be screwed. But since I know the calculus, I can set up the integral and solve for the stress (and make my boss happy).
Without knowing calculus, I wouldn’t really have any insight into why the formulas are the way they are, or why certain things behave the way they do. I’d just be blindly plugging numbers into formulas, and I’d be a pretty lousy engineer. And I think that’s true in any technical field.
Another (non-engineering) example: suppose you have an algebraic formula for determining something, like say the projected profits of your company for the next fiscal year. But some of the inputs into the formula aren’t numbers you know exactly - they’re guesses which are within a certain margin of error. Now your boss wants to know what the impact of the margin of error on the projected profits is due to the margin of error on each of the inputs. How do you analyze the formula to find out? (Here’s a hint - you use a certain branch of mathematics that starts with the letter C).
And, hey, Mr. Non-Calculus-Using Computer Programmer. I’d like you to write me a 3-D computer basketball game. And I’d like the basketball to behave just like it does in the real world. But you can’t use calculus. Good luck!
So you think calculus is holdover from the quaint olden days, which nobody uses anymore, just like Latin? Sheesh!
“For what a man had rather were true, he more readily believes” - Francis Bacon
I guess I must be “Mr. Non-Calculus-Using Computer Programmer” Fine, I embrace the title.
Didn’t you read my original post? I wouldn’t be doing work like that.
[list=a][li]It doesn’t interest me[/li][li]I have far more (good paying) work than I have time for already[/list=a][/li]
That’s why I posted about computer programming being such a huge field. Plenty of the areas never touch calculus. Might as well ask me to wire up a circuit board for you. It’s not difficult if you know how to do it, it’s just not what I do!
Kind of like telling my mom she needs to know calculus because she’s going into “medicine” and it’s so very important to the field of medicine. Well, that may be true, but my mom is a nurse. What she did need to know where general techniques for chemical calculations. While just about every type of math or equation can be related to calculus, it was nothing near what was called “calculus” at my university.
There are plenty of fields where it’s just baggage.
I already knew how to program before taking calculus. I took two semesters of it (Engineering Calc I and II), and I must say it’s given me squat “insight” into anything useful. Most of my classmates that went into the same lines of work agree.
Oh yeah, I just wanted to make sure this point got through:
That’s exactly what I’m not saying. I’m saying calculus is used by some people, just as Latin is (see my previous post about that)! But some people don’t. And they have no need to!
My degree’s in chemistry; 15 credit hours of calculus* were required.
I have since used every bit of it; not necessarily “on the job”, but in other, later classes which covered material which I do use on the job.
I guess that we could have treated that as a black box: “Here’s the equation; don’t worry about where it came from, it works… most of the time.” But that doesn’t really help you predict times when it won’t work, or understand what’s wrong when it doesn’t, or how to fix it.
I personally think that calculus serves another purpose: for many people it’s the first subject they’ve ever had which is truly difficult in several different ways. For majors where it’s required, the skills required to pass calc are often quite similar to those required to pass the more advanced courses which are actually part of the major discipline… but calc happens a lot sooner.
It’s better all the way around if you find out early on that a particular subject is just not for you, while you can switch majors without losing several semesters worth of classwork in the process.
Okay, so it’s harsh, but: if you can’t pass calc, your chances in physical chemistry are pretty dismal… and you won’t find that out until you’re a junior or senior, by which time you’ll have accumulated 30 or so now-useless-except-as-electives credit hours.
(Okay, so maybe you’ll wind up getting a job where you use some of what you learned in those classes; they still don’t help with the immediate goal, which is to get a degree.) You’ll probably know whether you can pass calc or not by the end of your freshman year, or early in your sophomore year at worst.
- The 15 hours were divided 3 classes of 5 credit hours each. Actually, probably at least 2 credits out of the total were spent on analytic geometry instead, but the college didn’t divide it out into a separate class. I agree that analytic geometry is probably less than useful to, say, an economy major.
Sorry, SadisticWeasel. I wasn’t responding specifically to you. That comment was in response to curious george, who implied that calculus was an outdated thing used by PhD’s and academics, but irrelevent in the real world. As a BSME who uses calculus all the time, I got a bit of a chuckle out of that.
By the way, just out of curiousity, what kind of programming you do, which has never required you to use calculus?
