300 Matching Annotations
  1. Jul 2022
  2. Jun 2022
  3. May 2022
    1. We don’t know how many media outlets have been run out of existence because of brand safety technology, nor how many media outlets will never be able to monetize critical news coverage because the issues important to their communities are marked as “unsafe.”
    1. With Alphabet Inc.’s Google, and Facebook Inc. and its WhatsApp messaging service used by hundreds of millions of Indians, India is examining methods China has used to protect domestic startups and take control of citizens’ data.

      Governments owning citizens' data directly?? Why not have the government empower citizens to own their own data?

    1. **The Cauchy-Schwarz Inequality** $$\left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right)$$

      This sentence uses $ delimiters to show math inline: $\sqrt{3x-1}+(1+x)^2$

    1. ```html

      <script type="application/ld+json"> { "@context": "https://schema.org", "@type": ["MathSolver", "LearningResource"], "name": "An awesome math solver", "url": "https://www.mathdomain.com/", "usageInfo": "https://www.mathdomain.com/privacy", "inLanguage": "en", "potentialAction": [{ "@type": "SolveMathAction", "target": "https://mathdomain.com/solve?q={math_expression_string}", "mathExpression-input": "required name=math_expression_string", "eduQuestionType": ["Polynomial Equation","Derivative"] }], "learningResourceType": "Math solver" }, { "@context": "https://schema.org", "@type": ["MathSolver", "LearningResource"], "name": "Un solucionador de matemáticas increíble", "url": "https://es.mathdomain.com/", "usageInfo": "https://es.mathdomain.com/privacy", "inLanguage": "es", "potentialAction": [{ "@type": "SolveMathAction", "target": "https://es.mathdomain.com/solve?q={math_expression_string}", "mathExpression-input": "required name=math_expression_string", "eduQuestionType": ["Polynomial Equation","Derivative"] }], "learningResourceType": "Math solver" } </script>


  4. Apr 2022
    1. The symbol dx has different interpretations depending on the theory being used. In Leibniz's notation, dx is interpreted as an infinitesimal change in x and his integration notation is the most common one in use today. If the underlying theory of integration is not important, dx can be seen as strictly a notation indicating that x is a dummy variable of integration; if the integral is seen as a Riemann integral, dx indicates that the sum is over subintervals in the domain of x; in a Riemann–Stieltjes integral, it indicates the weight applied to a subinterval in the sum; in Lebesgue integration and its extensions, dx is a measure, a type of function which assigns sizes to sets; in non-standard analysis, it is an infinitesimal; and in the theory of differentiable manifolds, it is often a differential form, a quantity which assigns numbers to tangent vectors. Depending on the situation, the notation may vary slightly to capture the important features of the situation. For instance, when integrating a variable x with respect to a measure μ, the notation dμ(x) is sometimes used to emphasize the dependence on x. Source: http://en.wikipedia.org/wiki/Integral#Terminology_and_notation

      Why is there a \(dx\) at the end of the integration notation?

    1. In this case, for a test to be statistically significant, p-value must be lower than 0.05.

      statistical significance should be less than 5%

      tf your confidence that the results are not due to chance is 95%

    1. We are 99% confident that the true average “attitude” difference betweenliving environments is between 1.32 and 7.88. At a significance level of 0.01we can say that living in a minority environment is associated with higherscore

      99% confident that the true average (result) is between these two numbers;

      at 1% (0.01) significance, we can scientifically assume there is a causal relationship

    1. While it was once regarded as a low-level, “primitive” instinct, researchers arecoming to recognize that imitation—at least as practiced by humans, includingvery young ones—is a complex and sophisticated capacity. Although non-humananimals do imitate, their mimicry differs in important ways from ours. Forexample, young humans’ copying is unique in that children are quite selectiveabout whom they choose to imitate. Even preschoolers prefer to imitate peoplewho have shown themselves to be knowledgeable and competent. Researchshows that while toddlers will choose to copy their mothers rather than a personthey’ve just met, as children grow older they become increasingly willing tocopy a stranger if the stranger appears to have special expertise. By the time achild reaches age seven, Mom no longer knows best.

