Why do so many college majors require Calculus?

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?

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.

Well, mostly.

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: PI*R^2. But how do we know its PI*R^2? Trial and error? No. It is derived using calculus. The area of a circle is r*dr*d(theta) integrated over all angles from theta = 0 to 2*PI and all radiuses from r=0 to r=R. When you solve the integral, you come up with the familiar formula PI*R^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!


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"For what a man had rather were true, he more readily believes" - Francis Bacon

Mark Mal>

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][*]It doesn't interest me[*]I have far more (good paying) work than I have time for already[/list=a]

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:

So you think calculus is holdover from the quaint olden days, which nobody uses anymore, just like Latin? Sheesh!

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.

Oh yeah, I just wanted to make sure this point got through:

quote:

So you think calculus is holdover from the quaint olden days, which nobody uses anymore, just like Latin? Sheesh!


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!

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?


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"For what a man had rather were true, he more readily believes" - Francis Bacon

By the way, just out of curiousity, what kind of programming you do, which has never required you to use calculus?

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:

• managing database connection and data transfer
• sending/processing messages over a network
• modelling a system of real-world objects with software representation, allowing the user to simulate a possible configuration of these real-world objects

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.

Buck>

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.

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.

Mark Mal: By the way, just out of curiousity, what kind of programming you do, which has never required you to use calculus?

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).

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Tom~

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!)

I have absolutely no math skills. I never even took algebra in highschool. Thus, when I approached the local college, the woman took one look at my transcript and laughed. Can't get in unless you've had it.

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When life hands you lemons, throw them at somebody.

Yeah, but I think most are in agreement that algebra is the base level of knowledge you do need. It really is something you should learn in high school.

There are plenty of fields where it's just baggage.

Please don't say this about mathematics.

I agree, the mathematical theories and formulas have no use in everyday life. But, as Elijah says, it's not the formulas that are important, it's the method.

Mathematics disciplines and organizes your mind. It puts every value in solid black and white. I know in the real world nothing is truly set in black and white, but it helps one's judgment if certain values are more firmly placed.


For an example I'll use a mugging. You get mugged. What are the values in balance here? A) The mugger wants your money. B)You want your money. A.1) The mugger threatens your life. B.1) You want your life, and perhaps very reasonably consider your life more valuable than your money at hand. A.2) The mugger wants the least risk in getting your money. B.2) You will take every action not to give the mugger your money.

My point is, the more solidly your values are placed, the better judgment you can make. For instance, you can see in the mugger that he is nervous. You can capitalize on this by saying, "Dude, I just got mugged 10 minutes ago!" And as the mugger tries to contemplate this in his fury of thought, punch him in the face. On the other hand, if you see true intent to kill, then gladly fork over the wallet.

Perhaps this isn't a good example. I can't think of a better, or more concise, one now.

Mathematics has helped me to think laterally. Mathematics is not a science, but a philosophy. All humans think logically. I have no basis for this hypothesis, but in my experience it is true. When people are wrong, it's mostly because their postulates are wrong. It's rarely logic, although I've met some pretty circular people. But in my experience, most people will not disagree when it comes to logic. They will disagree on values and postulates, but not logic.

I don't remember much of the formulas or theories of math. But I do have to say that I will never forget the methods, or algorithms. Logical thought has benefitted me greatly.




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¾È ³ç, ÁÖ µ¿ ÀÏ

Me:

There are plenty of fields where it's just baggage.

Beeruser:

Please don't say this about mathematics.

I didn't say it about mathematics, I said it about calculus. Apparently, calculus didn't help you with those reading comprehension skills. Sorry, I couldn't resist.

Anyhow, I don't believe it was mathematics that taught me the critical thinking you've tried to illustrate. I credit that to literature, of all things. Art and music have been shown to have a great influence on "intelligence", also. Yet where are these subjects in our grade schools and colleges? Oh yes, they've been cut, cut and cut a little more.

I remember the movie "Dead Poets Society."

