# Useless math

I am a computer science student and have completed Discrete Mathematics and Calculus I so far as far as math goes. I've never quite figured out why they make you take so much math. I mean I still have to take Calculus 2, Statistics, and Linear Algebra. Why all of these math courses when I could be taking more classes about programming or learning more IT-related topics? It seems like I'm spending more time trying to complete all of the math classes. Ah well...

ahrkron
Staff Emeritus
Gold Member
You never know, Caldus. You may end up working for a company that develops software for finite element analysis, computer graphics, or simulation of physical processes, all of which may require the math that you still have not taken.

Math not only gives you tools to solve specific problems, but also (and mainly) helps you develop abstract problem-solving skills, plus, the many techniques you learn can often be applied in quite different settings if you are able to establish solid analogies.

RE: "... and theoretical physicists and chemists do what? Useless stuff?"

I hope not, as I'm a theoretical physicist.

But keep in mind that my examples were aimed at the algebra/pre-algebra level. Is it really efficient to focus on techniques that only 0.1% of the students will ever use?

Consider polynomial long division. If a teacher never shows how polynomial long division can be used to help plot a function, or optimize a computer code, should they teach it at all?

What I find in most mathematics books is a complete disconnect between mathematical techniques and their practical use. (And contrived word problems don't count.)

Calculus 2, Statistics, and Linear Algebra

Actually that's pretty skimpy. Aren't you required to take a few more discrete math, calculus III, and some numerical analysis.

Most of computer science deals with developping data types and algorithms. IT ISN'T about writting a text editor with pink and blue text.

Goalie_Ca said:
Actually that's pretty skimpy. Aren't you required to take a few more discrete math, calculus III, and some numerical analysis.

Most of computer science deals with developping data types and algorithms. IT ISN'T about writting a text editor with pink and blue text.
I don't know why Calculus is required for CS majors. Most problems in computer science make no use of Calculus at all. I think more Discrete Maths. would be appropriate. Of course, all of what I'm saying applies to undergraduate studies. I mean, if you're going to do research in quantum computing, the more maths. you know the better.

"Writing a text editor with pink and blue text" does require knowledge of data types and algorithms, so I find this argument rather flawed.

matt grime
Homework Helper
JohnDubYa said:
What I find in most mathematics books is a complete disconnect between mathematical techniques and their practical use. (And contrived word problems don't count.)

And in when learning the basics of French they don't teach you how to use metaphor and simile using the complexity of the language to enrich your written and oral style. There's no reference to Balzac, and you're not learning to act like Madame Bovary.

Finding a subject uninteresting and worthless because of these reasons seems peculiar to mathematics. You are presumably at University so the motivation should be yours. But I do sympathize as I have taught pointless courses, or rather potentially pointful courses (but the habit of setting partial credit ruined that) to some particularly odd sections of the undergraduate community. If anyone can tell me why an Architecture student was made to do multivariable calc I'd be grateful, it's been puzzling me for a while now.

Hurkyl
Staff Emeritus
Gold Member
I mean I still have to take Calculus 2, Statistics, and Linear Algebra.

It takes more than basic arithmetic to analyze algorithms.

RE: "Finding a subject uninteresting and worthless because of these reasons seems peculiar to mathematics. You are presumably at University so the motivation should be yours."

No, I am talking about teaching these concepts to middle school and high school students.

Math for math's sake is another matter entirely. I have no problem teaching unpractical topics out of sheer interest to college students.

matt grime
Homework Helper
But my comments are even more valid there. Maths is the following of rules. We don't see the need to explain to high school students *why* it goes amo amas amat, it's just the rules of latin. Similarly it is just the rules of maths that mean log(xy)=logx +logy, nothing more. Follow the rules, get good marks, it's not very hard, and all will be well. I don't understand why we *must* motivate, with some higher reasons, the study of mathematics when we don't do so for any other subject. Maths isn't really about concepts, there's no need to pretend it is, it is only the rules that govern an object in mathematics that are important to learning it. Anyone with half a brain and a slight inclination to do so can learn mathematics, perhaps we ought to examine the mentality of people who say things like: you do maths you must be so clever, I couldn't do mathematics at school. Would that person go up to a journalist and say: oh, you use words, you must be so clever because I'm completely illiterate? No, it's an attitude that people believe maths must be motivated by the real world and bear relevance to it, and that only through application to real life situations can any meaning be taken from it. Utter garbage obviously. Otherwise practically no research into pure mathematics, or applied for that matter if were honest, could ever be undertaken.

Zurtex
Homework Helper
I know what you mean matt grime, I've always been talented at mathematics throughout my life so far and I've always had the automatic assumption from people that I must therefore be really clever and it's just not true lol.

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Well think about it, most people cannot grasp the concept that is math. Look how many morons fail high school math.

In those morons' defense, the most common reason a student fails math is because they don't really want to pass. And by the time they do want to pass, they're usually so far behind that they're screwed.

Why would I have to be able to determine when the function:

x^3 + 2x^2 - 5

Is concave up or concave down as a computer scientist? Or better yet, why would I have to be able to do a lot of this stuff without a calculator when I could just use a calculator at the place I happen to work at? I just don't get that.

actually, its probably a good thing to know when doing optimization problems. Quickly noticing whether something is concave up or down (isn't that how now common) is good when solving for (forget name, i think langrange uses it, or maybe i'm mixed up). Well, anyway, sure you'll probably end up using maple and/or matlab to do it but you'll need to know that for more theory.

