Most Useless Math Topics for Experienced Scientists & Educators

[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.

 

[krab]

regardless of practicality.

BTW, that should be "regardless". English does have some mathematical rules: e.g. a double negative becomes a positive.

What about the other 55%?

I would say, make sure you have the respect of your students. Teach enthusiastically and if they cannot be made to see the beauty of mathematics, then at least they will come away with an impression that there is something there that some people can appreciate.

 

[HallsofIvy]

Teach enthusiastically and if they cannot be made to see the beauty of mathematics, then at least they will come away with an impression that there is something there that some people can appreciate.

Very well said. They may think you are a fool but they will remember that you care!

 

[e(ho0n3]

Speaking of useless maths., whatever happened to Lamba Calculus? There are very few universities offering this course and all the books I know on the subject are getting old now. The only thing I remember from Lamba Calculus is the weird symbolism.

 

[JohnDubYa]

RE: "BTW, that should be "regardless". English does have some mathematical rules: e.g. a double negative becomes a positive."

Groan.

RE: "I would say, make sure you have the respect of your students."

Respect must be earned. The best way to earn respect is to show your students that you are acting in their best interests. When I teach English, I show my students why the material we learn can help them. (One of my first assignments is a letter of inquiry. They learn immediately that they would be in real trouble in the real world unless they pick up significant writing skills.)

RE: "Teach enthusiastically and if they cannot be made to see the beauty of mathematics, then at least they will come away with an impression that there is something there that some people can appreciate."

Teaching enthusiastically with no regard for the benefit to the students is called "self-absorption." Have you ever had such a professor? They go on, and on, and on. At some point you wonder if they would continue lecturing if everyone left the room.

Again, how do you respond when a student says "So what?"

 

[styler]

BTW, that should be "regardless". English does have some mathematical rules: e.g. a double negative becomes a positive.

sorry to interrupt but this is NOT true.
Irregardless means regardless. As inflamable means flammable. There are other cases too. These are somewhat informal but they were never meant to be antonyms.

Not the best authorties but:

irregardless definition

more

http://web.uvic.ca/wguide/Pages/UsIrregardless.html

scroll down

http://www.wsu.edu:8080/~brians/errors/irregardless.html

 

[arildno]

I quote the entry from the dictionary in full:

"ir·re·gard·less ( P ) Pronunciation Key (r-gärdls)
adv. Nonstandard
Regardless.


--------------------------------------------------------------------------------
[Probably blend of irrespective, and regardless.]
Usage Note: Irregardless is a word that many mistakenly believe to be correct usage in formal style, when in fact it is used chiefly in nonstandard speech or casual writing. Coined in the United States in the early 20th century, it has met with a blizzard of condemnation for being an improper yoking of irrespective and regardless and for the logical absurdity of combining the negative ir- prefix and -less suffix in a single term. Although one might reasonably argue that it is no different from words with redundant affixes like debone and unravel, it has been considered a blunder for decades and will probably continue to be so.

 

[Zorodius]

When a tutee of mine is expressing their dislike for math, if they are not persuaded by whatever example I can come up with where they would use the subject matter in real life, I show them some renderings of the mandelbrot set that I always have handy. Many students in earlier math classes do not understand how conceptually meaningful and elegant math is, but few fail to see the beauty in the graceful curves and swirls of a fractal set. Being shown that math is not all rote and pedantry can soften them up towards the subject.

Of course, the ultimate "reason why I should learn this garbage" is, "because you would like to pass the class." That's a perfectly valid response, if someone has rejected the other possible motivations for studying the material.

 

[JohnDubYa]

RE: "When a tutee of mine is expressing their dislike for math, if they are not persuaded by whatever example I can come up with where they would use the subject matter in real life, I show them some renderings of the mandelbrot set that I always have handy."

And the tutee then asks "How is this related to polynomial long division?"

No one has answered my question: You are lecturing on (say) factoring of polynomials. A student asks "So what?" (A perfectly legitimate question, I might add.)

What do you say in response? Because it's beautiful? Because I'm interested in it?

RE: "Of course, the ultimate "reason why I should learn this garbage" is, "because you would like to pass the class." That's a perfectly valid response, if someone has rejected the other possible motivations for studying the material."

Well, that will motivate them to reach at least a D.

 

[JohnDubYa]

BTW, I'm not trying to antagonize anyone. Those who teach will encounter this situation, and I think it behooves future teachers to be prepared. Showing pictures of Mandelbrot sets is not going to motivate someone to learn factoring.

 

[Zorodius]

RE: "When a tutee of mine is expressing their dislike for math, if they are not persuaded by whatever example I can come up with where they would use the subject matter in real life, I show them some renderings of the mandelbrot set that I always have handy."

And the tutee then asks "How is this related to polynomial long division?"

No one has answered my question: You are lecturing on (say) factoring of polynomials. A student asks "So what?" (A perfectly legitimate question, I might add.)

I was not bringing up the fractals in response to a specific topic, like polynomial long division, but rather as a response to someone who is frustrated with math in general and has not experienced its elegant side. Resenting a subject makes it much more difficult (or impossible) to learn that subject. When someone discovers a subject has an appeal that they were previously unaware of, it can reduce their level of resentment towards it, making it easier for them to proceed.

You are correct that some of what is taught in math classes will not be of direct use to most of the students who take the class, and that polynomial long division fits into this category. However, even if you never actually wind up wanting to divide one polynomial into another, it's still good practice at manipulating algebra, and can be viewed as a "case study" in following an algorithm to arrive at a result.