      Studies have shown that humans are highly selective about whom they choose to imitate. Children up to age seven show a propensity to imitate their parents over strangers and after that they primarily imitate people who have shown themselves to be knowledgeable and competent within an area of expertise.

      This has applications to teaching with respect to math shaming. A teacher who says that math is personally hard for them is likely to be signaling to students that what they're teaching is not based on experience and expertise and thus demotivating the student from following and imitating their example.

    1. Learning to "factor an equation" is the process of arranging your teepee. In this case: If x=−3 then Component A falls down. If x=2, Component B falls down.

      doesnt really explain how to get the factors. Which for most binomials is done by creating a table of numbers that multiply to create the last number while adding up to create the middle x

    1. We invented the decimal point to handle the crazy idea of a number more than zero but less than one.

      Zeno's paradox comes to mind. The idea is that you never get from zero to one or vice versa, but rather infinity closer to one or the other. But what does getting to 2 mean? A "leap" through 1? Infinitly close to 1 - twice?

    2. using the symbol 0 to represent nothingness

      is there another symbol for potential like a placeholder character?

  5. Mar 2022
    1. 618034

      "The first known calculation of the golden ratio as a decimal was given in a letter written in 1597 by Michael Mästlin, at the University of Tübingen, to his former student Kepler. He gives "about 0.6180340" for the length of the longer segment of a line of length 1 divided in the golden ratio." from https://mathshistory.st-andrews.ac.uk/HistTopics/Golden_ratio/

  6. files.mgonzalezm.com files.mgonzalezm.com
    1. 39.2m3+m?—3m,m—n—m+mn, 2m?+2mn+3m+3n.
    2. 38.x—y,x2—y,x3—y5,x1—y.
    3. 37.x1—16,x?+5x+6,x2+x—6.
    4. 36.2x?—4xy42ax —4ay,6xy—12by—12y? +6bx,3xy+3ab +3ay +3bx.
    5. 35.x?—x—2,x2+4x+3,a2+x—6.
    6. 34.x1—1,x3+1,2x2+2.
    7. 33.a?+ab—2b%,3a® +4ab—4b*.
    8. 32.6x?,3xp2,12x%y.
    9. 31.2x2+3x—2, 6x2—7x+2.
    10. 30. 8—8x? + x3—35.
    11. 29. 4x2y2 — (x2 + y? —2?)*.
    12. 28. a1 + b1—7a%b”.
    13. 27. x+x'+1.
    14. 26. x% 4 x2+1.
    15. 25. 1 + my—y? — my.
    16. 24. a —bs.
    17. 23. a%bs + 27%d9.
    18. 22. 8x35—64y3.
    19. 21. 8x3 — 12x*y + 6xy? — y*.
    20. 20. x3 + 642y + 12xy? + 8y%.
    21. 19. 4a?mx + Ba?nx — 2a?my — 4a*ny.
    22. 18. 3ax? — 6by + 9ay — 2bx*.
    23. 17. x? + 3x— 2xy — 6y.
    24. 16. x2—2xy + y2 + 6x—6y + 8.
    25. 15. x2 + 2xy + y? +x+y—e6.
    26. 14. 2a? + ab—6b2.
    27. 13. 10m? — 13mn — 3n2.
    28. 12. 2x? + 3xy— 2y.
    29. 11. 12x?— 29x + 15.
    30. 10. 6b? + 135 —28.
    31. 9. 6a? + 5a—6.
    32. 7. m*—b —2mn + n*.
    33. 8. x?—x—20.
    34. 6. a? + b — ?— 2ab.
    35. 5. 224 2y + y? —a.
    36. 4. 9u?—47?,
    37. 3. Bb?m? + 24b?mn + 18b?n”.
    38. . 16a* — 24a*b + 9b?.
    39. 1. 2x%y?— 6xy3.
    40. 22. (x1 + 2x3 + 3x?—4x + 2) + (x3 -+ x2—x+1).
    41. 21. (a*—a%—ab3 + b1) = (a? + ab +b*).
    42. 50. (2w—x + 2y—2z)2.
    43. 49. (a—b + c—d)*.
    44. 48. (x2 + x + 1)(2—x + 1)(x1—4 +1).
    45. 47. (x* + 1) (x2+ 1)(4— 1).
    46. 46. (a +b)'.
    47. 45. (3m-—2n2)3,
    48. 44. (202 + d'):.
    49. 43. (4x—2)(3x +2).
    50. 42. (2x + 5) (3x—2).
    51. 41. (a—b+c)(a+b+ec).
    52. 40. (x2 + x + 1)(42 + x—1).
    53. 39. (ax + xy) (ax— xy).
    54. 38. (a2 -+ 3) (22—3).
    55. 37. (a?—ab)”.
    56. 36. (2x?—3y2)?.
    57. 35. Comprobar el resultado del ejemplo 1 del Art. 2.6 utilizando el Teore-ma 12.
    58. 34. Utilizando dobles signos expresar en un solo enunciado: (a) los tipos6 y 7; (b) los tipos8 y 9.
    59. 31. Comprobar por multiplicación directa los tipos 8 y 9.
    60. 30. Comprobar por multiplicación directa los tipos 6 y 7.
    61. 29. Comprobar por multiplicación directa los tipos 4 y 5.
    62. 28. Comprobar por multiplicación directa los tipos 1, 2 y 3.
    63. 20. (x3 + 2x2 — 3x + 4) + (a2—x +2).
    64. (3a2— 10ab + 3b?) + (3a—b).
    65. (2 + xy—6)*) + (x+29).
    66. 19. (4at + 205 —4a? + 3a—7) = (2a—1).
    67. (a?—a + 1) (a*—a? + 1) (a% + a + 1). Comprobar el resultado ha- ciendo a = 2.
    68. (a* + a% + a®b? +ab® + b*) (a—b).
    69. (a2—ab+b2+a+b+1)(a+b—1).
    70. (x2—x—1)2(x2 + x + 1).
    71. (x+a)(y +a)(z +a).
    72. (2 + 322 + 5) (x*—1 + 4x).
    73. (m3 —m? + m-—-1) (—m3 -+ m—m +1).
    74. (x2 4 y2 + 22— ay — az — yz) (x + y + 2).
    75. (a?— 2ab + 4b?) (a + 2b). Comprobar el resultado haciendo a = 2
    1. The current mass media such as t elevision, books, and magazines are one-directional, and are produced by a centralized process. This can be positive, since respected editors can filter material to ensure consistency and high quality, but more widely accessible narrowcasting to specific audiences could enable livelier decentralized discussions. Democratic processes for presenting opposing views, caucusing within factions, and finding satisfactory compromises are productive for legislative, commercial, and scholarly pursuits.

      Social media has to some extent democratized the access to media, however there are not nearly enough processes for creating negative feedback to dampen ideas which shouldn't or wouldn't have gained footholds in a mass society.

      We need more friction in some portions of the social media space to prevent the dissemination of un-useful, negative, and destructive ideas swamping out the positive ones. The accelerative force of algorithmic feeds for the most extreme ideas in particular is one of the most caustic ideas of the last quarter of a century.

    2. Since any powerful tool, such as a genex, can be used for destructive purposes, the cautions are discussed in Section 5.

      Given the propensity for technologists in the late 90s and early 00s to have rose colored glasses with respect to their technologies, it's nice to see at least some nod to potential misuses and bad actors within the design of future tools.

    1. JavaScript 的数学运算

      基于 Math 类 Math.ceil() Math.floor()

      3.1415926.toFixed(2) // 保留小数位 99.89233.toPrecision(5) // 整体长度,含整数部分

      全局对象 window 的方法

      parseInt('100') parseInt(100.12) parseInt('string') // => NaN

      Number("string") // => 0


      | 0 , 和 0 按位或 ~~ ,两次按位非

      0,右移 0 位 << 0,左移 0 位

      0,无符号右移 0 位

  7. Feb 2022
  8. files.mgonzalezm.com files.mgonzalezm.com
    1. 6. (x2—3xy + y*) (2x— 3y + 2).
    2. 5. (a? + 2ab— 2b*) (3a—7b).
    3. 3. xy(x2—2y + 4).
    4. 4. (2x2—5y) (4x + 2y*).
    5. 2. (—ab2c) (3a2bc) (2abc?).
    6. 1. (8a2b) (—2ab2).
    7. (4abx — 8b%x?y) + (2bx?).
    8. 2. (5a*min*t) = (—Sam*n?).
    9. . (8x%%2) + (—Ax?y*z).
    10. Demostrar el Teorema 3 del Art. 2.4.
    11. Demostrar que la suma de cualquier número negativo con su valor abso- luto es igual a cero.
    12. 21. m + 2n— (3m— 2m + n— (2n — [m — 4n])).
    13. 20. 4a—[6b + (2a—[3b + a—b+ 4a}}].
    14. 19. x-+ 2y— (4y —x + [3x— 2y] — (2x—2y)).
    15. 18. 4 + [5—(6—9+ (7—2)) — (12—5).
    16. 17. 5— (2+3— (4—3—2) + [5—8]).
    17. Demostrar que la suma de todas las expresiones en los ejercicios 11-15 es igual a la expresión en el ejercicio 11.
    18. Calcular B— A4 —C.
    19. Calcular B—4 + C.
    20. Calcular 4 —B—C.
    21. Calcular 4 —B + C.
    22. Calcular 4 + B—C.
    23. m* + 6m$ — 7m? + 8m — 9, 2m? + Im?—4m — 3.
    24. 2a + 4by — 2ey? + dys, 2dy> — 2by —a + 30y”.
    25. a — 3a”b + 3ab? —b, a5 — 4a*b + 2ab? + b.
    26. x3—4x? + 2x—5, —a3 + 2x2—3x —3.
    27. 3a—2b + 4c — d, 20 + b—3c—d.
    28. E2 + 2cd — 2d, 3c — 3cd — 2d?, e? 4+ 4d — 2c + 2d?.
    29. 3x3 — 8x? + 9x, —a3 + 3x2—8, 2x3 — 2x?—7x 5.
    30. x2-—4xy + 3y, 2x? + 2xy-—2y?, 2xy — y? —22.
    31. 4m? — 3mn + 2n?, Gmn-—2n? + 5, 3n2 — 3—2m.
    32. 2a> — 2a?b + 2b5, Yu?b — 4ab? — 4b3, dab* —m.
    33. 10. (m*—nt) + (m—n).
  9. Jan 2022
  10. Dec 2021
  11. Nov 2021
  12. Oct 2021
    1. https://www.theatlantic.com/ideas/archive/2021/10/facebook-papers-democracy-election-zuckerberg/620478/

      Adrienne LaFrance outlines the reasons we need to either abandon Facebook or cause some more extreme regulation of it and how it operates.

      While she outlines the ills, she doesn't make a specific plea about the solution of the problem. There's definitely a raging fire in the theater, but no one seems to know what to do about it. We're just sitting here watching the structure burn down around us. We need clearer plans for what must be done to solve this problem.

    1. Alicia Boole Stott

      Alicia was the only Boole sister to inherit the mathematical career of her parents, although her mother Mary Everest Boole had brought up all of her five children from an early age 'to acquaint them with the flow of geometry' by projecting shapes onto paper, hanging pendulums etc. She was first exposed to geometric models by her brother-in-law Charles Howard Hinton when she was 17, and developed the ability to visualise in a fourth dimension. She found that there were exactly six regular polytopes in four dimensions and that they are bounded by 5, 16 or 600 tetrahedra, 8 cubes, 24 octahedra or 120 dodecahedra.

  13. Sep 2021
    1. We teachers can help our students with this. Let them know when the most difficult work is coming. Help them prepare for that work, then admit that the challenge is real and it is difficult.

      But let's also be aware of the all-too-prevalent math shaming that occurs when we say "math is difficult". That definitely isn't productive.

  14. Aug 2021
  15. Jun 2021
    1. cheap trick

      Does Morningstar think that math too suffers from the same issues he finds in critical theory, or just Godel's incompleteness theorem (I'm assuming that's what Morningstar is alluding to)? Explore a deep discussion about whether Godel's incompleteness theorem is a cheap trick.

  16. Apr 2021
  17. Mar 2021
    1. In computer science, a tree is a widely used abstract data type that simulates a hierarchical tree structure

      a tree (data structure) is the computer science analogue/dual to tree structure in mathematics

    1. I'd say an equation is anything with an equals sign in it; a formula is an equation of the form A= stuffA= stuffA={\rm\ stuff} where AAA does not appear among the stuff on the right side.
    2. I think that over time the distinction is lost. My math teacher, 35 years ago stated "formulas are used in chemistry, in math we have equations". To this day, the word 'formula' in math seems wrong, but I'd accept it's used commonly.
    3. An equation is meant to be solved, that is, there are some unknowns. A formula is meant to be evaluated, that is, you replace all variables in it with values and get the value of the formula.
    4. The key idea is that the equation captures not just the ingredients of the formula, but also the relationship between the different ingredients.
  18. Feb 2021
    1. In fact, the Product comonad is just the dual of the Writer monad and effectively the same as the Reader monad (both discussed below)
      • Establish the number of Rubik's cube combinations.
      • Establish "algorithm" capabilities based on the x12 "impossible" cubes.
      • "Signmaster notation" for describing algorithm moves.
      • x2 links to youtube tutorials.
    1. (The forms !=, /= or <> are generally used in programming languages where ease of typing and use of ASCII text is preferred.) x ≈ y means x is approximately equal to y. This may also be written ≃, ≅, ~, ♎ (Libra Symbol), or ≒. G ≈ H means that group G is isomorphic (structurally identical) to group H.

      what does that have to do with this game?

    1. Critical and creative thinkers engage in active planning and forethought to set goals, outline strategies, and determine the best methods through which they can achieve their goals

      Head Scratcher: How are we promoting critical and creative thinkers in our instruction?

      As a high school math teacher this can be easier at times, and more difficult at times depending on the class and the course material. At times it is easy to promote creative when dealing with honors classing and higher math courses. But when working with remedial Algebra classes it can be more difficult to promote creativity and critical thinking because of high levels of apathy and prior knowledge. Sometimes the best way to promote success in those classes is through repetition and memeorization of steps to solve common test promblems.

    1. All those names of things - topology, complex analysis, and differential geometry - might not sound like much to you now, but you'll soon learn that they're really just describing the shapes of things in our Universe, and the way those shapes change in time and space are explained by things like calculus and chaos theory.
  19. Jan 2021
    1. A big reason for GPUs popularity in Machine Learning is that they are essentially fast matrix multiplication machines. Deep Learning is essentially matrix multiplication.

      Deep Learning is mostly about matrix multiplication

    2. A matrix is a linear map but linear maps are far more intuitive to think about than matrices
    3. I often get asked by young students new to Machine Learning, what math do I need to know for Deep Learning and my answer is Matrix Multiplication and Derivatives of square functions.

      Deep Neural Networks are a composition of matrix multiplications with the occasional non-linearity in between

    1. New Quantum Algorithms Finally Crack Nonlinear Equations
      • We can’t predict the weather, among many other complex issues, because computers still can’t solve nonlinear equations.
      • But this might change soon, as two different research teams created algorithms that can be used for nonlinear modelling on quantum computers.
      • Their techniques still need refining, and won’t be real-world ready for years, but these studies are another stepping stone towards truly useful quantum algorithms.
  20. Dec 2020
    1. Ergodic theory is a forbiddingly technical branch of mathematics.

      It's supremely sad that a paper in Nature should "math shame" ergodic theory this way. What the hell is going on?

