Calculus Boredom: Is It Common in Undergrad Math?

[trancefishy]

In cacl I, it was really fun. Quite mind blowing when I was first exposed to it a little over a year ago. I decided I wanted to major in mathematics. I took calc 2 concurrently with "matrix theory and linear algebra". calc 2 was boring, just techniques of integration, highly mechanical. matrix theory was alright, completely different, and i don't think i could appreciate it until calc 3.

i'm in cacl 3 right now. at first, it was pretty cool. i like how we are doing stuff in 3d, but, it is still so mechanical. for every question it's an easy solution, just figure out if you need to use a graidient, or what you need the volume of. there isn't much creativity involved.

Is this common? Is it because I'm at medium sized school (10,000 or so undergrad) and so it's more about "job training" than really learning stuff? is it because there is very little class discussion (everyone, myself included, is just very quiet, very passive... i wish i could talk more, but, i just don't ever see anywhere to diverge)

i'm taking abstract algebra next fall, and I'm hoping that is going to be more interesting. lots of stuff related to solving puzzles. I'm also thinkign about taking an independant study course to nurture my love for mathematics that i first felt in cacl1

thoughts?

 

[cronxeh]

you are boring.

 

[Math Is Hard]

you are boring.

and you are mean and horrible...
but funny!

 

[Pengwuino]

you are boring.

lol greatest response ever

In response to the thread though. Math is very boring lol. Its practically the definition of mechanical. Math is a very concrete science, there's no room in mathematics for 'creativity' because for every problem, there's 1 single answer (unless you get into grad stuff or research) to everything and nto a whole lot you can relate to the real world.

 

[SpaceTiger]

thoughts?

All subjects are boring until you get the chance to experience their power firsthand. After I started doing research, I rediscovered a lot of subjects I had previously dismissed as mind-numbing (such as linear algebra).

 

[Data]

Go beyond the class, if it's not thorough enough for you. Once you get into analysis and modern algebra it will get much more abstract, and much more fun.

 

[trancefishy]

I disagree. mathematics can and is a creative art as much as a science, at least, i feel as though that is the case. it's beautiful. I'm just, i guess sick of going through the motions. i was really good at first of building it up by hand, knowing all the proofs, or, at the least, where things came about, how they worked, and why they worked. now i just don't do that, don't have time, dont' care because at a glance i think "well, yeah, i guess i can see how that would relate... somehow...".

i am excited for my independant study class. also, fall of 2006 i am going to go and do the "Math in Moscow" program, which I'm sure will accelerate me into some really great stuff... i guess i just got to sit tight...

 

[Pengwuino]

I disagree. mathematics can and is a creative art as much as a science, at least, i feel as though that is the case. it's beautiful. I'm just, i guess sick of going through the motions. i was really good at first of building it up by hand, knowing all the proofs, or, at the least, where things came about, how they worked, and why they worked. now i just don't do that, don't have time, dont' care because at a glance i think "well, yeah, i guess i can see how that would relate... somehow...".

Well i think he's new to it so that's why its boring. You can't tell me your creativity flourished in the first 3 semesters of calc hehe. And like i said, once you get into grad, it gets fun.

 

[Data]

"he" being the original poster, and the person you were replying to!

 

[Pengwuino]

"he" being the original poster, and the person you were replying to!

Im horrible when it comes to keeping track of who I am talking to lol. You should see the first forum I am frome. Names are small and all we have is hte avatar to really pay attention to. Man... got people confused like nobodys business (there were a lot of default avatars to choose from

 

[hypermorphism]

In cacl I, it was really fun. Quite mind blowing when I was first exposed to it a little over a year ago. I decided I wanted to major in mathematics. I took calc 2 concurrently with "matrix theory and linear algebra". calc 2 was boring, just techniques of integration, highly mechanical. matrix theory was alright, completely different, and i don't think i could appreciate it until calc 3.

i'm in cacl 3 right now. at first, it was pretty cool. i like how we are doing stuff in 3d, but, it is still so mechanical. for every question it's an easy solution, just figure out if you need to use a graidient, or what you need the volume of. there isn't much creativity involved.

Is this common? Is it because I'm at medium sized school (10,000 or so undergrad) and so it's more about "job training" than really learning stuff? is it because there is very little class discussion (everyone, myself included, is just very quiet, very passive... i wish i could talk more, but, i just don't ever see anywhere to diverge)

i'm taking abstract algebra next fall, and I'm hoping that is going to be more interesting. lots of stuff related to solving puzzles. I'm also thinkign about taking an independant study course to nurture my love for mathematics that i first felt in cacl1

thoughts?

This description makes it sound as if your classes have not been challenging you. Grab a copy of "Calculus on Manifolds" by Spivak or Differential Calculus by Courant, or if you're feeling adventurous a book on intro. topology and go through it with your favourite math professor (a reading course). This will alleviate your boredom.