Robin Williams says something to the effect of: Science and mathematics and engineering are things we need to live. Literature, art, and music, these are the things we live for.

The arts shouldn't forcibly be taught. This is the good stuff. To really appreciate art, one has to seek it on his/her own.

Higher level mathematics has a certain beauty and elegance. It really has nothing to do with the real world. It can be considered an art from this standpoint.

And it looks like I've contradicted myself. If calculus is "higher mathematics," then maybe it shouldn't really be pushed so hard in college. Only those who really want to learn it can appreciate it fully.



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¾È ³ç, ÁÖ µ¿ ÀÏ

Beeruser>

This had always been my view of art. I didn't really think it should be taught alongside "real" subjects (i.e. science).

But the more research that's coming out about the effects of art and music instruction, the more I stop believing that.

After all, look at how immersed in art and music the society was from which calculus sprung forth...

calculus can come in handy if you're a cartoonist. . .
http://www.csun.edu/~hcmth014/comics/ca20.jpg

Okay now I have to get off the internet and take my linear algebra final. Once I'm done with that course and my grades are in, I'll start a thread about what on earth we need to know Linear Algebra for

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"I'm just too much for human existence -- I should be animated."
--Wayne Knight

I think the reason for requiring calculus in many fields where practically it will never be used, is the same reason that I (as a chemist turned biophysicist) had to take 4 semesters of French. I certainly never use it. I never plan on going to France; and, even if I did, it probably wouldn't be job related. So why was I required to take it?

I think the answer lies in the fact that a University or college is supposed to each you more than just a trade. If they just locked you up in a room for 4 years and taught you only the things you needed to succeed in your particular little niche, then you would be a skilled laborer and not an "educated" person.

Not that there is anything wrong with skilled labor, but I think you get my point. N'est pas?

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"If you stick your finger in a pie, whatever is in the pie will be on your finger, and whatever is on your finger will be in the pie...unless you wear a rubber glove"----some demented old lady

I have two problems with this.
[list=a][*]If they stuck to your "trade", it wouldn't take 4 (or 5 as is increasingly becoming the trend) years. It would be more like 1 or 2.[*]It doesn't work. I've seen far too many college graduates to think "education" is a result of college. I think that kind of thing is really determined sometime in elementary school. I think most people that go into college as "educated" will come out as "educated". Others will go in as dullards and come out as dullards. Being forced to take a class does not make it education. In fact, it usually has the opposite effect. When people take the incentive to seek learning on their own - that is when they get "education."[/list=a]

Personally, I think that the main reason for having to learn calc in college is as was stated earlier, the university is attempting to create people with a rounded education. The university doesn't know if the Comp Sci person is going to be programming an ATM or if the person is going to be writing software to chart Wall Street economic trends, nor should they, the BS in CS should be a generalized degree, designed to put out someone who can write code for any situation as needed. And for that attitude, one can see the need for Calc, as well as for many other educations. With regards to people who feel that the university should know what sort of programs that the student will be writing, so that the student can specialize early, all I can say is that is a trend I deeply hope will soon reverse.

"A human being should be able to change a diaper, plan an invasion, butcher a hog, conn a ship, design a building, write a sonnet, balance accounts, build a wall, set a bone, comfort the dying, take orders, give orders, cooperate, act alone, solve equations, analyze a new problem, pitch manure, program a computer, cook a tasty meal, fight efficiently, die gallantly. Specialization is for insects." --R.A. Heinlein

Something I've always believed.

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>>while contemplating the navel of the universe, I wondered, is it an innie or outie?<<

---The dragon observes

I took four semesters of calculus in high school and college, and never used it, and never plan to. Then again, I *did* switch out of sciences into creative arts...

Narille>

One can think of a plethora of classes that a student "should" take to get a "rounded" education. Two that aren't required right now would be physics and chemistry. I'm sure I could think of more if need be.

But the basic point is, you can keep loading up more and more stuff ad nauseaum. Unfortunately, you don't get the lofty goal of a rounded education. Instead, you dilute all these classes by not prioritizing them.