Well think about it, most people cannot grasp the concept that is math. Look how many morons fail high school math.

That seems a bit harsh to generalize all who couldn't pass high school math as morons. When I was in high school, I had other ambitions that were heavily at odds with physics and math. I couldn't stay awake long enough to read the first page of the chapter we were studying, let alone try to grasp the material. This kept me from getting past algebra II, since I couldn't even slide by with a D. This even led me to not being able to graduate high school, since I didn't meet the math requirements. It wasn't until some subsequent soul searching, that I realized physics was my future in some form or another. I enrolled in a local JC and proceeded to get straight A's through all my science and math classes, and got accepted to UCB, UCSD, UCSB and Cal Poly. So i've been on both sides of the fence. I guess my point is, don't be quick to criticise those who aren't fortunate to have the same interests as you.

matt grime
Homework Helper
I certainly don't support the view that all people who fail maths must be morons, though presumably if you're a moron you will fail it, and everything else. I do dislike the culture, prevalent in England certainly, which means that this is found acceptable, or at least notinh to worry about, and often seen as a badge of honour in certain parts.

Hurkyl
Staff Emeritus
Gold Member
Or better yet, why would I have to be able to do a lot of this stuff without a calculator when I could just use a calculator at the place I happen to work at? I just don't get that.

Because the calculator won't suggest to you that concavity might be something useful to use.

Hurkyl
Staff Emeritus
Gold Member
Some things that a computer scientist will specifically find useful from calculus are limits (asymptotic analysis), infinite summations, and the general method of estimating functions by finding good upper and lower bounds.

Furthermore, some techniques of discrete math bear strong relation to those of continuous math; for example, differences correspond to derivatives, finite sums correspond to definite integrals. The techniques are often easier to learn in the continuous setting.

Statistics is also generally useful. Many very useful algorithms have abysmal running times; the most prominent example is that quicksort, in the worst case, is a $\Theta (n^2)$ algorithm... absolutely horrible for sorting techniques... but it almost always beats out "better" algorithms like heapsort and mergesort. Why? Because, statistically, quicksort has an average case running time of $\Theta (n \ln n)$.

Also, many problems simply cannot be solved in a reasonable amount of time... but probabilistic algorithms can be effective. Without knowledge of statistics, how could you design or analyze such an algorithm?

As for linear algebra, it's just so pervasive throughout mathematics that you'd be disadvantaged without it.

Okay, in defense of my statement about morons failing high school, i do realize that not everybody who struggle was a moron. I do realize that others who excel at the arts or at something else may totally suck at math or just not care. But from my own experiences most people who fail math were not that smart to begin with though but they'll likely pass their other courses.

RE: "I don't understand why we *must* motivate, with some higher reasons, the study of mathematics when we don't do so for any other subject."

I have taught physics, math, computer science, and English. I try to relay the importance of each subject I teach.

But you are correct -- we don't have to motivate our students. We don't have to teach in a manner that produces a quality learning environment.

JohnDubYa said:
RE: "I don't understand why we *must* motivate, with some higher reasons, the study of mathematics when we don't do so for any other subject."

I have taught physics, math, computer science, and English. I try to relay the importance of each subject I teach.

But you are correct -- we don't have to motivate our students. We don't have to teach in a manner that produces a quality learning environment.

Why is it assumed that teaching students "practical" uses of math is the best way to motivate them?

While some people really are motivated by seeing an example of math being used in another, it's been my experience that most people who complain about a lack of practical uses are never satisfied. "Practical" is usually defined in such a way as to intentionally exclude math.

matt grime
Homework Helper
I didn't say we shouldn't have to motivate, i said we shouldn't have to motivate with some higher reason, writing as a (university level) teacher of pure mathematics. I don't mean without reference to a practical application, but that there often is no high metaphysical/philosophical reason why something is true in mathematics. How Euclid's algorithm works is a simple consequence of the rules of the ring of integers. But at school mathematics isn't taught like that. And I feel that it is because maths is lumped in with science that people treat its results as theories and not theorems. If it were taught as rule following, just like conjugating verbs, then people might be in a better frame of mind when it came to actually having to do some *real* mathematics. (real mathematics of course in my case has nothing to do with reality.) There is then the need to teach the application of these rule following constructs to the real world., of course.

I didn't say we shouldn't have to motivate, i said we shouldn't have to motivate with some higher reason, writing as a (university level) teacher of pure mathematics. I don't mean without reference to a practical application, but that there often is no high metaphysical/philosophical reason why something is true in mathematics.

Again, you are thinking of a college course. I am talking about mathematics as taught to middle school and high school children.

My philosophy has been: If a student asks "So what?" and you cannot respond, then step down from the podium.

After all, if you cannot relate the importance of a topic, then how can the student be convinced the topic is important? And if you cannot convince the student that the topic is important, then how are you going to motivate them to work hard?

RE: "Why is it assumed that teaching students "practical" uses of math is the best way to motivate them?"

Well, what IS the best way to motivate a typical high school student to study math?