Basically you're looking for points x such that for any positive real r there is a point y in E less than a distance r away from x. In other words you want every ball around x to contain points in E.

The given information tells you the limit does not exist. The function representing the situation is a step function. Because the left-hand limit (0.06) and right-hand limit (0.08) don't match up, the limit does not exist. Simple enough, right?

1210

Okay so just to be explicit, do you mean what is written in my attached image? If this is the case, then what you want to do initially is follow the order of operations
(http://en.wikipedia.org/wiki/Order_of_operations#The_standard_order_of_operations)
to simplify the left hand side of your equation. And what the order of operations says to do here is evaluate the parentheses first, which yields: 7*8 - 1*66 = 3x. Still following the order of operations and because there are no exponents nor roots here, we move on to evaluating multiplication (no division), which yields: 56 - 66 = 3x. The next stage in the order of operations is addition and subtraction, so do that: -10 = 3x. Now the thing about equations is that whatever you do to (whatever is used to operates on) one side of an equation, you must also do to (must be used to operate on) the other side of the equation for the equation to still hold true. In this case, what you want to do is divide both sides of the equation by 3: -10/3 = x.

>>289
Thanks man, I know Im a bit late on the response, but yeah...much appreciated.

>>297
Sure thing, was no trouble. :)

I'm pretty sure thats wrong.

>>293
thanks! should've tested it before trying to prove it

>>278
Not a problem, I actually thoroughly appreciate the honesty in the criticism, I'd much rather be told I'm wrong than continue believing something that's known to be untrue.

Found a few more links that will hopefully be of use to some of you, enjoy. Comments, questions, and criticisms are always welcomed and appreciated :]

(How to become a pure mathematician/statistician)
http://www.stumbleupon.com/su/1xdzYO/:1sc2GuN3j:IuFZXYP7/hbpms.blogspot.mx/

This link below is closely related to the field of "predictive analytics". I have a friend who's an engineer at Sandia Labs up in Albuquerque, NM; he's been studying this in his free time because he's been calling it "the future goldmine of statistics". Apparently jobs for these positions are going to be in very high demand in the next 10 years, and currently only 2 colleges have degree programs for the field. Salaries (from what he's told me) range around a comfortable 80-100k per year. Below are some of the maths that are to be used for this field.

http://www.stumbleupon.com/su/1xdzYO/:1sc2GuN3j:IuFZXYP7/hbpms.blogspot.mx/

And lastly a LaTeX tutorial video library I found on YouTube based off of popularity and positive feedback

http://www.youtube.com/watch?v=SoDv0qhyysQ

Message too long. Click here to view the full text.

>>278

Seconding this. If you're planning to go onto grad school in applied, you're still going to have to take a bunch of undergrad (some grad) courses in pure math. So, proofs won't be a big part of your professional life, but you're going to need to get a handle on it anyhow.

@centerofmath
@AnalasystFact
@AlgebraFact
@mathematicsprof
@MathDaily

All excellent twitter feeds for daily mathematics news, philosophy, and problem solving

>>283
don't forget TopologyFact!

Wondering if there were any useful applications for calculus in the stock market, investor Jim Cramer's said that 4th grade math is all you need to become a successful investor, but I'm a little skeptical. Resources would be nice if anybody has them. Thanks in advance!

It is possible, I did it in calculus II, using the Power Series expansions. You can also use the limit definition, and polar coordinates. It shouldn't be too hard to find these proofs floating around on the web.

>>227
actually now that i think about it, you don't need to know anything about derivatives. All you need to do is show that sin is indeed equal to that sum.

>>227
Yes, it is possible to find the derivatives of sine and cosine without the Pythagorean theorem. In fact, the only trigonometric identities required are the angle addition formulas, which do not require the Pythagorean theorem for their derivations either. Curiously, the Pythagorean theorem can be derived from Euler's formula:

http://www.mandysnotes.com/Trigonometry-With-Complex-Numbers/Complex-Trigonometry/The-Pythagorean-Theorem-from-Eulers-Formula

The writer of the derivation I linked to messed up and threw in a + when there should have been a -, but you get the idea. Anywho, what I'm getting at is that Euler's formula actually cannot be derived from the Pythagorean theorem, but it is the other way around.