I also find your idea of a "rounded" education interesting. By taking calculus in technical degree tracts, these students become more "rounded". I would have thought it arts and music would have much more of a rounding effect on these people. Instead, you're just throwing more technical information at them.

As per your Heinlein quote, I think it's complete BS. I can either excel in a few fields, or attain mediocrity on a broad scale. I'll choose excellence.

Sadistic>

I vote we should attain mediocrity on a broad scale, and excel in a few fields. We shouldn't limit ourselves to one or the other.

Now that I think of it, that's what college is for.



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¾È ³ç, ÁÖ µ¿ ÀÏ

Bravo! beeruser.

Ya know, it seems somewhat ironic to me that there is such a reluctance to acknowledge the importance of a well rounded education in this particular forum.

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"If you stick your finger in a pie, whatever is in the pie will be on your finger, and whatever is on your finger will be in the pie...unless you wear a rubber glove"----some demented old lady

Ya know, it seems somewhat ironic to me that there is such a reluctance to acknowledge the importance of a well rounded education in this particular forum.

I think not. My disagreement is in what exactly constitutes this well-rounded education and whether or not it's the university's right to force me to pay them to take certain classes.

My other main point was that self-education holds a great deal more value when it comes to this. I just don't feel that force feeding of "culture" to everyone who passes through a college's doors is right. Most will just cram and learn the mechanics of the class, not the meaning. And those who learn the meaning would (according to my theory) have sought out the knowledge on their own. It's that old "leading a horse to water" chestnut.

I'm a software engineer who studied greek and latin in college... and I have to say, the greek and latin have been more useful to me than calculus. I've been coding for 10 years now, and have NEVER used anything more complicated than algebra. I write mostly stuff involving OS Internals right now... file system & backup type stuff.

When it comes right down to it, I think the bulk of what's taught in ANY degree program is filler. Look at the number of non-degree related classes you have to take to get any degree... it's HUGE! Imagine if you actually spent four years in college learning your trade! We'd actually see programmers coming right out of college who knew how to code. As it is, most places I've worked know that if you hire right out of school, you have to spend the first few months showing them how to work in the real world.

I found out that up until recently the local university (a BIG school, well known) taught the first year or two of programming courses in Pascal. Completely useless, in my opinion. Yes, it teaches basic programming concepts, but the only reason to stay with Pascal that I can think of is that the university didn't want to pay their professors to develop a curriculum in C. And, of course, first year students don't know any better, so no one complained.

OK, I'll stop my rant now. I just wish that universities taught actual real-world skills every once in a while.

Obviously Sadistic, I disagree with you. I'd rather excell in one or two areas and know many more. You see the quote is not saying that you should choose mediocrity over excellence, rather that you should choose a wide range of subjects over a narrow one. It can be argued that Heinlein was promoting the Reneasance(sp) man ideal, and noting that the greatest intellectuals were not limited to one subject, Aristotle, Plato, Leonardo, Euler, Openhiemer, Feynmann all had wide ranging interests. One can take great satisfaction in life when one can understand Shakespeare in context, notice historical parallels, appreciate art, comprehend physics, and program well.

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>>while contemplating the navel of the universe, I wondered, is it an innie or outie?<<

---The dragon observes

Squid: you were required to take four semesters of _French_ for a chemistry degree? That's bizarre. Or was it just a "four semesters of a single foreign language" requirement, and you happened to choose French?

Athena: Pascal was designed as a teaching language; I suspect Wirth is as astonished as anyone that some people actually try to use it for real work.

Calculus is how we describe the physical universe through mathematics. Just because you took chemistry or physics and never saw a differential equation, don't assume it wasn't there. It was just solved for you. Until Newton came along with calculus, physics was essentially a bunch of empirical knowledge picked up as man went along. By using calculus to describe what we already knew, Newton was able to predict things that were then discovered to be true later !

