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    The Shape of Spacetime.

    Just as an outsider reading this whole twofish-Ken G debate going on, I'll have two comments to make: 1) It has been very entertaining and as an undergraduate I have learned a lot from looking up a paper on a topic I did not know about when it was mentioned. 2) Twofish looks like he has a...
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    Is it normal to not understand any homework questions?

    Don't be disheartened if you can't figure out questions after trying for a long time. I took a upper-division logic class on Godel's Incompleteness Theorems, Model Theory, etc. and it took me a few hours to understand what the questions on the assignments were EVEN ASKING. I spent over 100 hours...
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    What math topics to learn next

    The following is the sequence I would recommend given your background. First and foremost: 1) Learn Linear Algebra! If you want a proof based approach I would recommend reading the chapter you need from Hoffman/Kunze, otherwise you can learn the computations and basic ideas from Gilbert Strang's...
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    Math REUs 2012

    Has anyone heard back from UCLA Logic Summer School? I haven't received a rejection letter but I also haven't heard ANYTHING. Has anyone else been rejected or accepted to this program? Does this mean I'm on a wait list?
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    Our picks for fourth quarter 2011 MIP (most important QG paper)

    Which is exactly why I voted for Shape Dynamics and Shape Dynamics only.
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    Characterizing Affine Independence

    Thank you very much, that clarifies a lot.
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    Characterizing Affine Independence

    Hello, I'm currently self-studying "An Introduction to Convex Polytopes" and I'm having some trouble understanding the different characterizations of affine independence. I understand that for an n-family (x_{1},...,x_{n}) of points from R^{d}, it is affinely independent if a linear combination...
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    How to figure out which deal on Soap is the best?

    Yes, I understand that now. Hopefully that helped.
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    Cos(x) question! How would you call 'x'?

    A variable? There's no set word to describe whatever variable you insert inside of a trigonometric function. You just say that it is the parameter in terms of which the function is defined...?
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    Cos(x) question! How would you call 'x'?

    Integration by Substitution? Let x = \theta ? The symbol \theta is pronounced theta? No idea what you are talking about. Just so you know, there is no simpler form to: \frac{sin(\theta)}{cos(2 \theta)} IT DOES NOT EQUAL: tan(\frac{1}{2} \theta) No idea if this helps, still have no...
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    How to figure out which deal on Soap is the best?

    Oh no it doesn't. Sorry I thought you meant 1 bar of 120g soap costs $2 and you want 2 of them, so that would be $4. Yeah, that doesn't affect anything. Just follow the ratios and you'll be fine! :D
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    How to figure out which deal on Soap is the best?

    Both of those deals are exactly the same. Check the ratio of the grams of soap you are getting for the amount of money. First one: \frac{120g}{\$2} = \frac{60g}{\$} So we have 60 grams per dollar for the soap. Second one: \frac{90g}{\$1.50} = \frac{60g}{\$} So, again...
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    How to figure out which deal on Soap is the best?

    Both of those deals are exactly the same. Check the ratio of the grams of soap you are getting for the amount of money. First one: \frac{120g}{\$2} = \frac{60g}{\$} So we have 60 grams per dollar for the soap. Second one: \frac{90g}{\$1.50} = \frac{60g}{\$} So, again we got 60 grams...
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    Functional Derivatives/Euler-Lagrange

    Homework Statement Hi, I'm working on research and I hit a roadblock with something that should be very simple but I can't solve it because it gets so messy. If anyone can let me know how to do this, it would be greatly appreciated. I have a functional T: T = \int_{\lambda_{1}}^{\lambda_{2}}...
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    Research vs Home for the summer

    If this is the summer between your first and second year then definitely go home and see friends and family. Spend your quality time during the summer having a break and just don't worry about school! If this was in between your second and third year then I may have different advice, and if this...
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    Courses What math courses are useful for physicists?

    Would it be a good idea, in preparation for a PhD program in Theoretical Physics, to just double major in Math as well as Physics in order to get a really firm grounding in Math?
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    Is this too much for a semester?

    Yeah, I did a combined honours degree in both Physics & Mathematics at UBC, I took 6 one semester. -3 Math Courses (1 300-level, 2 400-level) -2 Physics Courses (both 400-level) -1 Philosophy Course (300-level) And it was absolutely insane! 9 classes is absolutely impossible, I don't believe...
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    Is this too much for a semester?

    No way! Zif. 8 or 9 classes? That's literally impossible. I did 6 classes one semester and was totally swamped... there's no way they did good in those classes. 4 is a light-load if you are working part-time or something, 5 is the regular amount for full-time school, and 6 is really hard!
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    Trig Driving me Insane Take a look at this article and see if it answers any questions. If you still has some come back here and ask and I (or someone else) will answer you!
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    Studying Studying vs doing homework

    For a 3.8 - 4.0 GPA I would suggest to study for 50 hours a week outside of class during undergraduate school. You can afford to uphold a schedule like that (~10 hours a week per class) easily with taking most of saturday and sunday off and having two 4-hour outings throughout the week. Just be...
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    Emf of a single loop wire around a solenoid

    Are you sure the solenoid doesn't create a magnetic field?
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    Category theory

    Thanks so much for the material micromass! I've been very interested in Category theory recently as well. :D
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    What are some hot and new fields of research?

    Any idea what the prospects are like for Topology?
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    Teaching Conic Sections

    Show this animation in class! [Broken] It will be very helpful for the students who are not as good at mathematics and have a hard time visualizing the double-napped cone and intersections.
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    How can i calculate the attached integral?

