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07072012, 07:59 PM  #1 
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Another question about Math...
My question revolves around the fact that math seems to be the only constant in the whole universe the laws governing of each planet may differ in strength and the forces that go into making the slightest carbon atom may vary as well.
Since math seems to be the only constant in the universe, do you think it should be considered the most important subject? Although I consider myself decent and have a genuine curiosity for mathematics, I am intimidated by anythings past Calculus I and don't really need to learn differential equations or linear algebra for my major (biology). On a related note, is mathematics the purest form of logic? Also, if I know the fundamentals of mathmultiplication, division, subtraction, variables. Is every process in differential/upper level calculus using an operation like the ones above? Are higher level math classes used as applications of those operations as well as linear algebra being the exception by rotating or bringing down terms in matrices. I know I don't sound exactly clear but any help is appreciated. Thank you for taking the time to answer this if you get a chance! 
07072012, 08:13 PM  #2  
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There's all kinds of operators besides the basic four, like the modulus operator for example. Good math courses that cover most of what you'll ever need. Calc. linear algebra probability and statistics. Discrete math is good also as well as advanced calc. Enjoying the struggle calmly was what helped me. 

07072012, 08:25 PM  #3  
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Math is certainly a fundamental part of an education that is complex and difficult to master. That is why a strong foundation of math leads to the most highly skilled jobs in the world. A very close yes. But realize that any mathematical formula may be disproved at any given time. String theory is one of those subjects where higgs bosen theoretical equations may be challenged due to the recent discovery of the "god particle" (though they still have to conduct more experiments to confirm their findings. Quote:
You only touch a small sliver of what is to be learned in higher level math.
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07092012, 12:25 PM  #4 
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It's nice to know that you have genuine interest in math. Let me give you a brief overview of what math is.
I don't what it means to say that math is the only "constant" thing in the universe. If by this you mean, math is the only "true" thing in the universe, you might want to define "truth." Math is true only with respect to the current accepted axiomatic framework. Some axioms that mathematicians accept are the ZFC axioms of set theory and the Peano axioms. Now, any axiomatic system with arithmetic (of natural numbers), has inherent limitations, in that some mathematical statements about natural numbers can't be proven to be true nor proven to be false. Such statements are said to be undecidable. Here's an example of an undecidable statement: Take any natural number n. If n is even, divide it by 2. If n is odd, multiply it by 3 and add 1. Repeat the process and you'll eventually reach 1. Let me talk about algebra, and the theory behind when polynomials are solvable by radicals. You know that a polynomial with degree 2 is clearly solvable by radicals, since the roots are given by the quadratic formula. The question of when a polynomial of any degree (with rational coefficients) is solvable by radicals can be answered using group theory. Definition: A group is a set G with a binary operation * that satisfies the following properties: For any x,y,z in G  x*y is in G  x*(y*z) = (x*y)*z There exists an identity element e in G such that e*x = x*e = x Every element has an inverse element b such that x*b = b*x = e Notice that I haven't mentioned commutativity. If the operation satisfies commutativity then our group (G, *) is said to be an abelian group. Some example of groups are the integers with addition, the real numbers with addition, the rational numbers with addition, and the rational numbers without 0 with multiplication. Typically they're written as (Z, +), (R, +), (Q,+) and (Q, *) respectively. Now we can have functions between groups that satisfy certain properties. Let G, H be groups (let's drop the operation sign for simplicity). A function f: G > H is said to be a homomorphism if for any x,y in G f(xy) = f(x)f(y) An example of a homomorphism is f: Z > Z defined by f(x) = x. Typically, functions like these that send every element to itself are called identity functions. We also have what's called a subgroup of a group, which is simply a subset of a group that also forms group under the same operation. If H is a subgroup of G, then we write H < G to indicate this. Now back to homomorphisms, we must be aware of a certain class of homomorphisms called isomorphisms. Isomorphisms are homomorphisms that are invertible (equivalently bijective homomorphisms). The identity map mentioned earlier is clearly an isomorphism. There are special types of subgroups known as normal subgroups. For a subgroup H < G if a is in G, we let aH ={ ax : x is in H}, that is the set of all elements of H multiplied (on the left side) by a (note: if the operation of the group isn't mentioned, we just call it "multiplication"). We define Ha similarly. If it turns out that aH = Ha, H is said to a normal subgroup of G. What's so interesting these is that they allow us to construction a new group called the quotient group of G by H denoted G/H. We define G/H as {aH : a is in G}. That is the set of cosets of H. The operations is simply aH *bH = abH. This defines a group with the identity element being H itself. Now let's tackle the question we asked at the beginning. Given a polynomial p(x) with rational coefficients, we define a splitting field of p(x) to be the smallest extension of Q(the rational numbers), over which p(x) factors as a(x  b1)(x  b2).....(x  bn) For instance, the polynomial x^2  2 has the splitting field Q(√2) which is defined to be {q(√2)/r(√2) : q, r are polynomials with rational coeffs and r(√2) =/= 0} Let's introduce a couple more concepts from group theory. A group G is said to be solvable if it has subgroups G1,.....Gk such that {1} < G1 < .... Gk < G and each subgroup is normal in the next and Gk/Gk1 is an abelian quotient group. Note that here, 1 = e Let E be the splitting field of p(x). We define the galois group of E over Q , denoted Gal(E/Q) to be the set of all isomorphisms that fix Q pointwise that is {f: E > E : f is an isomorphism and f(x) = x for every x in Q} This forms a group under the operation of function composition. Theorem: A polynomial p(x) with rational coefficients is solvable by radicals if and only if Gal(E/Q) is a solvable group. The proof is way too long to give here, but here's a nice corollary. Corollary(AbelRuffini): The general polynomial of degree greater than or equal to 5 with rational coefficients (quintics or higher) is not solvable by radicals. That's a taste of what math is. Last edited by Claudius : 07092012 at 01:08 PM. 
07092012, 02:07 PM  #5  
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From my perspective, I'd say that language is probably the most important. Because without any kind of language, I really can't communicate thoughts or ideas. Some forms of art might even be considered language. Science (which includes mathematics) is probably least important. I also enjoy math. But most need very little of what they learn. If you want a fun math subjectarea to explore  take a look at axioms. Axioms are the lowestlevel, machinelanguage instructions of mathematics. It is really amazing to explore the few very simple rules that all of mathematics derives from  and then explore more complex derived axioms.
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07092012, 02:48 PM  #6  
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Though I was an applied math and econ major, so I may be a little biased. I'm sure I'll offend some people here but, if you suck at math you're probably stupid. Can't just memorize useless facts.
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07092012, 08:34 PM  #7  
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But I know alot of people are bad at it b/c they hate it, and they hate it b/c of the poor instruction they received. 

