Most Useless Math Topics for Experienced Scientists & Educators

[matt grime]

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]

I mean I still have to take Calculus 2, Statistics, and Linear Algebra.

It takes more than basic arithmetic to analyze algorithms.

 

[JohnDubYa]

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]

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]

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.

 

[Goalie_Ca]

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

 

[cookiemonster]

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.

cookiemonster

 

[Caldus]

OK, answer me this...

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.

 

[cookiemonster]

To impress your boss and freak out your coworkers, duh!

cookiemonster

 

[Goalie_Ca]

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.

 

[Gza]

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 criticize those who aren't fortunate to have the same interests as you.

 

[matt grime]

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]

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]

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.

 

[Goalie_Ca]

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.

 

[JohnDubYa]

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.

 

[master_coda]

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]

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.

 

[JohnDubYa]

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?

 

[JohnDubYa]

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?

 

[matt grime]

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


What other answer than: because mathematics is important, it is used in... used for...? can we offer? Exactly the same reasons as why we teach French, History, Biology and so on. The difference seems to me to be that students expect some better answer in respect of mathematics because it is perceived to be geeky and dull, and they need to be convinced before they'll study it. It is perhaps the indirect nature of the application of mathematics that is the problem.

However, we should draw a distinction between why we learn mathematics as subject, which we should explain, and why you are taught are particular technique, which shouldn't need an explanation.

 

[Math Is Hard]

My little sister (in high school) has the same gripe about her English classes. She says, "I don't care about this, I don't want to be a writer, and I have all the English and writing skills I need."
She sees absolutely no pratical reason for her composition classes, and she's stubborn as a mule.
I think math teachers aren't the only ones who have to put up with this attitude.

 

[franznietzsche]

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?

So they can calculate the life-long expense of their drug habits.

The typical high school student (in this country anyway) not only doesn't care, but won't ever. You can't convince them, its beyond their understanding.

 

[JohnDubYa]

RE: "My little sister (in high school) has the same gripe about her English classes. She says, "I don't care about this, I don't want to be a writer, and I have all the English and writing skills I need."

Her English instructor has probably not done his or her job very well. I teach an English course right now and every one of my students knows exactly why they need to work hard in my class. I craft my assignments to demonstrate the importance of solid English skills.

And if I can do that in an English course, why shouldn't I be able to do that in a math course?

RE: "She sees absolutely no pratical reason for her composition classes..."

Probably because she has never been shown a reason, yes?

 

[JohnDubYa]

RE: "Exactly the same reasons as why we teach French, History, Biology and so on. "

And what are those reasons? And are these reasons likely to motivate a student? If not, what do you do to motivate students.

So put yourself in the role of the teacher. The school principal is sitting on your course for an annual review. You have just finished a lecture on (say) polynomial long division, and a student says "So what?"

What do you say in response?

 

[JohnDubYa]

RE: "The typical high school student (in this country anyway) not only doesn't care, but won't ever. You can't convince them, its beyond their understanding."

I would guess about 5% of the class will study mathematics for its own sake. They have genuine interest in the subject on its own merits, regardless of practicality.

Roughly 40% of the students are probably unreachable. They will not put out any effort no matter how important they perceive the subject.

What about the other 55%?

"Screw 'em! If they don't see that mathematics is the most wonderful subject in the whole world, then let them drift off while I teach my beloved 5%."

Is that the attitude that a high school teacher should adopt towards his students? Would you hire that teacher?

 

[Math Is Hard]

Probably because she has never been shown a reason, yes?

Either that or she hasn't been shown any consequences for not doing the work. She managed to squeak by with a D minus, and was satisfied with that.

Maybe I'll pack her up and send her to you!

p.s. after Algebra 1, I never thought I'd see polynomial long division again, but it made a cameo appearance in Calc 2.

 

[Goalie_Ca]

I see it every now and then, but most of the time I'm using it, I'm using maple anyways.

 

[Caldus]

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.

But what if I'm just going into a job where I program all day at a cubicle or be part of a software engineer team. Where would all of this math stuff come in? I mean I would just have to know how to write good documentation and good code. And as far as sorting algorithms go, couldn't I just use a built-in sorting function (or choose from different ones) for Java or whatever language I happen to be coding in? I wouldn't even have to know how the sorting algorithm itself works or how efficient it is.

 

[Hurkyl]

Then don't call yourself a computer scientist, and hope you're never expected to write efficient code.