    This is so beautiful!
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    Alright PF logged me out and erased all my work

    Give me a minute, I'll solve this. EDIT: Before I do anything. Are you sure that your expression here is correct?: I_2 B_1 = I_1 B_2 When I expand from: |F_{12}| = |-F_{21}| I get: I_1 l_1 B_1 = I_2 l_2 B_2 Where the lengths of the wires can cancel since they are the...
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    Convert to exponential form.

    I typed the LaTeX wrong the first time, the last expression should read: ({6x})^{3/4} Give that one a shot yourself and tell me where you get stuck, I'll be here reading this so I can help you along. :) (\sqrt[4]{(a^3)(b^5)})^{1/2} Hint: Remember roots are on the bottom, so convert the...
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    Convert to exponential form.

    (\sqrt[4]{6x})^3 Step 1: (({6x})^{1/4})^3 Step 2: ({6x})^{3/4} Technically, you can go farther but this is the simplest and most compact form. Remember when you are converting the square root into a fraction before you use the fractional exponent rule that, "Roots are located on the...
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    Help I can not solve this integral

    So, which question is it? (Before I spend a year doing partial fractions, completing the square, substitution, and god knows what else)
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    Help I can not solve this integral

    Did you use partial fractions to get that result? I think he may be referring to: \int{\frac{{x^2}+1}{{x^4}+1}dx}
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    I would like to argue about .999

    /thread This thread is INFINITELY hilarious because people don't need to say anything other than, "oh wow this proof is great."
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    Studying I'm doing EVERY exercise in munkres' topology textbook

    I thought I was ahead of the game when I took AP Calculus in Grade 11 (at age 15) and finished Multivariable Calculus when I was 16... since when is it normal for people to know calculus when they are 8-11 years old? D:
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    1 Divided by 3

    1 = 0.999... Proof: x = 0.999... 10x = 9.999... 10x - x = 9.999... - 0.999... 9x = 9 x = 1 :)
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    Simulating Galactic Evolution in a Game

    First off, I would just like to say that this an awesome project! Please don't give up working on it and I want to play when it's finished! Sounds like you've got a great plan going, would you be able to explain a little bit about what you intend to do with the game play aspect of it and why...
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    Schools Getting into grad school with a below 3.0 gpa?

    So what exactly did you major in? And why didn't you apply for Grad school? Why didn't you take the GRE?
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    Speed Writing

    Thanks for letting us know. GTFO
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    Why Is Perpetual Motion Impossible?

    Why does it violate the conservation of energy? Could a perpetual motion machine not be created that converts one form of energy into another by the use of a superfluid, so there is no loss of energy to the environment through friction...?
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    Why Is Perpetual Motion Impossible?

    Hey, Is the only reason for a perpetual motion machine being impossible, both in theory and in practice, simply due to friction? Because there are substances, such as superfluids, and potentially other forms of matter that could be discovered in the future where there is zero friction, so would...
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    Physics by correspondence

    I would recommend doing this if it means that it opens his possibilities for taking Physics 30 (Grade 12) and higher level physics. People NEED to know physics, I just stress that. Scientific literacy is so important today in order to have responsible citizens with a cosmic perspective that have...
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    Support PF: Buy your textbooks here

    DAMMIT. I just bought like $600 worth of textbooks and stuff right before I saw this post. :( OMG, so unfortunate.
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    Math mistakes

    Haha, that 2pi and 0 one canceling is absolutely hilarious!
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    Faster than light travel proved sort off

    You are NOT right all along, and you make so many inconsistent and absolutely appalling claims. The universe does not care if you believe a certain way, it will still behave according to its physical laws. You still don't understand the difference between weight and mass, why are you...
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    News Beginning of the end for government-funded scientific research [in America]?

    Yes, the United States has little to no chance of recovering back to what it once was. I suggest all scientists attempt to make their way to Canada and Europe.
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    Historical and Philosophical Foundations for Mathematics, Writing a Math Book There we go. Sorry, I just uploaded it to a random file hosting site... not trying to give people a virus or something, its like a 50kb word document X:
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    Historical and Philosophical Foundations for Mathematics, Writing a Math Book

    Hello, Recently I've been attempting to put together a brief book on mathematics. The first section is short and introductory as I lead up into calculus. I kind of feel bad that I skipped over conics, geometric series, permutations and combinations, transformations of functions, and so many...
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    Go slow or fast when teaching yourself math?

    That's great! Glad to hear that you are so ahead on math and are keen on learning more. :D Please keep up the good work!
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    NASA's future

    The eventual goal is to colonize the entire solar system and when all of the solar systems energy has been harnessed, or our sun comes closer to expanding into a red supergiant, we move to another star/planetary system. The entire point of living is to colonize the galaxy and immortalize the...
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    NASA's future

    Apparently, AIG is more important than creating a space-faring civilization as they received a bailout that rivaled the entire cost of the Apollo program and your projected $100 Billion. IMO, establishing a permanent base on both the moon and Mars >>...
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    Go slow or fast when teaching yourself math?

    I would suggest getting a handle on introductory: -Geometry (Areas, Volumes, etc.) -Trigonometry (to the extent that you understand the Unit Circle, the trig ratios, graphs, and functions) -Permutations and Combinations (not necessary, but will be later on in University) -Functional Analysis...
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    NASA's future

    I would argue that the overinflated portions of the budget that Defense and National Security get are not useful. The United States does not need to have military bases around the world or still be fighting wars in Afghanistan and Iraq. No one is attacking the United States. 9/11 was a one-time...