If you're going to engage in product design, you have to deal with calculus. The area of any planar surface and the volume of any solid can be calculated using calculus; not just the conveniently shaped ones that have formulas in a handbook. Also, the mathematics underlying any type of computer modeling (weather forecasting, stress analysis, automobile/aircraft performance, etc) are all derived using calculus.

I'm sure there are plenty of Computer Science majors who couldn't solve a differential equation a to save their lives, even though they had 2-3 semesters in college. That's fine. However, consider that you may have become the equivalent of a car mechanic. You can fix the problem, but you may not know why it occured, or why the fix worked.

For business majors who don't want to study calculus, OK with me. You're now at the mercy of the mathematicians who wrote your security analysis programs using calculus. (Before any of the programmers flame me, remember, if YOU don't know calculus, you're just doing what a mathematician/engineer is telling you to do.)

And speaking personally, I wouldn't mind one bit if even less people studied calculus. That will only result in more demand and higher pay for my already and increasingly rarer skills.

Torq-

You're right. I wasn't specifically required to take French. Everyone in the college of LAS at the University of Illinois(with a few exceptions) is required to take 4 semesters of a foreign language, or, show the equivalent knowlege of. But that really emphasizes my point. It didn't matter what language, just that you were exposed to some other language. The point of taking a foreign language is to help you think outside your normal "box". Thinking of concepts in the constraints of language is, well...constraining. The same is true of calculus. Apart from the practical application of calculus, learning it causes you to think in ways you may not normally do. You may never use calculus, but I'll bet you use the critical thinking methods you developed learning it. There are certainly other disciplines that utilize this way of problem solving, but calculus is the instument most universities use to (some might argue forced) get you to learn it.


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"If you stick your finger in a pie, whatever is in the pie will be on your finger, and whatever is on your finger will be in the pie...unless you wear a rubber glove"----some demented old lady

Bobber: Your arguments are flawed and miss the point...

Calculus is how we describe the physical universe through mathematics...

So what? This thread is not a forum on the value of calculus to physics or science or even to the world at large, it is about whether it is a legitimate graduation requirement for curricula like business or computer science. It would be absurd and highly insulting if you're implying that ignorance of calculus makes one ignorant.

If you're going to engage in product design, you have to deal with calculus. The area of any planar surface and the volume of any solid can be calculated using calculus...

Do you actually think that the planar surface or volume of a solid is of critical importance to your average product designer? That's a matter for mechanical and manufacturing engineers (and as I said earlier, the utility of calculus for such fields is not in question). Most product designers are probably much more interested in features and styling and whether the market demands that it can be fitted nasally when desired.

Also, the mathematics underlying any type of computer modeling (weather forecasting, stress analysis, automobile/aircraft performance, etc) are all derived using calculus.

This is a mere truism. All this amounts to is that knowledge of calculus is required for tasks that require a knowledge of calculus.

Please see my earlier discussion of my experiences with an aerodynamics group at NASA. These people spent their entire careers learning their craft. If I wanted to be able to apply my knowledge of calculus to their field, I would have to become an aerodynamicist! Otherwise, they would be as justifiably insulted by any attempts on my part to tell them their business as I would be if they tried to teach me mine.

I'm sure there are plenty of Computer Science majors who couldn't solve a differential equation a to save their lives, even though they had 2-3 semesters in college.

That's precisely my point. People don't retain what they don't use or need. I contend that only a tiny minority of computer science majors have ever needed to solve a differential equation in the course of their work. Just like only a tiny minority of them would ever need to use quantum optics to calculate the spatial resolution of x-ray crystallography measurements. Does the fact that some comp-sci major somewhere might need to do this mean we should all be required to learn advanced physics?

... However, consider that you may have become the equivalent of a car mechanic. You can fix the problem, but you may not know why it occurred, or why the fix worked.

I'll assume you meant no offense to auto mechanics; otherwise, this statement would be damned offensive, Bobber. Surely any competent auto mechanic can isolate and correct a problem -- and know full well why it worked -- even without ever hearing of Newton or Leibnitz, not to mention the calculus. Don't be so elitist.

