Why do so many college majors require Calculus?

Factual Questions
41

Bobber: Your arguments are flawed and miss the point…

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.

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.

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.

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?

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.

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!

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!

42

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 may 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.

43

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.

44

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.

45

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.

46

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

47

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

48

(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

49

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.

50

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

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”!

51

Ambushed: Sorry, didn’t mean for you to take “monkey business” as a personal insult. I was making a joke on curious george’s moniker. I did not mean to seem demeaning, but I can see, given the context how you could take it that way. I apologize.

But I think the question, as I understood it, was “why do schools require calculus for so many majors where it isn’t used day-to-day?”. I think the reason is, the schools are looking to educate, that is teach us ways of thinking, not just particular skills. How much do you use French, European History, Philosophy, etc.? But they provide a common base of knowledge in terms of which we can discuss things. ANY things. You can get by without them fine, but that’s not the point. You can get by fine without any college courses at all, just by taking a few skill-building classes and some OJT!

Now if you argue that too many people go to college that don’t need to, and that we need an alternate system for people who aren’t interested in the traditional education model but just want to learn the skills they need for their jobs, I might agree with you. That would probably be a good thing.

DrJ: I didn’t take calculus in HS either, and when I took it in college I didn’t get it. I had to go off on my own and teach myself, which I only did because of a sense of the subject’s importance. Thank God I did! But I agree with you that it is usually tought terribly.

52

And so is spelling.

53

The reason you have to take calculus has nothing to do with academics; it has everything to do with economics-----the economic well-being of the school, you see. If they foist these classes off on the students that the students don’t actually need in their field, the students nevertheless still have to PAY for the classes, and voila! “Next year we’ll be adding a new administration building and two parking lots!” I was a history major, and had to take eight credits in algebra as well as statistics. How this was supposed to help me understand how Horatio Gates surrounded General Burgoyne at the Battle of Saratoga was never adequately explained to me. Have I ever used the stuff? Are you kidding? If I were an astrophysicist, maybe, but in history you don’t spend a lot of time trying to determine the value of X in a double-negative polynomial equation. Personally, I think all math majors should be required to take at least twelve credits worth of history classes—good stuff like Trade and Religion In Ancient Mesopotamia, Culture and Conflict in the Third Reich, and Military and Social Constructs During the American Civil War. That’d fix their wagon.

54

What kind of business jobs do you people have where you haven’t used advanced math in three years? How do you evaluate investments, returns, and the risks associated thereon - without calculus?

What kind of lives do you lead where you never use advanced math? Even just for fun?

True, students at a truck driving school probably don’t need calculus to function at their profession, but it seems to me that a lot of the people here have humanities and liberal arts degrees. Surely you didn’t go to college specifically to get a job in your field, did you? Me personally, I went to college because I wanted to learn and I wanted to improve myself and my experiences.

That’s the whole point of college - I would argue - to broaden one’s experiences and to improve one’s mind, and if that’s the point of college, then why would the school just let you focus on one narrow field for the entire four years?

The school isn’t interested in mass-producing psychologists or writers, the school is interested in producing educated people.

Knowledge is valuable for its own sake. Certainly advanced math isn’t taught because everyone is expected to use it, per se. Math is taught because it teaches you new ways to think and new ways to comprehend things that happen to you every day. Just as a physicist would be incomplete without exposure to literature, I would argue that an novelist would be incomplete without an exposure to calculus.

Colleges have figured this out and that’s the answer to your question.

55

What kind of business jobs do you people have where you haven’t used advanced math in three years? How do you evaluate investments, returns, and the risks associated thereon - without calculus?

What kind of lives do you lead where you never use advanced math? Even just for fun?

True, students at a truck driving school probably don’t need calculus to function at their profession, but it seems to me that a lot of the people here have humanities and liberal arts degrees. Surely you didn’t go to college specifically to get a job in your field, did you? Me personally, I went to college because I wanted to learn and I wanted to improve myself and my experiences.

That’s the whole point of college - I would argue - to broaden one’s experiences and to improve one’s mind, and if that’s the point of college, then why would the school just let you focus on one narrow field for the entire four years?

The school isn’t interested in mass-producing psychologists or writers, the school is interested in producing educated people.

Knowledge is valuable for its own sake. Certainly advanced math isn’t taught because everyone is expected to use it, per se. Math is taught because it teaches you new ways to think and new ways to comprehend things that happen to you every day. Just as a physicist would be incomplete without exposure to literature, I would argue that an novelist would be incomplete without an exposure to calculus.

Colleges have figured this out and that’s the answer to your question.

56

What kind of business jobs do you people have where you haven’t used advanced math in three years? How do you evaluate investments, returns, and the risks associated thereon - without calculus?

What kind of lives do you lead where you never use advanced math? Even just for fun?

True, students at a truck driving school probably don’t need calculus to function at their profession, but it seems to me that a lot of the people here have humanities and liberal arts degrees. Surely you didn’t go to college specifically to get a job in your field, did you? Me personally, I went to college because I wanted to learn and I wanted to improve myself and my experiences.

That’s the whole point of college - I would argue - to broaden one’s experiences and to improve one’s mind, and if that’s the point of college, then why would the school just let you focus on one narrow field for the entire four years?

The school isn’t interested in mass-producing psychologists or writers, the school is interested in producing educated people.

Knowledge is valuable for its own sake. Certainly advanced math isn’t taught because everyone is expected to use it, per se. Math is taught because it teaches you new ways to think and new ways to comprehend things that happen to you every day (or at least that’s my experience).

Just as a physicist would be incomplete without exposure to literature, I would argue that an novelist would be incomplete without an exposure to calculus. Colleges have figured this out and that’s the answer to your question.

57

I’ll go along with that.

58

As a Math Grad, I may point out that you are probably using calculus and not realizing it because the number crunching is being done for you by a computer, pre-printed amortization table, etc. In other words, you learned basic skills that theoretically enable you to calculate amortization tables yourself, should you find yourself stranded on a desert island. Besides, just because your specific job you have today doesn’t require you use calculus, you may apply for a new job tomorrow that assumes you know calculus.

59

I graduated with a BA in english after 17 years of college. I think that may be a record of some sort. I went to 11 different universities. I also changed majors a lot. Every scholl I went to required at least 8 credits of liberal arts in addition to an advanced writing class (which meant you had to take a basic writing class first unless you could pass a test).
One of the reasons I finally got my degree is that I kept taking Literature courses for the fun of it. I studied math for two years (through Partial Diff. Eq.) and found it easy but uninteresting. I think that schools do a pretty good job with their requirements.

60

Good god, johnnyharvard! Are you actually telling us that you calculate these things with paper and pencil using calculus?? Didn’t Hahvahd have any of them new-fangled computemo thangs around? Sheesh!

And I admit I’m not up on my accountancy, but is calculus really necessary for those things?

More interesting ones than you, one might be forgiven for suspecting!

As for the rest of your harangue, you insist on completely missing the point. If any given university were to require a single introductory course in calculus for all students in the interests of “broadening their educational horizons”, I would probably have no objections. But this is not what we’re talking about!! Clearly, your facility with calculus hasn’t helped your reading skills very much. :wink: