221 Matching Annotations
  1. Jan 2017
  2. Nov 2016
  3. Oct 2016
    1. 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.)

  4. Sep 2016
  5. Jul 2016
    1. 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
  6. Mar 2016
    1. 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.

      http://arxiv.org/abs/1603.03720

  7. Feb 2016
    1. Free courses and tutorials from the Santa Fe Institute on subjects related to complex systems science.

  8. Jan 2016
    1. 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.
    2. 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?
    1. 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.

    1. Category Theory for the Sciences by David I. Spivak<br> Creative Commons Attribution-NonCommercial-ShareAlike 4.0<br> MIT Press.

  9. Mar 2015
    1. θ dμ ≥ p 16 π | Σ |

      Qual a relação dessa desigualdade com a dita desigualdade de Penrose Riemanniana provada por Huisken-Ilmanen e Bray?

    2. GIBBONS-PENROSE INEQUALITY

      Qual a relação dessa desigualdade com a dita desigualdade de Penrose Riemanniana provada por Huisken-Ilmanen e Bray?

    3. θ dμ ≥ p 16 π | Σ |

      Isso significa que a taxa expansão nula futura (para fora) \( \theta \) é no mínimo $$ \sqrt{16 \pi |\Sigma|} $$

  10. Jan 2015
    1. 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

    2. f:R→R as a shorthand way of expressing that f is a function from R onto R.
  11. Sep 2013
    1. 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.