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07092012, 11:06 PM  #8  
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Some of us love mathematics. Others hate it. But those people are also glad there are others in the world who love it.
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07102012, 08:20 AM  #9  
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This post says a lot... and not all math related. 

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07102012, 10:41 AM  #10 
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What do you mean by "not all math related"?

07102012, 11:18 AM  #11 
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not getting that one.
anyway no discussion about P NP? might be a little "heavy" for most...based on this peeps observation.
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07102012, 11:28 AM  #12 
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Indeed. It is so much easier to be "good" at humanities than the be good at something objective, like mathematics.
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07102012, 11:48 AM  #13 
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"Shakespeare was a dumb*****"  Eph
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07102012, 12:11 PM  #14 
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07102012, 12:16 PM  #15 
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What's more sad is that here in the US at least it's socially acceptable to be bad at math.
In fact, people wear it like a badge of honor. Off topic kinda but, the other thing that gets me is people who consider themselves "bad test takers." So you struggle with the part where we find out what you know? (Tosh reference)
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I'm a poser and a wannabe but still probably better than you. Last edited by krz : 07102012 at 12:18 PM. 
07102012, 12:32 PM  #16 
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Really? People display being bad at math like a badge of honor? Can you give an example? I've never experienced that the people I know in the humanities wish they could do math, and are not proud that they cannot.
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07102012, 03:38 PM  #17  
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07102012, 09:18 PM  #18 
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He is probably talking about those guys that really don't give a rip about math, and are not shy about saying they will "never use it in their life" and "math is for nerds". Then, they complain about the drama that is happening at the local fast food restaurant they have been working at for the past few months.
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07102012, 10:46 PM  #19 
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What is math? I've heard of maths but not math, is that some kind of weird new subject?

07102012, 11:24 PM  #20 
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My response to, "I was never good at math" is "But you can read, right?"


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