factor out the GCF for the polynomial 75m(to the 5)n(to the 7) - 45m(to the 3)n(to the 4) + 90m(to the 4)n(to the 6)
factor out the GCF for the polynomial 7x(2m-5) - 4y(2m-5)
Grrr…GCF, I hate problems like these. I was doing cool up until here!
NVD I GOT IT :bgrin:
math is depressing…
Ive spent the last 4 years trying to become an actuary, and lack of success has finally caught up to me.
I havent studied for a month… and the exam (MFE) is next week!!!
f(0,0) = (0,0)^2 + (.5,.5) = (0,0) + (.5,.5) = (.5,.5)
f(.5,.5) = (.5,.5)^2 + (.5,.5) = (0,.5) + (.5,.5) = (.5,1)
f(.5,1) = (.5,1)^2 + (.5,.5) = (-.75,1) + (.5,.5) = (-.25,1.5)
f(-.25,1.5) = (-.25,1.5)^2 + (.5,.5) = (-2.1875,-.75) + (.5,.5) = (-1.6875,-.25)
f(-1.6875,-.25) = (-1.6875,-.25)^2 + (.5,.5) = (2.7852,.84375) + (.5,.5) = (3.2852,1.34375)
Not sure why if it "escapes" the unit circle of radius 2 then its as good as gone
I used to ask my dad for help with my math homework at school (lol), but he’s never seen a mandelbrot set before which was surprising. Hes got a phd in oceanography and wrote his dissertation on “equilibrium solutions of the global-scale water masses, meridional circulation, and heat transport with isopycnal ocean models” so once he gets up to speed on this fractal stuff he could probably figure it out.
And here I thought I was the only (prospective) actuary on SRK.
Something I wrote when I was bored. I figured this would be the place to put this.
[media=youtube]WbfYHagAQeI[/media]
edit: I just looked at some of the other math raps on Youtube. Them shits is corny as hell. I don’t know how I can get more hits, but I’d like to have something more listenable to combat the bullshit.
Oh GRE Math Subject exam… studying for you takes away my attention from the math I’d rather do…
Man, my Linear Algebra professor is kicking my butt. He’s such a tough grader it’s ridiculous. I guess this is my punishment for having an easy Calc 3 Professor.
The semester is coming to an end soon and in my Calc 2 class my prof saved the best for last… infinite series and sequences !
It could be just the professor, but Linear Algebra is the class where the level of rigor goes up a bit. It’s sort of expected. Bear with it though, Linear Algebra is worth it!
Those are pretty fun, albeit there are going to be about 6-7 tests you will have to learn. If you plan on taking Real Analysis later on, pay particular attention to sequences. Also, it doesn’t work on every series, but the Root and Ratio tests are pretty useful in general to start evaluating an infinite series (though I don’t know if the prof will allow you to use them early on… still, once you actually get there, you’ll get almost as much mileage out of them as you will testing to see if the sequence in the infinite series goes to 0 or not)
In my college, I’m allowed to take Linear Algebra and Calc 3 for next semester. Do you think that’s a good idea?
Depends on your goals and what you want to do. If you’re a math major, you’ll have to take linear algebra, so that is moot. As for Calc 3, well, if you were good in Calc I and Calc II, then Calc III takes the same ideas but adds an extra variable. It’s useful in a lot of areas. You can model 3d vectors, the partial derivatives you’ll learn will be useful in Complex Analysis for the Cauchy Riemann equations. Theres a chapter on vectors, dot products, and cross products that intersects with one of the chapters you’ll be doing in Linear Algebra. I’d definitely recommend it, but only if you’re comfortable with Calc I and II.
I should add this is a conversation you should have with your advisor.
Maybe I should rephrased what I meant. I’m an EE major so I have to take those classes anyways haha. My question is, is it smart to take both of those classes at the same time. Or should I just spread it out.
That’s a tricky question because I don’t know if there is a Linear Algebra class at your institution that is divorced from focusing on proofs and is for non-math majors. Linear Algebra for math majors typically begins with a basic intro to logical proof. You learn various proof techniques and focus on utilizing those. From there you start learning Linear Algebra and there is a mild nudge towards proving things. It’s not as rigorous as say real analysis, but it isn’t always as simple as “use formula x to answer question y.” My point is that if you are comfortable with spending some time thinking about how to prove theorems, then go ahead and take both. Otherwise you may wish to spread it out. Also, Linear Algebra is a bit more abstract and it isn’t always obvious how it would apply to EE. If you are a visual person you might struggle with it since outside of 3 dimensions you can’t really “see” what is being taught. If you’re comfortable with more abstract thinking though, this might not give you such a problem. Find out who the professor(s) is that will be teaching Linear Algebra and ask him about how the course is taught.
Since you are an EE major, I’m assuming you are taking the 2nd in the series of Physics for engineers, so that would be a pretty good load right there.
2nd(or 1st) Physics, Calc 3, Linear Alg. You will have no life, but you will be on the right track. This is what some people are doing in my LA class.
Right now I’m doing the 1st in the Physics series (classical mechanics), Organic Chem. 1, and L.A.
My life sucks.
Linear Algebra is not difficult… it’s just very abstract, and due to my other classes, this one has been on the back burner all semester X_X. Not that it’s easy, all of the stuff with basis, vector spaces, sub spaces, etc., really mind blowing stuff.
Infinite dimensions? What the hell is that even supposed to mean?
edit: if you have a job, quit. i’m pulling 30 hours a week, and though i can study at work, i’ve never wanted to get out of a situation so bad, but i am stuck…
Your first part of your response has to do with the second. So, here’s a recap:
A set is just a collection of objects with some property. We also say that an element of this set is a member of this set For instance, We can let S represent the set of all people in the world who have an SRK account. You, me, and everybody with a SRK ID can be considered an “element” of this set.
So now we consider a different set with different elements. The set is the set of all vectors that have a fixed number of components. So, for simplicity, lets just focus on the set of all vectors with two components. This set is labeled R^2. The elements of this set are simply any vector with two components. Examples are (0, 0), (1/2, e), (- Pi, 5). If one already knows that this set satisfies the 10 vector space axioms, then one labels this set a vector space. It then follows that this set, and every element in this set has the 10 vector space properties.
We say a subset of a set is simply some collection of the elements in the original set. This could be ALL the elements, some of the elements, or none of the elements. If S represents our original set of SRK’ers, then we could consider the set of all people who post in this thread a subset of S.
So, a subspace of a vector space applies a similar idea: For instance, in R^2, We consider the set of some vectors that are already in this set, such as the set of all vectors with 0 as the second coordinate. If we already know that the subspace we are considering is a part of a vector space, then we only need to check for two things: If I add 2 vectors in this subspace, will I get a vector that is contained only in this subspace? Similarly, if I take a vector and multiply it by a scalar, will I get a vector that is contained only in this subspace?
The answer to this question for this subspace is yes since for any real numbers a, b, and scalar k we have (a, 0) + (b, 0) = (a + b, 0) and k*(a, 0) = (ka, 0). Notice that the result maintains the property of the subset: that is, a vector whose second coordinate is zero. Had we come across even one vector that did NOT have this property, then we would have concluded that this is NOT a subspace.
What we are looking to do is to find a way to write ANY vector in a vector space using only a finite number of vectors. This is the idea behind a basis: If I have a basis for a vector space, I can write any vector in that vector space by adding some combination of ONLY these vectors, well, I should say some scalar multiples of these vectors.
For example, A basis for R^2 is the following two vectors: (1, 0) and (0,1). Give me ANY vector with two components, and I can write it using only scalar multiples of these two vectors.
e.g. (2, 3) can be written as 2*(1, 0) + 3*(0,1) = (2, 3)
This of course is not the ONLY basis for R^2. Bases are not unique. For example, (0, 2) and (1, 9) could be used, (5, 3), (2, -1) could be used, etc. What the vectors must have in common is that they must be linearly independent and they must span the vector space that you are looking for a basis for.
It should be noted though that one way to check to see whether some set of vectors forms a basis is whether or not their determinant is nonzero. This is how I picked those vectors for the bases up there. There is a big list of equivalency statements that you MUST know to navigate around linear algebra and this is a couple of them for an nxn matrix A: The determinant of A is not zero iff the column vectors form a basis for R^n iff the reduced row echelon form of A is the identity matrix. So, rather than do row reduction for simple 2x2 matrices, just check if the determinant is nonzero and you verify that your vectors is a basis.
BUT, what can we say about the number of vectors for a basis of a vector space and its dimension? Simple, they are one in the SAME. The dimension of a vector space is the number of basis vectors that make up its basis. So, a vector space with infinite dimensions is simply one that have an infinite number of basis vectors. You won’t need to worry about this unless you go on to grad school and take a more advanced linear algebra course and/or functional analysis, which actually focuses on doing linear algebra in infinite dimensions.
Well, that should catch you up. Have fun
Man, some of you guys can help me I bet. I love math, just cuz it was always fun and always made sense to me. Thing is, I wasn’t really formally educated. I.e. I was supposed to take a trigonometry class but instead I decided to just do credit by exam. Having had no trig under my belt, I found out what book the class used, read through the book like a text book for a week (no pen, no paper, no practice) and then took the final. I passed. Problem with that is that I’m pretty sure, I didn’t retain most of it. I still have never taken a class that used matrices, but I know when I took that exam I had them down.
Warrior’s Dream, u seem like you really love this math and like to share it. I swear I’m super passionate about math, but I’m probably super ignorant on the subject. You think you could teach me on ur free time? I wanna learn all this stuff, even if I’ll never actually use it.
I’d recommend getting this: Dictionary of Mathematics Terms (Barron’s Professional Guides)
I recently started going to school again to study math and this book has been immensely helpful. I started reading from the preface and from there it’ll have you look up definitions (which have you look up more). From that I’ve been able to relearn and get a better grasp of the fundamentals. It’s also good for whenever you see an unfamiliar term or if you have a few spare minutes.
Another book I’ve been getting into is “How to Calculate Quickly” which is more or less a course on quickly working with large numbers in your head. Also a great book to read every now and then when you have free time (teaches by short exercises as opposed to reading a lot of text)
Sure. Post questions and I will answer them
Is there anything that can’t be represented/explained mathematically?
Women.