>>242

Yeah, that's why i wanted it.

http://www.boards.ie/vbulletin/showthread.php?t=2056785182

>>242
Thanks!

I came up with about 3.85 inches. I realized that if I constructed an inverted cone tangent to the other cones with its base "level with the [other] cones' tips", then the problem reduces to a more familiar one: determining the radius of a sphere inscribed in a cone. Because the base radius of the cones is given, it follows that the distance between the tips of the cones is 10 inches. Usin' that good ol' Pythagorean Theorem (30-60-90 triangle ratios in this case) and the fact that the base of the constructed cone contains the tips of the three given cones, I calculated the radius of the constructed cone as 10/sqrt(3) inches. Because the axes of the constructed cone and the given cones are all parallel, the constructed cone must be similar to the given cones. I used this similarity relation and the height of the given cones to find the height of the constructed cone: 12/5 = (10/sqrt(3))/h ==> h = 8*sqrt(3). Knowing the base radius and the height of the constructed cone, I carried out the same calculations in the attached image to obtain the exact answer of 20*sqrt(3)/9 inches.

this is awesome, sticky please

I just learned a cool tip! You can make shortcuts for longer commands that you use often (for those of you writing longish reports, not equations online)

So if you wanted to replace \mathbb{N} with \N you could do:

\newcommand{\N}{\mathbb{N}}

And put it anywhere before you plan to use the shortcut, I'd assume. I usually just do it after I list my packages.

(I've never sat down and read a full guide for latex, so maybe this is common knowledge, but I never realized it until I saw a prof do it.)

http://books.google.ca/books/about/Elementary_Analysis.html?id=5JxHZNpMq3AC&redir_esc=y
This book is fantastic. It very gently and rigorously goes from building the reals to integration. It's very very nice and understandable.

http://en.wikipedia.org/wiki/The_Library_of_Babel
This is just a short story but its pretty interesting to from a math point of view. It's basically the story of a giant library which comprises all of the known universe for the characters and which presumable contains all possible books of a certain length

http://books.google.ca/books?id=ebILwSGlUlgC&printsec=frontcover&dq=library+of+babel&source=bl&ots=eVHY6d4K-W&sig=I6WkNTsdEVcDfdGPOwrpQIBUR3Y&hl=en&sa
=X&ei=QqB9UN7QJKre0gG9_oE4&ved=0CDEQ6AEwAA
This is a nice exposition of the Library of Babel.

http://books.google.ca/books?id=_F0nAQAAIAAJ&q=topology+sheldon+davis&dq=topology+sheldon+davis&source=bl&ots=c1bUv_nWhL&sig=yhfG1rv0Ir-3vg4fyzclMcFzP
7Q&hl=en&sa=X&ei=haF9UP2wAsyJ0QHqiYHgBw&ved=0CDEQ6AEwAA

I forgot this one, sorry for the double post. I taught myself out of this book. It's pretty good, the proofs skip few steps so if you're new to upper math it can be pretty helpful.

Wow thanks for the quick and great response. I'll be taking that list to the library today.

How dare you double post on /calc/? There's so much traffic, I'd bet that someone's constructive and insightful post was pushed back a few pages by your indiscretion!

I'm going to school - I'm in my mid twenties - and I'm in the same boat. I recommend that you take the classes you need, so you absolutely positively have the math you need mastered.

>>154

broken links

>>178
Demonoid was permanently taken down.

SAGE has been used.

http://www.mediafire.com/?ad441dkk6kppgw3

Khan Academy, got me up to speed, now I'm rocking calculus I.