And you know what? I can isolate and correct a software bug and know full well why the solution worked completely without recourse to my knowledge of semiconductor electronics, let alone my (long unused) knowledge of calculus.

Does a painter need to know the calculus describing the physics of optics in order to create a masterpiece? If they don't know calculus, does that reduce him or her to the equivalent of a "paint mechanic"?

Just because calculus can be construed to underlay a certain technical aspect of a field, it certainly doesn't follow that one cannot excel in that field without a command of calculus! Just as it doesn't follow that just because computer software can be applied to mathematical problems one must be a mathematician before one can excel at the design and development of software systems.

For business majors who don't want to study calculus, OK with me. You're now at the mercy of the mathematicians who wrote your security analysis programs using calculus.

This is almost too silly to rebut. Now you're implying that you can't be successful in business without being a mathematician who writes security analysis programs? Oh, please!

(Before any of the programmers flame me, remember, if YOU don't know calculus, you're just doing what a mathematician/engineer is telling you to do.)

You arrogantly imply a false hierarchy, with mathematicians and "engineers" lording it over us poor dumb software coolies by possessing the Secret Knowledge of The Calculus. Such a biased perspective!

First, I do know calculus; it's just that in over twenty years I've never had even the remotest call for it. Second, I am an engineer: a software engineer. My job is to design and develop software systems and subsystems that solve a context-specific set of problems in an arbitrary domain. Believe me, this is hard enough without also being required to be fluent in every field of knowledge that intersects with any problem domain!

Second, if you insist on a hierarchy, it's the mathematicians who often dance to the tune of the engineers. For example, at NASA the mathematicians didn't lead projects, and very few of them were needed. Their role was to assist mechanical, aerodynamic, structural and even software engineers in analysis or finding a shortcut or alternative approach on those rare occasions when one was needed for a specific problem. In short, their position might be seen as the reverse of what you suggest: it could be reasonably maintained that the mathematicians answered to the programmers and engineers.

But in fact no such hierarchy exists. I don't know what kind of work experiences you've had, but they must have involved awfully small projects. Everywhere I've worked, the various engineers and designers worked together and the work was distributed logically. It makes no more sense for a software engineer to do mechanical engineering than for an ME to develop software.

Finally, have you read much code written by mathematicians or physicists? While there are certainly exceptions, in my experience the quality of their programming is typically atrocious. Yet does that mean that I'm "superior" to them? Certainly not! People simply have different sets of skills.

Face it, Bobber: You're a math bigot!

It might be helpful to remember these two points:

1. Different types of schools and different types of degrees have different functions and purposes.

2. A specific school or degree will require the courses it thinks will best prepare the student for a wide range of jobs.


So, a liberal arts college has a different mission from a technical school. A liberal arts degree prepares people for a different job (if any ) than does a science or professional degree.

But here's the catch for the poor calculus-weary originator of this discussion: they all pretty much agree that you should take calculus.

As other posters have shown, you [b]may[b] need calculus for business, and for computer (and all other) sciences. All tech institutes and B.S.s will require Calc, just in case. Sorry if you personally don't use it, but if they didn't teach it, the guy who does need it will loose out on a job and then sue the college for failing to give him what he needed. Some do use it. You have it if you need it.

With the Liberal Arts degree, as the name implies, you should have exposure to all fields of learning as a matter of principle. You may decide to never be involved in politics or ever to vote, but you'll still have to take Western Civilization I & II and Economics. Same with Calc. That's what a B.A. is all about.

The only way to get around this is to eschew the hegemony of the traditional degree system. Take the classes you want or think you need and screw the diploma.

Or, go to a highly specialized vocational-technical shool that just teaches you how to do it, without much theoretical background into why it works.

