Why study math?

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math is the structure and skeleton of the universe. Science is the study of the results of that structure/skeleton and how it is expressed through the universe.

If life was like virtual reality, math would be the underlying code and science would be the expression of that code. Many people who do not study math believe it is vice versa and that science is responsible for everything and math is an after thought.

You should read the following then:

http://www.amazon.com/Where-Mathematics ... 465037712/

http://www.amazon.com/Metaphors-We-Live ... 226468011/

It will if not change your views of math at least enlighten you about what's been going on in the cognitive sciences.

I'm too stingy to buy those and too much a stickler for the rules to pirate them, so unless you're planning on sending them to me as a Christmas gift, I probably won't read them. Thanks for the thought though.

what all have you studied so far?

try betterworld.com

cheap used books

it funds literacy and saves old books from landfills.

I slept through garbage courses like geometry and algebra in high school, bullshitted my way through BC Calculus, and did poorly in linear algebra (on the exams, I've learned most of the material reasonably well) last semester. Next semester I will be studying abstract math and multivariable calculus. I hope to study discrete mathematics soon, but have learned that it sadly is not on my university's math track unless I go for concentrations in either probability/stats (NOT going to happen, as stats is a lower, bastardized form of math that I can not stand) or secondary ed (and I hate high school kids) so I might just study discrete on my own.

Bookmarked betterworld.com. Doesn't look to be much cheaper than other sources, but they're supporting a good cause so if I ever decide to pay for books I'll go there. Thanks for the link.

what college?

stats is useful... just subjective

I took
the Calc series (1,2, and 3)
the Analysis series (1 and 2) (2 was Graduate level)
Linear Algebra
Differential Equations
Foundations of Math
Logic and Computation (like discrete but way way way better)
Mathematical Biology
Probability and Stats (all theorems and proofs, no actual "applied stats" work so it was pretty sweet.)
Number Theory and Cryptography
Statistics for Science (useless piece of crap)
Applied Combinatorics

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.

University of Miami.

I'm only a freshman, hopefully I'll be able to get to most of the topics you mentioned.

Stats just doesn't feel like math to me. It's not as clean and pure as other areas of math. It's not as much fun, either.

actually probability and stats from a math perspective can be clean and pure. Its the applications that are subjective. At the math department I went to we derived equations and handled probability. No applications, just equations. It restored a little enjoyment in statistics.

Last edited by Shiggily on 23 Dec 2008, 5:29 am, edited 1 time in total.

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.

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?

Moreover, though, even when mathematics does not already serve as a foundation of science it may later turn out to be useful in other ways. For example, the study of large primes and its central role in cryptology.

Well, it's not mathematics, that's the thing.

I hated stats in first year and have ignored it ever since, but in retrospect I think I never really gave it a chance. When I thought of it naively I didn't distinguish probability theory (which is maths) from statistical analysis (which is not), and when I realised a couple of months before the exams that statistics wasn't what I thought it was I was shocked. If I saw it as another sort of discipline that happens to use mathematics, like physics, I could maybe have enjoyed (and understood) it more.

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.

Last edited by Awesomelyglorious on 23 Dec 2008, 1:27 pm, edited 1 time in total.

Actually, I do think that math is an afterthought, as many significiant scientific changes in thought have been made on questionable logical grounds, nothing to say about mathematical. This has led some philosophers of science to admit that science has a significant subjective element in determining how it changes, with philosopher of science Paul Feyerabend even seeming to be a complete subjectivist.

Many scientific discoveries do have some mathematical relation to them, however, math is a variation of logic(or vice versa, as I think the current argument is that logic and math both go back to set theory, which is in mathematics), and there are scientific discoveries lead to logical question, usually in the field of quantum mechanics. In any case, I would not say that math is a property of the universe, but rather simply the nature of description, the two are somewhat similar in meaning, however, if math is the skeleton of the universe, the question comes up on how a mind-independent abstraction exists, labeling math to be a property of description gets past this problem, I think. The major issue is that if math is mind independent, it could be argued to be transcendent, and arguments on this basis have been used in apologetics to argue for God.