Why study math?

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Why is the study of mathematics worthwhile?

It isn't.	11%	[ 6 ]
Because people with mathematical knowledge can get high-paying jobs.	2%	[ 1 ]
Because it is interesting/fun.	13%	[ 7 ]
Because it is possible to have complete certainty and thus to arrive at absolute truth.	11%	[ 6 ]
Because it has applications to other fields such as science, engineering, and economics.	25%	[ 13 ]
Other/more than one of the above.	38%	[ 20 ]

Total votes : 53

Awesomelyglorious
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23 Dec 2008, 1:26 pm

I actually enjoy stats a lot, and don't mind the subjective elements. Then again, I've taken 3 stats classes (AP stats, Engineering Stats, and Econometrics) already, so I'd better have learned to enjoy it. In any case, I usually enjoy math more if it has something to do with something I think is useful. I also will enjoy math more if it is a simple application, such as a simple derivation, perhaps an integration, Laplace transforms are enjoyable too, but math really gets annoying if it stretches out too far in complexity. I mean, I enjoy complexity when it involves plain logic, or simple organization of facts, however, a more formal system often suffers from the fact that it can be harder to conceptualize(lack of direct intuition) and because mistakes can lead to problems but be harder to catch.

Orwell
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23 Dec 2008, 4:22 pm

Shiggily wrote:

the following courses would be interesting for you

MTH 230: Introduction to Abstract Mathematics (the equivalent of my Foundations course... which I loved)

MTH 311: Ordinary Differential Equations (of course)

MTH 320: Introduction to Numerical Analysis

Single AND Multivariable Calc (in U of M its split into 4 classes, mine was 3)

MTH 505: Theory of Numbers (Number Theory is the sh*t)

MTH 506: Logic (logic is the other sh*t)

MTH 512: Elementary Complex Analysis

MTH 510: Linear Algebra

MTH 524: Introduction to Probability Theory

MTH 528: Combinatorics

(you may need modern algebra)

Now if you like applied math with an emphasis on computers

do the 500 differential equation series
MTH 509: Discrete Mathematics II
MTH 527: Theory of Automata
MTH 517: Data Structures and Algorithm Analysis
MTH 540: Algorithm Design and Analysis

If you like your math abstract and "pure"
hit all the analysis classes (real, numerical)
MTH 531: Topology I and II
Abstract Algebra

I never took discrete. I got the same information from a combination of Logic and Computation and Foundations of Mathematics and a touch of Combinatorics. But there is no such things as too many math classes.

Wow, you actually went to my school's website and found math courses for me.

Thanks for the recommendations; I'm already signed up for MTH230 in the spring along with multivariable calc. UM does it a bit differently; we have calc I, II, and III, but our class called "multivariable calculus" (which I am also taking in the spring) is basically a more advanced replacement for calc III at most places. It's not a sequential I, II, III, multivar, but rather I, II, then III if you're an engineer/physicist or multivar if you're a math major. Calc III also includes some intro to matrices, and multivariable goes a bit more in depth. ODE is probably coming next fall, and I'll take a look at the classes you've recommended and which concentrations those match up with. The idea of topology still frightens me a bit. My linear algebra professor showed us a little bit, and it hurt.

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Hector
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23 Dec 2008, 5:33 pm

Don't be so intimidated by a course in topology! The sort of general topology you may be taught at undergraduate level is actually quite intuitive when you get the hang of it, the key is to just make sure that you do (make sure that you understand the basic definitions as soon as possible). My class found it easier to remember the details of proofs for topology exams than abstract algebra exams, certainly.

Shiggily
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23 Dec 2008, 7:31 pm

skysaw wrote:

Shiggily wrote:

I want to split off an do both an applied and a theoretical approach, now. It will depend on where I end up. Right now there is no graduate college where I can study math.

Are you in the UK? Do you mean there are no graduate colleges near where you live, or none that offer modules you're interested in?

I am in Okinawa and island off of Japan.

Shiggily
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23 Dec 2008, 7:32 pm

Hector wrote:

For example, the study of large primes and its central role in cryptology.

ooooooo.... you just made me all woozy. For my Number Theory and Cryptography class we wrote a program on Maple using theories of prime number to write and decypher "secret codes". It is my goal to intern for 1 summer at either the NSA or the CIA to do more work in cryptography.