Odds are you're not bad at math, you just never really tried. Unlike other things you learn in school, being smart and having a decent memory aren't enough to get you by in math. You really have to practice, it's more comparable to a skill like playing an instrument or writing than it is to a subject like history or sociology.

Have you looked into all the online resources in that other thread (>>106)? Some of those might be helpful. Or if there's anything specific, please let us know so we can help out.

What level of math are you comfortable with? Algebra? Arithmetic? Probability? Are you looking to make video games or traditional games? I would love to help you gain a better understanding, so please let me know what I can do to help.

School maths is not maths at all. Nothing wondering that you can not learn it.

I've experienced similar, albeit drawn out issues I think. I didn't seem to have problems mindlessly grinding the content up until around the latter portion of highschool. At that point for whatever reason I developed a consuming interest in various gadfly philosophical persuasions and quickly lost confidence in mathematics as an infallible axiomatic system. Certain epistemological and mereological premises sort of espoused many spheres of mathematics to me as nothing more than perceptual hallucination, as the ideal geometric structures simply do not exist as isolated, non-dynamic physical entities. Choosing to isolate some perceived object from the dynamic flux which is external reality and just pretending that it isn't actively interacting at imperceptible levels with said environment, even going so far to regard it as an "object"; that is, crudely separating a manifestation of fundamental elements and properties and constructing some arbitrary, fictional boundary to isolate this portion of matter from the mire. Notions of "quantity" and the existence of a formal mathematical object was to me at this point mere social consensus.

My entry into some of my engineering program's advanced calculus content actively discouraging as the curriculum's integration of math seemed to orient towards problem solving for its own sake. A governing formula or theory is thrown at us within the context of some arbitrary puzzle and we solve its 2-3 possible permutations using a strict process. No theoretical background, historical context or possible flaws or fallibility are ever provided. I completely neglected the material at that point in light of my edgy philosophical insights and subsequently performed quite substandardly in the course. I was outperformed by peasants who don't seem even aware of quite what math is and are obviously grinding out success a la my pre-pubescant highschool methodology.

I guess my point here is that when you deal with the material in an academic setting you just have to play along with certain systems and axioms the courses dispense and set aside any philosophical grievances. It's symbolic logic; very arid and linear but extremely simple if you put forth a focused, systematic effort. Our, but possibly just my problem is that I prefer an analysis with a bit more undisclosed ambiguity; to blindly accept the as absolute truth the sheer volume of theories and conjecture which were being shat out at me was very difficult until I accepted this.

Here's a solution to the first one. I'll post my two new problems tomorrow.

3. x>7
Man I'm good at this math thing.

1. Prove that the integers mod p are a field for p prime.
2. Let 0={ }
1={ }U{{ }}
n=(n-1)U{(n-1)}
for all natural numbers n
Define natural number addition in terms of sets.

>>68
1. Prove that the limit of a sum is the sum of the limits. lim a + b = lim a + lim b for two sequences a and b, provided that both limits exist.

