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    Quantum QM Book for non-physisists

    Have a look at the open access textbook Quantum Computing for the Quantum Curious by Hughes et al. Description from the Springer website: "This book is open access, which means that you have free and unlimited access. Demystifies quantum computing, using only high school physics. Bridges the...
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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: http://mathforum.org/library/drmath/view/74063.html
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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: http://math.stackexchange.com/a/543800 And two more links for the proof of the sign-preserving property: https://math.la.asu.edu/~dajones/class/371/ch4.pdf...
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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 http://www.thefouriertransform.com/#introduction 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: https://www.youtube.com/watch?v=bFNjA9LOPsg
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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: http://www.personal.ceu.hu/tex/breaking.htm
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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 http://calculus-geometry.hubpages.com/hub/Disk-Method-Volume-of-Solid-of-Revolution...
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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.
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    What is the difference between a differential equation and a derivative?

    A differential equation is an equation that contains a function f(x) and one or more derivatives of f(x). Example 1: f(x) = -f ''(x) This is a differential equation since it contains f(x) and the second derivative f ''(x). The goal is to find a function f(x) that fulfills the differential...
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    Find orthogonal vector to current vector in 3D

    You can use the dot product. For example, if you have a vector v and want to find vector c that is orthogonal to v, then use the dot product <v,c> and set it equal to 0. Example: v = (4,2,3) c = (x,y,z) = ? (i) Set the dot product to zero: <v,c> = 4x + 2y + 3z = 0 (ii) Choose some...
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    The question is , if f(n)= 1+10+10^2 + + 10^n , where n is

    You can also find n by "brute force", i.e. check if f(1), f(2), f(3), ... is divisible by 17. Use http://www.wolframalpha.com/ or write a small program in your programming language of choice.
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    Started an experiment , triboluminescence

    I observed triboluminescence by using adhesive tape. However, I found that not every tape showed the effect. Even tapes of the same brand showed different behavior (they only differed in size). I also recommend staying in a very dark room for a couple of minutes such that your eyes adapt to the...
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    Java Java noob - help setting up eclipse

    Here is a youtube video that shows how to install Eclipse on Windows:
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    How to Get Good At Problem-Solving ?

    Problem solving is about asking the right questions. Polya, a famous mathematician, described these questions in his book "How to solve it". A summary can be found here: http://www.math.grin.edu/~rebelsky/ProblemSolving/Essays/polya.html http://www.math.utah.edu/~pa/math/polya.html
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    C/C++ Tutorial For Vectors in C++?

    Here are some articles on vectors using C++ in game programming: Math for game programmers 02 – Vectors 101 C++ Vector Class Youtube video: Advanced C++ Tutorials 1 : Vectors & Physics : Convert Polar to Cartesian Advanced C++ Tutorials 2 : Vectors & Physics : Cross Product
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    Question about .9999

    0.999... = 1 is not a definition. It is a result as mentioned by haruspex. 0.999... is defined as \sum_{k=1}^{\infty}9/10^k, i.e. it is the limit of the sequence s_n = \sum_{k=1}^{n}9/10^k. s1 = 0.9 s2 = 0.99 s3 = 0.999 ... One can show that this sequence converges to 1, i.e. if I...
  40. E

    Any Piano players out there?

    I've been playing the piano for about 3 years. I love it too! I find it super relaxing. The best thing about it is since I've started playing the piano I learned so much more music. I learned about classical music and jazz. Here is for example an inspiring talk about classical music...
  41. E

    Meaning of in partial fulfillment

    Thanks denjay!
  42. E

    Sum converging to 0

    If \sum ^{\infty}_{n=1}m(0.5)^{n} converges to m, then shouldn't m-\sum ^{\infty}_{n=1}m(0.5)^{n} converge to 0?
  43. E

    Meaning of in partial fulfillment

    Thanks. To me it sounded as if only parts of the requirements for the thesis have been fulfilled.
  44. E

    Meaning of in partial fulfillment

    Meaning of "in partial fulfillment" In a thesis one often finds this sentence: "A thesis submitted in partial fulfillment of the requirements for the degree of... ", e.g. here: http://dmg.caup.washington.edu/pdfs/Thesis.HunterRuthrauff.2012.pdf What does "in partial fulfillment" mean, in...
  45. E

    Lattice points on a circle.

    What do you mean by lattice points? Points (x,y) where x and y are integers? The circle with radius 1/sqrt(2) comes to my mind.
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    Physical meaning of curl

    Here's an intuitive explanation of the curl: http://youtu.be/Mt4dpGFVsYc
  47. E

    Boltzmann and Fourier for biologist

    The basic idea behind a Fourier transformation is to represent a function f(x) as a sum of other functions b1(x), b2(x), ..., bn(x): f(x) = c1*b1(x) + c2*b2(x) +...+ cn*bn(x) The c's are the coefficients. Let's take a very easy example: Suppose you are given the functions b1(x) =...
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    Recursive vs iterative approach

    I recommend looking at the factorial function. It can both be implemented iteratively and recursively. As already mentioned iteration involves using for loops. The recursive approach uses a function that calls itself. This sounds a little strange but let's have a look at how 3! is calculated...
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    What is the square root of x^2?

    I think the confusion stems from two things: 1. Solving for x in the equation x^2 = a. 2. Using the square root function. If you are given the equation x^2 = a, then there are two solutions, namely a positive and a negative: x = \sqrt{a} and x = -\sqrt{a}. However, if you are using the...
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    Felix Baumgartner and 120,000ft

    The moment when he was spinning was very scary. Here is an interview of him: http://kurier.at/video/nachrichten/1900974173001-felix-baumgartner-ich-hatte-traenen-in-den-augen.php In German Baumgartner: "It really started to get violent. For a few seconds I thought I would lose my...
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