 

[motai]

In cacl I, it was really fun. Quite mind blowing when I was first exposed to it a little over a year ago. I decided I wanted to major in mathematics. I took calc 2 concurrently with "matrix theory and linear algebra". calc 2 was boring, just techniques of integration, highly mechanical. matrix theory was alright, completely different, and i don't think i could appreciate it until calc 3.

i'm in cacl 3 right now. at first, it was pretty cool. i like how we are doing stuff in 3d, but, it is still so mechanical. for every question it's an easy solution, just figure out if you need to use a graidient, or what you need the volume of. there isn't much creativity involved.

I don't understand.. how can Calc 2 and 3 be any less interesting than Calc 1? Sure, the mechanics of the mathematics may be boring and even tediously long at times, but the concepts to me are quite fascinating. I had a fun time trying to think of solids of revolution with non-linear axies of rotation, where many wobbles and precessions take over. I also have a great deal of fun trying to teach others Calculus, conceptually explaining the topic and then going into the mathematics involved.

Try focusing on the concepts more so than the mechanics. Algebra itself can be dreadfully boring if all you think about are the x's and the y's. Get into the material like you did in Calc 1. Its much more gratifying. Continue to question everything that you are not sure of, and even apply the stuff that you do know in unrealistic and odd circumstances for fun.

Is this common? Is it because I'm at medium sized school (10,000 or so undergrad) and so it's more about "job training" than really learning stuff? is it because there is very little class discussion (everyone, myself included, is just very quiet, very passive... i wish i could talk more, but, i just don't ever see anywhere to diverge)

Simple.. talk more. In my class I find myself the only one talking, but I am also the only one asking questions about the concepts as well. It certainly is better than not doing anything at all and sitting in class. Even if you are the only one talking, don't let that keep you from trying to learn. Keep the passion alive, and it will work to your advantage.

 

[Peter VDD]

I agree with the initial poster, math in lower years (here especially before university) is incredibly boring and enerving. Still, it will get better when you climb up in university years :)

 

[Mark C]

Advanced math is not "boring mechanical calclation" it is about about proofs. Thats where the "non-mechanical" stuff kicks in. In advanced math classes, no one "counts" or integrates anything.

 

[Data]

Well, there are high-level calculation-based math courses too. But those are for engineers and physicists, not mathematicians~

 

[mathwonk]

so you are taking boring classes. why? are there no honors level classes at your school? are you unable to speak and ask questions in your class? are you unable to read and look up books in the library? are you afraid to meet professors and have conversations with them?

obviously many people find math fascinating. if you are not, is it someone else's fault?

 

[tongos]

you may call me a freak, but i think simplifying equations is fun!

 

[Gza]

obviously many people find math fascinating. if you are not, is it someone else's fault?

To a certain degree, I would think so. Learning math up through the high school level was one of the most unbearable educational experiences of my life. The teachers seemed to almost try to make the subject mind-numbingly dull (and in my case succeeded). It wasn't until junior college that I got a chance to take an introductory physics course with an excellent teacher, that showed me the true beauty of math in one of its many direct applications.

 

[scarecrow]

I've taken Abstract Algebra, and by far it is the most interesting, but the most difficult. I loved it. Highly doubt that you'll encounter "puzzles"...maybe tons of proofs.

 

[quantumdude]

calc 2 was boring, just techniques of integration, highly mechanical.

Dare I suggest that your Calc 2 class was subpar?

The main ideas in Calc I are limits and differentiation. It doesn't get more mechanical than that. Calc II, on the other hand, has as two of its main themes techniques of integration and infinite series. That demands creativity, because if you make a poor choice of integration techniques or tests for convergence/divergence of a series, your problem can be very difficult. But with clever choices, they become easy. Therein lies the challenge, and the fun.

 

[saltydog]

Seek the beauty. Do I have to explain that? I don't know. Maybe its just in me: I see beauty in Mathematics. Here's one I worked on some time ago and find especially so . . . beauty in simplicity:

$$f+\frac{\partial f}{\partial x}+\frac{\partial f}{\partial y}=\int_x^\infty \int_y^\infty f(u,v) dvdu$$

Oh yea, I'm not a wiz at any of this by any means and don't wish to give the impression of such. Anyway, anyone reading my postings here wouldn't worry about that!

 

[matt grime]

My God do some people have weird ideas as to what's beautiful in mathematics. Next thing someone will be saying that inverting matrices is their idea of fun.