Or, sit down with the muckety-mucks of the college and strike a deal with them. Draw up a degree program which substitutes the calc with some other type of math more suited to your vocation. I'm sure some schools will deal. It was your fault for not speaking up and saying, "Hey, the job I want doesn't use Calc, can I take Statistics and Mathematical Programming instead?"

Ah, but that's the problem with youth: we don't often know five years in advance exactly what we'll need for a job, and we expect (rightly or wrongly, for weal or woe) that the college will have our best interests at heart.

Peace.

Well, I'm a biologist of sorts and I use Calculus all the time, though I admit you can do work in biology without it. The thing is, I'm in a field where all the equations HAVEN'T been worked out. I have to figure them out, when it becomes possible, and it spills over beyond biology to the way I look at everything. And I'm convinced I view things more rigorously, more logically, and more abstractly than I would without having learned Calculus. THIS is one reason why I consider a person uneducated if they are not familiar with the basic concepts of Calc.

Another reason is that so much of the modern western world was built using these ideas. Even if YOU don't use them in your job, the method of thought is a central part of our culture, and without some understanding of it you are simply not well educated. I could say the same thing about the philosophical ideas of the Enlightenment, or about Christianity, or the study of Human Evolution. You don't have to be an expert, or even accept the ideas, but if you've never looked at them HARD, you're just not an educated American. Surely you don't use your knowledge of the American Revolution in your job every day, but you'd be considered an ignoramus if you didn't know something about it, and rightly so. This is why schools require these "useless" things; educating us is their job. Mere job training is for monkeys, you should want more.

But APB9999... by your definition, the bulk of humanity are uneducated. I don't believe that to be true. As I stated above, I'm currently working as a software engineer. I spent the bulk of my years in college studying Greek and Latin. I have not, however, ever taken a calculus course. I don't think I understand the "basic concepts of calculus." I've never had to use them.

Let's see... who else is uneducated? The Dali Lama, Bill Gates (who may have studied it in high school, but dropped out of college, but I'd bet money doesn't remember a damn thing), most liberal arts professors (last I checked, your basic English Phd does not include calculus). I could go on and on. We can hardly consider calculus to be a basic concept of education, such as reading, writing, and basic math.

What I object to is that you automatically treat me like an inferior!

Thanks for the interesting discussion and cartoon. I hope we can all get along.

(Note: These are not the crazed ramblings of a whiny math-phobic liberal artist. I got my BA in Math before I sold out and moved on to the more lucrative world of med school. Crazed ramblings and whiny, yes.)

I believe firmly that calculus should not be required in college, and should not be taught at all in high school.

I majored in math because it was neat, not because I thought I would ever use it. I admit that some of the ideas from calculus have helped me understand some biology concepts (especially in Physiology). My problem is, _that's not how it's taught_. If other calculus classes are anything like the ones I took, it's all about manipulating little equations on a piece of paper, and occasionally making that equation into a picture. The meaning, especially in a grand sense, is lost.

So essentially, the class does not help "organize the mind" or "clarify the thinking" of most people--it teaches them to manipulate equations in certain ways on a piece of paper. To the average anthropologist/journalist/biologist even, this is useless.

Those who champion calculus as a way of thinking are, by definition, people who think that way. I go to med school with the biggest crop of math-phobes you ever laid eyes on, and they all seem to do better than me. I look at compliance and say, "Oh, that's just the derivative of the volume-pressure curve", and they look at me like I just sprouted a second head. I look at it in those terms; others see it in terms of chemistry, anthropology, economics, or whatever their particular fancy is.

So my point is, calculus can expand one's horizons, but so can a lot of other things. If calculus were taught as something more conceptual and applicable (as many try to do and fail miserably), it would make more sense to require it, but as such, it is a waste of valuable class time for many.

As for high school, my beef is not with calculus being taught as much as it is with other things not being taught. We progress students through the Algebra/Geometry/ Calculus death march as if there is no other mathematics. An absolutely required HS course in my world would be a Practical Math course. (My HS had one, but it was something the people who failed Pre-Calc took and consisted of addition facts with dollar signs in front of all the numbers.) This would teach people how to use the years of number manipulation we've taught them--how to balance a checkbook, how to figure their gas mileage, figure the square footage of their house, understand statistics they read in the paper, etc.

