- Feb 2018
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yt-project.github.io yt-project.github.io
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Let’s use some common units as examples: gram (g), erg (erg), and solar mass per cubic megaparsec (Msun / Mpc33^3). g is an atomic, CGS base unit, erg is an atomic unit in CGS, but is not a base unit, and Msun/Mpc33^3 is a combination of atomic units, which are not in CGS, and one of them even has an SI prefix. The dimensions of g are mass and the cgs factor is 1. The dimensions of erg are mass * length$^2$ * time−2−2^{-2} and the cgs factor is 1. The dimensions of Msun/Mpc33^3 are mass / length33^3 and the cgs factor is about 6.8e-41.
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- Jul 2017
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www.degruyter.com www.degruyter.com
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satisfy the two usual distributive laws. Singlesemirings as well as classes of semirings form important structures in Automataand Formal Languages Theories [5
Like so.
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- May 2017
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coolwanglu.github.io coolwanglu.github.io
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1st order Eulerian numbers:Permutations
Annotate math with math!
$$\varepsilon = \frac{2}{h^3} \int_0^{p_F} \sqrt{p^2 c^2 + m^2 c^4} \cdot 4 \pi p^2 dp=$$
$$\frac{8 \pi}{h^3} \frac{m c^2}{\lambda^3} \int_0^x \sqrt{1+y^2} \cdot y^2 dy $$
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www.annualreviews.org www.annualreviews.org
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The first review, by C. Hendricks Brown et al., poses the issues raised by the growingrecognition
$$\varepsilon = \frac{2}{h^3} \int_0^{p_F} \sqrt{p^2 c^2 + m^2 c^4} \cdot 4 \pi p^2 dp=$$
$$\frac{8 \pi}{h^3} \frac{m c^2}{\lambda^3} \int_0^x \sqrt{1+y^2} \cdot y^2 dy$$
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- Apr 2017
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www.cogentoa.com www.cogentoa.com
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For detailed study of various properties, generalization and application of Wrightfunction and generalized Wright function,
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- Jan 2017
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betterexplained.com betterexplained.com
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Whether you're a student, parent, or teacher, this book is your key to unlocking the aha! moments that make math click -- and learning enjoyable.
You had me already at the Coffee Cup picture over the equations! :)
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academic.evergreen.edu academic.evergreen.edu
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LSB (least significant bit): The rightmost bit MSB (most significant bit): The leftmost bit
This only applies to Little-endian architecture. Big-endian is reversed.
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- Nov 2016
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www.knewton.com www.knewton.com
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x2
maybe it should be \(x^3\)
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- Oct 2016
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bullshit.ist bullshit.ist
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Sunil Singh asks us to stop promoting mathematics based on its current applications in business and science. Math is an art that should be enjoyed for its own sake.
This reminded me of A Mathematician's Lament by Paul Lockhart. This is a 25-page essay which was later worked into a 140-page book. (And Sunil Singh has read at least one of them. He credits Lockhart in one of the replies.)
It also reminds me of this article on the history of Gaussian elimination and the birth of matrix algebra. Newton's algebra text included instructions for solving systems of equations -- but it didn't have much practical use until later. (Silly word problems are as old as mathematics.)
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- Sep 2016
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en.wikipedia.org en.wikipedia.org
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A forest is just a collection of trees. The main difference is that a forest does not necessarily need to be connected.
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- Jul 2016
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www.quantamagazine.org www.quantamagazine.org
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hyperuniform distribution - Appears random at smaller scales, but more predictable at larger scales.
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steinhardt.nyu.edu steinhardt.nyu.edu
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The first set, called Math Instructional, was for apps that would make math relevant for students by linking it to their lives and enabling students at different ability levels to work together
This has real potential because of the research base that supports the instructional approach.
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- Mar 2016
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www.quantamagazine.org www.quantamagazine.org
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New property of prime numbers discovered. Primes greater than 5 can end with 1, 3, 7, or 9. The next prime is less likely to end with the same digit, and biased toward one of the remaining three. For instance, a prime ending in 3 is most likely to be followed by a prime ending in 9. The bias evens out as the primes get larger, but only very slowly.
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- Feb 2016
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www.math-cs.gordon.edu www.math-cs.gordon.edu
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Number Theory: In Context and Interactive, Karl-Dieter Crisman (online textbook)
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linear.pugetsound.edu linear.pugetsound.edu
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A First Course in Linear Algebra, Robert A. Beezer<br> Free as PDF or online.
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www.complexityexplorer.org www.complexityexplorer.org
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Free courses and tutorials from the Santa Fe Institute on subjects related to complex systems science.
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- Jan 2016
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blogs.scientificamerican.com blogs.scientificamerican.com
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P(B|E) = P(B) X P(E|B) / P(E), with P standing for probability, B for belief and E for evidence. P(B) is the probability that B is true, and P(E) is the probability that E is true. P(B|E) means the probability of B if E is true, and P(E|B) is the probability of E if B is true.
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The probability that a belief is true given new evidence equals the probability that the belief is true regardless of that evidence times the probability that the evidence is true given that the belief is true divided by the probability that the evidence is true regardless of whether the belief is true. Got that?
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www.gutenberg.org www.gutenberg.org
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I would like to see an accurate array of photographs of these tasty lunch options. What does a a "Princess Sandwich" even look like? Is a "Celery Sandwich" satisfying? I'd be pleased to see precise measurements of the ideal "Tea Biscuit" Sandwich.
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category-theory.mitpress.mit.edu category-theory.mitpress.mit.edu
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Category Theory for the Sciences by David I. Spivak<br> Creative Commons Attribution-NonCommercial-ShareAlike 4.0<br> MIT Press.
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Open source textbooks approved by the American Institute of Mathematics.
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- Mar 2015
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arxiv.org arxiv.org
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θ dμ ≥ p 16 π | Σ |
Qual a relação dessa desigualdade com a dita desigualdade de Penrose Riemanniana provada por Huisken-Ilmanen e Bray?
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GIBBONS-PENROSE INEQUALITY
Qual a relação dessa desigualdade com a dita desigualdade de Penrose Riemanniana provada por Huisken-Ilmanen e Bray?
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θ dμ ≥ p 16 π | Σ |
Isso significa que a taxa expansão nula futura (para fora) \( \theta \) é no mínimo $$ \sqrt{16 \pi |\Sigma|} $$
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- Jan 2015
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mathinsight.org mathinsight.org
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A function like f(x,y)=x+y is a function of two variables. It takes an element of R2, like (2,1), and gives a value that is a real number (i.e., an element of R), like f(2,1)=3. Since f maps R2 to R, we write f:R2→R. We can also use this “mapping” notation to define the actual function. We could define the above f(x,y) by writing f:(x,y)↦x+y. To contrast a simple real number with a vector, we refer to the real number as a scalar. Hence, we can refer to f:R2→R as a scalar-valued function of two variables or even just say it is a real-valued function of two variables. Everything works the same for scalar valued functions of three or more variables. For example, f(x,y,z), which we can write f:R3→R, is a scalar-valued function of three variables.
f:R^2 \rightarrow R demek f(x,y)=z | Skalar-Değerli f f:R \rightarrow R^2 demek f(x)=(y,z) | VektörelDeğ f
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f:R→R as a shorthand way of expressing that f is a function from R onto R.
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- Sep 2013
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en.wikipedia.org en.wikipedia.org
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A computable Dedekind cut is a computable function which when provided with a rational number as input returns or ,
This definition of computable Dedekind cut is wrong. The correct definition is that the lower and the upper cut be computably enumerable.
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