“For what a man had rather were true, he more readily believes” - Francis Bacon
A lot of user-interface stuff. Making applications easy to use and (hopefully) intuitive. Though I have done a lot of the behind the scenes work like:
[ul][li]managing database connection and data transfer[/li][li]sending/processing messages over a network[/li][li]modelling a system of real-world objects with software representation, allowing the user to simulate a possible configuration of these real-world objects[/ul][/li]
Calculus does figure into some of the complete packages that we deliver. One example would be the module that forecasts water flow and demand patterns for a water utility. But that module is developed by someone whose primary training is in the field of mathematics and physics.
I take care of my areas of work and just get the data I need to display from the other modules. It’s a lot more efficient use of time to get people to specialize in the different areas. Of course, there are some programs that don’t require anything from calculus at all (a word processor springs to mind).
Computer programming is a huge industry these days. Calling someone a programmer is really is comparable to calling someone a “scientist”.
What I got out of college and classes like calc. is that if you make it, you prove to the world that you can be trained.
True. But unfortunately it doesn’t really say anything about the most question of work in the real world: Can you train yourself?
That is a good point. I saw many 4.0 students in college that were dumb as rocks. There is a long bridge between book smarts and street smarts.
ed, Mark, et al have pretty well covered why calculus is useful. I can’t say I didn’t have to fight the good fight to get all the way through it, and I probably have not actually done any calculus w/paper & pencil in 15 years & would need a little time and a calc book to do so now. But I never would have comprehended physics w/o it. And I still use it at least a few times every week - the software does the work now, so I can forget my trig functions; but you still have to understand what the software is doing to set the problems up correctly.
But I think it’s required in many curricula because the degree paths offered are general and meant to equip you to pursue the many different paths one field can offer. It would probably be difficult and counter productive for the schools to try and break down the various programs to reflect the specialization that characterizes the different fields.
I don’t do it myself every day, but I’m glad I took it.
I took Latin, too.
You weren’t addressing me, but I would point out that after 18 1/2 years in programming, I only know a handful of programmers who have even studied calculus (I’m not one of them) and I rarely even use algebra. As SadisticWeasel pointed out, it is a huge industry. Analyzing the business of a customer and developing ways for him/her to market product, accept orders, ship product, create invoices, track receivables, and then analyze all those actions from a marketing perspctive does not generally require higher math.
I am not arguing that calculus is not useful. If my high school math grades had been better, I’d have taken calc and would now enjoy articles on physics, biology, and astronomy even more than I do. Since I got out of college, I have gone back to take some remedial math, but I haven’t gotten to calc, yet. On the other hand, a business application programmer rarely runs into calculus on a daily basis (unless he/she is maintaining inventory forecasting).
As this thread illustrates, computer science/programming seems to attract people with two different sets of skills: the mathematically inclined, and those with strong verbal/logical aptitudes. Every programmer I’ve ever discussed this with has identified themselves primarily with one camp or the other, although of course they all had ample skills in both areas.
I count myself among the latter group, but for those in the former – who approach the subject from a mathematical orientation – a fondness for calculus and a conviction of its essential utility should hardly be surprising. And in physics and many types of engineering, it is obviously of critical importance.
But in my twenty-two year programming career – emphasizing systems and real-time software design and development, chiefly in the aerospace and digital communications arenas – there’s never been even the remotest call for anything more complicated than grade school algebra! This was true even during my stretch at NASA working with the flight dynamics and simulation groups, where one might expect a thorough knowledge of calculus to be mandatory (it wasn’t even useful).
Obviously, the aerodynamic engineers and scientists had to be fluent in higher mathematics. But an important part of their jobs was to translate abstruse aerodynamic equations into a set of discrete software design requirements. From this stage onward, calculus was entirely irrelevant.
In all my years in this business, not only have I never needed calc or other higher math, but neither has any programmer or designer I’ve ever worked with (to the best of my knowledge, of course). So I reverse Mark Mal’s question and return it to him: what kind of weird programming tasks have you done that actually required calculus? I’m genuinely puzzled.
Finally, returning to the original topic, I too want to voice my complaints about the calculus and higher mathematics requirements, at least for a Computer Science degree. I’m convinced that they’re an obsolete holdover from the ancient days when one couldn’t conceive of using a computer for anything but number crunching and calculating firing trajectories. In my day, all of the purported C.S. courses were taught under the auspices of the mathematics department, and thus the curriculum and course requirements were mandated by mathematicians. It is probably for this reason alone that calc has been and remains a prerequisite for graduation. But except perhaps for a tiny minority of specialists, calculus is utterly and completely useless to professional programmers and software engineers. It should be an optional course.
(sorry about the double spaced paragraphs!)