Everyone who does mathematics ought to know a little graph and number theory, it'd make their lives so much fuller (mathematically). Then there's the Euler characteristic, Dynkin diagrams (not only do they parametrize simple Lie algebras but finite representation type quivers, and many more things I've never even heard of), the prime number theorem, Z is a P.I.D. (which apparently also means pelvic inflammatory disease as well as principal ideal domain), every semi-stable ellptic curve is modular (FLT), the links between the Riemann hypothesis random matrices and spectra of physical systems (Berry, Keating et al), character theory of finite groups...

 

[mathwonk]

links of hypersurface singularities, riemann roch theorems and characteristic classes, complex valued functions of several variables and domains of holomorphy, exceptional intersection theory, moduli spaces for curves and abelian varieties, dirchlet's proof of the theorem on primes in arithmetic progression, riemanns singularities theorem,...

 

[marcusesses]

...adding, subtracting, dividing, square rooting...

 

[marcusesses]

haha...i'm sorry, but i have no idea what those concepts Mathwonk mentioned are, so I'm trying to add some humour for those people in the same boat as me

No offense...

 

[Moo Of Doom]

Bah, you forgot multiplication! :P

Well, my AP Calc BC class is not necessarily uninteresting, but I just can't seem to will myself to do the homework - I always get side tracked with random (un)related mathematical curiosities like base representation theorem, pascal's triangle, and freaky geometry puzzles. >.<

 

[Data]

That's just fine (probably better than doing the homework, actually! ). I don't think I did a single math homework question in my last two years of high school, since I was also busy doing my own~

 

[matt grime]

I'm not sure if mathwonk was just having a subtle dig at me or not, but there are lots of areas of mathematics that are out there to learn about that are truly elegant. Ok, they tend to be learned at a lter stage, and I obviously wouldn't expect anyone to learn them in the sense of "for a degree" but there are a lot of books out there that explain someof the impications in layman's terms. So far the list of things given as interesting to people reads as though it's written by engineering undergraduates, so I was just trying to add in some mathematics as a mathematician may think of it.

(Dirichlet's primes in an arithemetic progression was a proof we were asked to reproduce for an examples sheet (homework), and Riemann Roch was also part of our course on algebraic curves, all as an undergraduate, so we aren't really talking about things that are completely unrealistic)

I suppose one of the simplest parts of mathematics that is elegant and would be usefully understood is the notion of Compactness. Who wouldn't like to see all the epsilon and delta arguments removed from analysis?

 

[BobG]

My God do some people have weird ideas as to what's beautiful in mathematics. Next thing someone will be saying that inverting matrices is their idea of fun.

I thought that went without saying.

What could be more pleasing than finding a matrix of integers whose inverse is also composed of all integers? The fact that both matrices are integers make for a pretty good encryption and decryption key (transmitting integers sucks up much less bandwidth than transmitting rationals).

Meh, maybe finding the inverse of orthogonal rotation matrices is more fun - at least it's easier to do.

 

[waht]

re

Actually i found calc 2 way more interesting than calc 1 but that's bacause i knew a lot about calculus before I took it. I recommend you download the fermat's last theorem proven by Wiles and knock yourself out.

 

[JFo]

Actually i found calc 2 way more interesting than calc 1 but that's bacause i knew a lot about calculus before I took it. I recommend you download the fermat's last theorem proven by Wiles and knock yourself out.

I downloaded it... It might as well have been written in hyroglyphics (sp?). In all of about 100 pages, I could only recognize a Ker(V) here and there, but of coarse had no clue what was going on. It was kind of interesting just to see what terminology is out there, since I think this paper uses just about all of it.

 

[matt grime]

The proof of FLT is only one very tiny aspect of one part of mathematics. However, it is an interesting thing to learn the circumstances under which it was proven, the conjectures involved and the time it took. I doubt anyone here would understand the proof, but they could learn about how mathematics gets done, though there are those who dislike the secretive approach he took. But that's just another interesting facet in the story. There are plenty of accounts of it out there for people to look up.

(it's hiero, not hyro, i think)

 

[JFo]

It is very interesting... I've read parts of the book by Simon Singh, and it was fascinating to see how a real mathematician works. When you say there are those who dislike his secretive approach, do you mean that people think he should have opened his work as he was doing it, rather than hiding it till he was completely finished with the theorem? I'm curious what you think. Do you think mathematicians have a responsibilty to disclose results as they discover them?

by the way, your right, it is hiero - thanks for the correction.

 

[mathwonk]

anyone with the ability to do what wiles did is pretty much granted leave to do it in any fashion that suits him.

when it takes 350 years for someone to prove something that interests pretty much every high school student, we usually do not place further restrictions on how publicly they should prove it.

 

[Gza]

But I think the way the media covered it, made it seem to support the notion of the mathematician as being a fragmented individual; hunched over in his basement, scribbling incoherent symbols on paper, with no contact with the outside world. Math as far as I know, is never created within a vacuum, and I'm pretty sure he had to be soaking up ideas from outside sources.