2. Find the eigenvalues of the matrix:
[ 1 6 9 ]
[ 2 5 0 ]
[ 0 0 2 ]

>>73
First of all I don't know how to post properly...
As for "1. Prove that the limit of a sum is the sum of the limits. lim a + b = lim a + lim b for two sequences a and b, provided that both limits exist."
Let X be a subset of R, let E be a subset of X, let x[0] be an adherent point of E, and let f:X->R and g:X->R be functions. Now, suppose that f has a limit L at x[0] in E, and g has a limit M at x[0] in E. Then f+g has a limit L+M at x[0] in E since x[0] is an adherent point of E, then we can construct a sequence (a[n])n=0,infinity, consisting of elements in E, which converge to x[0]. Since f has a limit L at x[0] in E, (f(a[n]))n=0, infinity must converge to L. Similarly, (g(a[n]))n=0, infinity converges to M. By the limit laws for sequences (that is: lim of n->infinity (a[n]+b[n])= lim of n-> infinity a[n]+ lim of n->infinity b[n], since the sum of Cauchy sequences is Cauchy (Let x=lim n->infinty a[n] and y=lim n->infinity b[n] be real numbers. Then x+y is a lso a real number as for every epsilon>0 the sequence (a[n]+b[n])n=1, infinity is eventually epsilon-steady, show that (a[n]) is delta-steady, set delta equal to epsilon over 2, and show that this is eventually true for n>=N, similarly show this for (b[n]), this implies that a[n]+b[n] is eventually epsilon close when you add them) we conclude that ((f+g)(a[n]))n=0, infinity converges to L+M. this implies that f+g has a limit L+M at x[0] in E.
Sorry for getting a bit careless halfway, the typing was getting a little annoying, writing it down is much easier as you can clearly see everything.
PS: I just noticed I didn't directly answer your question, but also showed that this is true for added limits of functions :)
PPS: I just also realized I should answer in a picture... but last time I tried to upload a pic I got a temp. ban for some reason... sorry?

this might be a dumb question, but can't you just solve the DE's with the parameters as arbitrary constants?

>>159
I could, but they are arbitrary, large, and nonlinear, so it would be a lot of work, both to program it up and to compute it. Parsing the input strings is already kind of a headache, so if that's the best way to optimize it, I'll leave it for future work.

Actually, is there an algorithm for analytically solving any system of ODEs?

Have you checked if any Laplace transforms fit your setup? Make them all linear then, solve out the system in terms of the transform, then try to invert the transforms?

>>172
I actually have never used multidimensional Laplace transforms. Do they generalize pretty intuitively?

Just go to the library and find some relevant books. It should be pretty easy to find them.

Also stats isn't real math, go away!

>>53
Well since a deterministic model is simply a special case of a stochastic one (with probability=1), I have to disagree.

stats sux

I feel your pain OP

>>55
You're obviously feeling some other pain. I think statistical modeling is very interesting and has loads to offer as a mathematical field.

Well, you don't particularly need a calc background for intro stats. The reason the tell you look things up on the z table is because, for the most part, it's easier than computing an integral. I mean, what is the z table other than the integral of the bell curve with the same lower bound and varying degrees of upper bound? Though the math behind it is interesting, it doesn't really give the average person an understanding for the practical application of stats. That's why it's intro stats man hahaha. Go take some higher level stats courses, or get on 4chan/sci and check out the website in the very top thread. You'll find lots of resources there.

oh, now this looks ugly. Basically I'm asking for C_{0 }^{\infty}

C_0^\infty(\Omega) usually means the set of real-valued compactly supported smooth functions defined on \Omega. These functions are very useful tools in real analysis.

thanks a lot!

>>22
>Paul Erdos (" over the o)
¨ + o = ö

;-)

>>139
Ő, not Ö

SAGE has been used.

>>140
Well, given his linguistic peculiarities, I think that an ö would do.

I am surprised that no one has mentioned Benoit Mandelbrot. He is the man that made "fractals" a recognizable word, and in doing so tossing the importance and novelty of Euclidian geometry aside. In his famous book "The Fractal Geometry of Nature", he explains how ubiquitous fractals are in life, earth, physics, chemistry, art, ect… We probably would have the technological advancements of the 1990's if it weren't for him. Pic related.

David Hilbert. Mathematician that had an incredibly wide interests, also a logician.

To me, one of the most important things about the eigenvalues of a matrix is that the product of all of them equals the determinant of that matrix. When I first heard this, I had an overwhelming sensation of euphoria. Angels sang.

I'm sure there's more to be posted in this thread.

I always imagined them like: the eigenvectors of a matrix are the vectors that don't change direction when multiplied by that matrix, and the eigenvalues are how much the eigenvectors change in size.
So they're similar to fixed points.

>>149
Yes, eigenvectors as invariant linear subspaces is a very good way of interpreting them, especially if you're studying dynamical systems (see OP's pic).