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23 Dec 2008, 7:35 pm

Hector wrote:

I never got a change to study topology so I am a little jealous. But I did get into fractals and chaos theory a bit in Mathematical Biology which was a class that sprung from a research project of cell signaling so now I want to take Cellular Automata as well.

Shiggily
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23 Dec 2008, 7:39 pm

Awesomelyglorious wrote:

Shiggily wrote:

How much math have you studied?

A significant amount. I used to be an electrical engineering major, almost pursued a math minor, but I changed my major for the first, and as for the latter something screwed me over, but I've taken a significant amount of math, and was only 2 classes away from a minor before everything happened. In any case, I study a field where mathematical expressions are used daily, and where advanced studies involve a lot of technical detail.

You took a "significant amount" of math and almost got a minor?

I don't think I took much math and I consider all the math I took to be "lower level" math and I have a B.S. in Mathematics.

You haven't taken a "significant amount" unless you either have a Master's degree, Doctorate. Or you have taken the equivalent amount of math without the degrees.

Shiggily
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23 Dec 2008, 7:48 pm

Orwell wrote:

Wow, you actually went to my school's website and found math courses for me.

Should I have not done that?

Orwell
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23 Dec 2008, 7:52 pm

Shiggily wrote:

Should I have not done that?

I don't mind, it was just a bit of a surprise to see you posting UM course numbers in reference to what I should take.

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Shiggily
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23 Dec 2008, 8:26 pm

Orwell wrote:

Shiggily wrote:

Should I have not done that?

I don't mind, it was just a bit of a surprise to see you posting UM course numbers in reference to what I should take.

what else would I post? You are going to UM, why would I post a different college?

Orwell
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23 Dec 2008, 8:33 pm

Shiggily wrote:

what else would I post? You are going to UM, why would I post a different college?

It is odd in that it probably is not typical to bother researching the website of another forum poster's college, go through the course listings, and pick out interesting options for them. I can tell that it was very well-intentioned and appreciate the helpfulness, but, unless I am mistaken, it goes against the general social protocol. (Not that that matters very much on WP! :wink:

)

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Shiggily
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23 Dec 2008, 8:38 pm

Orwell wrote:

Shiggily wrote:

what else would I post? You are going to UM, why would I post a different college?

)

I will refrain from doing it again.

Awesomelyglorious
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23 Dec 2008, 9:03 pm

Shiggily wrote:

You haven't taken a "significant amount" unless you either have a Master's degree, Doctorate. Or you have taken the equivalent amount of math without the degrees.

Shiggily, the term "significant amount" *is* subjective, or didn't you know that? If you compared me to the average college student or graduate, then what I took was a significant amount of mathematics. So therefore your criticism is a bit wrongheaded.

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23 Dec 2008, 9:07 pm

Fun thread!

Since I was forced to settle on only one decision, my choice had to do with ultimate truth, though my interest and curiosity for the subject are an equally valid reason, and application to science is an additional driving force.

To me, I guess, I see it as a sort of prime beauty. I'm kind of a meek, insecure kid and to engage in an activity (even if I am not quite as good as I would like to be) that probes the nature of patterns and absolute truth is, to me, one of the closes things a non-religious person like myself can get to divinity.

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Shiggily
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23 Dec 2008, 10:02 pm

Awesomelyglorious wrote:

Shiggily wrote:

You haven't taken a "significant amount" unless you either have a Master's degree, Doctorate. Or you have taken the equivalent amount of math without the degrees.

I presume you put a subjective amount because you didn't want people to know how much you had. Compared to the average college student Calc 2 is a significant amount of math.

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23 Dec 2008, 10:08 pm

Aesthetic appeal. The more math you study the more you derive a sense of sublime profundity from it.

Well, as for truth, it is dubious to say the least to claim that math is true (not that that's going to stop me), but I don't regard anything as understood if it has no mathematical formulation. In that sense math gives the substrate of all real knowledge, which in itself carries a bit of profound weight.

(speaking of aesthetic appeal, I've not got around to taking a proper course in complex variables, but I was tinkering with domain coloring and day-um! can you get some mighty fine results.)

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