    1. The company’s early mission was to “give people the power to share and make the world more open and connected.” Instead, it took the concept of “community” and sapped it of all moral meaning. The rise of QAnon, for example, is one of the social web’s logical conclusions. That’s because Facebook—along with Google and YouTube—is perfect for amplifying and spreading disinformation at lightning speed to global audiences. Facebook is an agent of government propaganda, targeted harassment, terrorist recruitment, emotional manipulation, and genocide—a world-historic weapon that lives not underground, but in a Disneyland-inspired campus in Menlo Park, California.

      The original goal with a bit of moderation may have worked. Regression to the mean forces it to a bad place, but when you algorithmically accelerate things toward our bases desires, you make it orders of magnitude worse.

      This should be though of as pure social capitalism. We need the moderating force of government regulation to dampen our worst instincts, much the way the United State's mixed economy works (or at least used to work, as it seems that raw capitalism is destroying the United States too).

  21. Nov 2020
    1. We say i (lowercase) is 1.0 in the imaginary dimension Multiplying by i is a 90-degree counter-clockwise turn, to face “up” (here’s why). Multiplying by -i points us South It’s true that starting at 1.0 and taking 4 turns puts us at our starting point: And two turns points us negative: which simplifies to: so

      Great explanation of why \(i=\sqrt-1\)

    2. Imaginary numbers seem to point North, and we can get to them with a single clockwise turn. Oh! I guess they can point South too, by turning the other way. 4 turns gets us pointing in the positive direction again It seems like two turns points us backwards

      Imaginary numbers explained in plain-english

    3. Imaginary numbers let us rotate around the number line, not just move side-to-side.

      Imaginary numbers Another graph:

  22. Oct 2020
    1. 两个向量的外积,又叫向量积、叉乘等


    1. Espen Slettnes 3rd degree connection3rd Espen has a account BMC-Upper Monthly contest designer and local coordinator at Berkeley Math Circle
    1. But these lookalike audiences aren’t just potential new customers — they can also be used to exclude unwanted customers in the future, creating a sort of ad targeting demographic blacklist.
    2. How consumers would be expected to navigate this invisible, unofficial credit-scoring process, given that they’re never informed of its existence, remains an open question.
    1. YouTube doesn’t give an exact recipe for virality. But in the race to one billion hours, a formula emerged: Outrage equals attention.

      Talk radio has had this formula for years and they've almost had to use it to drive any listenership as people left radio for television and other media.

      I can still remember the different "loudness" level of talk between Bill O'Reilly's primetime show on Fox News and the louder level on his radio show.

    2. A 2015 clip about vaccination from iHealthTube.com, a “natural health” YouTube channel, is one of the videos that now sports a small gray box.

      Does this box appear on the video itself? Apparently not...


      But nothing on the embedded version:

      A screengrab of what this looks like:

    3. When Wojcicki took over, in 2014, YouTube was a third of the way to the goal, she recalled in investor John Doerr’s 2018 book Measure What Matters.“They thought it would break the internet! But it seemed to me that such a clear and measurable objective would energize people, and I cheered them on,” Wojcicki told Doerr. “The billion hours of daily watch time gave our tech people a North Star.” By October, 2016, YouTube hit its goal.

      Obviously they took the easy route. You may need to measure what matters, but getting to that goal by any means necessary or using indefensible shortcuts is the fallacy here. They could have had that North Star, but it's the means they used by which to reach it that were wrong.

      This is another great example of tech ignoring basic ethics to get to a monetary goal. (Another good one is Marc Zuckerberg's "connecting people" mantra when what he should be is "connecting people for good" or "creating positive connections".

    1. A more active stance by librarians, journalists, educators, and others who convey truth-seeking habits is essential.

      In some sense these people can also be viewed as aggregators and curators of sorts. How can their work be aggregated and be used to compete with the poor algorithms of social media?

    1. Meta co-founder and CEO Sam Molyneux writes that “Going forward, our intent is not to profit from Meta’s data and capabilities; instead we aim to ensure they get to those who need them most, across sectors and as quickly as possible, for the benefit of the world.”

      Odd statement from a company that was just acquired by Facebook founder's CVI.