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    Quantum Springer discount code CYBERWEEK19 - English IT books only 7 Euro

    Use the discount code CYBERWEEK19 to purchase English IT eBooks from Springer online for only 7 Euro. Go to the checkout and enter the code. Afterwards, you can proceed browsing the book list and it automatically shows if the code was applied. Note: At the checkout read again if the discount...
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    Analysis Springer math books 40% off till Nov 30

    Springer math books are 40% off till Nov 30. Coupon code is MATH19PE. I bought Linear Algebra by Axler , the analysis books by Pugh and Abbott. Any further recommendations for good books?
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    I Merging neutron stars

    5 minute video by Veritasium (Derek Muller) on the event:
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    I Contradiction vs contraposition

    You are asking about the difference between "Proof by contraposition" and "Proof by contradiction", and here is an example. To prove p \rightarrow q: - In proof by contraposition you start by assuming that \neg q is true and derive the statement \neg p. Here, the path is clear, i.e. you start...
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    B Help simplifying an equation

    I typed your equation and "simplify" into wolframalpha, and this is what I got It has a simpler looking form for x, d and theta real.
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    Neural networks and the derivatives of the cost function

    Here is a derivation from stats.stackexchange that you may find helpful. It is basically about the chain rule for derivatives.
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    AlphaGo success

    Result of match 4: Article by GoGameGuru Article by Wired
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    AlphaGo success

    Great article on the third match between AlphaGo and LeeSedol.
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    AlphaGo success

    Result of the second match between AlphaGo and Lee Sedol.
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    YouTube Classics, Part Deux

    Look how beautiful the ostrich's running technique is! My favorite part is the left and right swerving, but why does the ostrich do it?
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    Google's AI beats world Go champion

    Go has been considered one of the games in which the human is superior to any AI. However in a first match Google's AI has beaten world Go champion Lee Se-dol. Earlier this year the AI beat the European Go champion.
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    I The Hamiltonian

    Right-click on the math error, go to Math Settings -> Math Renderer and try e.g. HTML-CSS (or some other renderer).
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    Insight/Intuition into rotations in R²

    Here is a good explanation:
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    Summation Convention – Substitution Rule

    Try to get an intuitive feeling for what the Kronecker-Delta \delta_{ij} does. Consider this sum: \sum_{j=1}^{n} c_j = c_1 + c_2 + \dots + c_n Now observe what happens if we multiply with the Kronecker-Delta: \sum_{j=1}^{n} \delta_{ij} c_j = \delta_{i1} c_1 + \delta_{i2}c_2 + \dots +...
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    Summation with no argument

    For a sequence (a_n)_{n \in \mathbb{N}} you can form the series \sum_{n=0}^\infty a_n = a_0 + a_1 + a_2 + \dots. If you take the sequence a_n = 1 and plug it into the expression above, then you get the series \sum_{n=0}^\infty a_n = \sum_{n=0}^\infty 1 = 1 + 1 + 1 \dots . Or consider the...
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    A Advanced LIGO detection

    This nature article mentions that other interferometers such as Geo600 in Germany and Virgo in Italy were not operating at the time . Is it known whether Geo600 would have detected the gravitational waves? What happens with gravitational waves? Do they exist forever or can they be absorbed or...
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    Proof: integral of continuous function is 0 so function is 0

    Here is a proof mentioned on math.stackexchange using the "sign-preserving property" of continuous functions: And two more links for the proof of the sign-preserving property:
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    Proof of limits

    One way to understand this is to interpret it as a two-player game, let's say between you and me. The game works as follows: I give you a number \epsilon > 0, and your task is to find a number \delta > 0 such that a certain condition is fulfilled. You can read about this two-player game...
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    How to become good programmer?

    You may find the course Programming Mobile Applications for Android Handheld Systems on Coursera interesting. It starts on Sept 26th 2014.
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    Enrollment in C programming course

    I recommend these C tutorial videos by iTzAdam5X. He uses CodeBlocks. Each video lasts for five to ten minutes.
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    What is ∞ exactly?

    Here is a definition of what the limit means when it involves infinity: \lim_{x \to +\infty}f(x) = +\infty if for every number M>0 there is a corresponding number N such that f(x)>M whenever x>N. Intuitively this means, if I give you a positive number M, then you can find a number N such that...
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    Fourier transform and the frequency domain

    Here are some nice videos that explain the time and frequency domain: Intro to Fourier Transform, see also the website Fourier Transform Introduction Fourier transform explained with an oscilloscope
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    How to write Math Proofs

    Approved textbooks by The American Institute of Mathematics (the books are open-access): 1) A Gentle Introduction to the Art of Mathematics by Joe Fields 2) Mathematical Reasoning: Writing and Proof by Ted Sundstrom
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    History of American PI

    Story told by Numberphile:
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    Tips for proofs

    Here's a thread with lots of links to material on proofs: How to write math proofs
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    LaTeX Double Line in LaTeX

    You have to use "\\" and not "//" if you want a linebreak. See here:
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    Subsequence that Sums Up to Half the Total Sum

    Look up the partition problem. It seems that it can be solved with dynamic programming.
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    How to determine volume from a picture?

    Do you mean by surface the purple curve? If yes, you could rotate this curve around the "x-axis" as shown here. You would have to adjust the jpeg to make the balloon symmetrical around the x-axis. The idea is to
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    Vector Projection

    The purple vector is the projection of \vec{u} onto \vec{v}. Now, you have to think of how the purple vector is defined. It has (i) a length and (ii) a direction. (i) The length of the purple vector is | \vec{u}| \text{cos}(\theta). (ii) The direction of the purple vector is the same as that of...
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    Vector Projection

    In case you are asking for the derivation of the formula I've drawn a sketch (see attachment). You can see that it is indeed just expressing the cosine in terms of the dot product.