The problem is the pride of parents, teachers, administrators, who want to say "Here at Cecil Adams High, our students learn calculus!" or "Little Cecil is taking calculus!" Practical math is just so. . .lowbrow. As a result, I'm sure there are people who can take derivatives all day long but would have trouble figuring up their gas mileage, or their return on an investment.

But Dr. J, you're saying, what about people who actually plan to take math in college? Don't they need a head start? No, and I'll tell you why. The rush to get students into calculus leaves enormous gaps in their understanding of math. I did not actually have Calc in HS; I had an extra year of algebra and geometry. As a result, when I actually started learning calc in college, there were lots of tricks and ideas that I knew that other people didn't. Odds are that you'll just have to re-take Calc I in college anyway, so it would be better to build a solid foundation before you start adding in derivatives and integrals.

Pre-college students get the shaft this way in high school. I think colleges should correct it by having a Useful Skills requirement for graduation. For instance, I can do Calc all day, but have a very tenuous understanding of car maintenance. Even a 1-hour class in college would have been a godsend. Cooking, carpentry, basic personal finance, all those things that the pre-college folk had to skip out on so they could take A.P. World History or that fourth year of French.

Sorry to ramble--had a big test this morning, glad to be able to waste time so freely.

Dr. J

You bring up an interesting point, DoctorJ. I had a similiar incident in high school. I was in all the "honors" classes through my junior year of high school. I set up my senior year of high school so that I didn't have to go to school past noon, as I didn't need the credits, and had a job in the afternoons. I did, however, need one last credit of science in order to graduate. I was unable to take the Honors Physics course that would have been the typical choice for me, as it was only offered in the afternoon. I ended up taking "Natural Resources" - not even the average level science class, it was the low-achievers science class.

I learned more practical things in that class than in any of the high-brow "honors" classes that I had taken. 'Twas amazing! I'm all for it, DoctorJ - they should teach real world things like balancing a checkbook, auto mechanics, that kind of stuff. How many 35 year olds do YOU know who have no concept of how to create a monthly budget? Tons, in my experience. Practical education, that's the ticket.

Now, I don't mean to imply that everyone who is uneducated is somehow inherently inferior! I never said that only educated people are deserving of respect. On the contrary, a lot of civilizations greatest achievements were by uneducated people. I'm not sure it' related to that last sentence, but Bill Gates, if he has no knowledge of the things I named IS uneducated, even if he is successful.

I would never hold myself up as a paragon of scholarship, but I do require someone to know a few things other than reading, writing, and arithmetic to be educated.

I don't know what the Dalai Lama has studied, but he comes from a different tradition; he may be educated in a different way. I was careful in my earlier post to say that I think one of the things required for an AMERICAN to consider him- or herself educated is at least a basic understanding of the structure and heritage of our culture. Since we are a very technological society, and the vast majority of that technology is not comprehensible without calculus, calculus is one such subject.

And yes, the vast majority of people in the world are uneducated or poorly educated. It doesn't mean they're stupid.

Even the best educated person has weaknesses. What I object to is the notion that calculus should, in general be one of them.

I understand your point, APB9999, but let me repeat what I wrote earlier:

This thread is not a forum on the value of calculus to physics or science or even to the world at large, it is about whether it is a legitimate graduation requirement for curricula like business or computer science.

Sure, calculus can be a rewarding and enlightening topic to study. So can philosophy, microbiology, political science, glassblowing, and 15'th century French poetry.

The question isn't:

"What should every 'educated' person know?"

it's:

"Does the typical student in this curricula require a strong grounding in calculus in order to excel in their chosen vocation or avocation, or even to achieve acceptable competency?"

Clearly, for some fields the answer is yes. But for those under consideration in this thread, the answer is demonstrably NO.

And that doesn't make me a "monkey"!