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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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    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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    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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    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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    Object Slowing on a Horizontal Surface after Rolling down an Inclined Plane

    Homework Statement Block A starts from rest and slides 8m down a frictionless 30 degree angled inclined plane. It then crosses a 4m horizontal surface where the coefficient of kinetic friction is 0.2. What is the velocity of Block A after it has finished crossing the horizontal surface...
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    Programs Bsc, PhD at one school. Is this bad?

    Hi, I'm going to be applying to graduate schools for next fall semester and am finishing my last semester in a Bsc (Honours) Astrophysics program at the University of Alberta. I know a lot of the professors in the department here and have some that I know would be more than willing to be my...
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    Uranus and Neptune Orbiters

    Not exactly sure what forum I should post this in, feel free to move it to a more appropriate forum if you wish! Following the successful Galileo and Cassini missions to Jupiter and Saturn, respectively, and with another mission to Jupiter (Juno) coming up shortly I think it is time that the...
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    Advice on Actualizing My Goals

    Well... although I thought of throwing my computer out the window a minute ago I think that it's fortunate that my entire life story I just typed up didn't get submitted due to the power going out (I hate wasting an hour of my life). I'll be far more concise this time and get to point about what...
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    Doubting My Math Skills, Going Into Engineering/Science

    Hello, I've generally never been a good math student my entire life and up until Grade 11 I was in Applied Math (rather than Pure, which is a step up in Alberta). In Grade 11 I switched into Pure Math 20 and studied extremely hard to end up with an 85%. I'm currently in Grade 12 and taking Pure...
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    Potential View of Cosmology?

    Hello, I've been thinking recently about the truths and realities that are found in the Universe and I just wanted to share a bit of what I have been thinking about. I'm 16 years old right now and I have a drive to understand the way nature displays itself to conscious beings. I'd like to...
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    Trouble Understanding Boson Decay

    Hello, Just to give a little background here, I am entering into a Bsc (Hons) Physics major next year at the University of Saskatchewan and I have just been reading some books and learning about the standard model over the summer and I had a quick question. Most recently I just finished 'Beyond...
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    Finding a Career in Space Exploration

    Hello! I wanted to see if anyone here would be able to help give me some advice about my University education. I've just graduated from High School and I got my marks on my Diploma Exams back (In Alberta, Canada there is a Standardized Provincial Exam at the end of each Grade 12 course that is...
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