339 Matching Annotations
  1. Apr 2021
  2. Local file Local file
    Hexaflexagons, Probability Paradoxes, and the Tower of Hanoi
    3
    1. chrisaldrich 02 Apr 2021
      In Germany the great Gottfried Wil-helm von Leibniz was sufficiently intrigued by the notion to incor-porate it into his scheme for a universal language;

      I wish he'd written more here about this. Now I'll have to dig up the reference and the set up as I've long had a similar thought for doing this myself.

      I'll also want to check into the primacy of the idea as others have certainly thought about the same thing. My initial research indicates that both François Fauvel Gouraud and Isaac Pitman both wrote about or developed this possibility. In Pitman's case he used it to develop his version of shorthand which was likely informed by earlier versions of shorthand.

      François Fauvel Gouraud Isaac Pitman shorthand Gottfried Wilhelm von Leibniz mathematics memory
    3. chrisaldrich 02 Apr 2021
      I know of no similar aids in English to recalle, the other commontranscendental number. However, if you memorizeeto five deci-mal places (2.71828), you automatically know it to nine, becausethe last four digits obligingly repeat themselves (2.718281828). InFranceeis memorized to 10 places by the traditional memory aid:Tu aideras rappeler ta quantit beaucoup de docteurs amis.Perhapssome reader can construct an amusing English sentence that willcarryeto at least 20 decimals.
      mathematics e memory mnemonic techniques

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  3. www.redblobgames.com www.redblobgames.com
    Red Blob Games: Hexagonal Grids
    1
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    redblobgames.com/grids/hexagons/
  4. Mar 2021
  5. web.cs.iastate.edu web.cs.iastate.edu
    _TZ_2629-ormosia.dvi
    1
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    web.cs.iastate.edu/~cs577/handouts/quaternion.pdf
  6. en.wikipedia.org en.wikipedia.org
    Taxonomy (general) - Wikipedia
    1
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    en.wikipedia.org/wiki/Taxonomy_(general)
  7. en.wikipedia.org en.wikipedia.org
    Graph (discrete mathematics) - Wikipedia, the free encyclopedia
    1
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    en.wikipedia.org/wiki/Graph_(discrete_mathematics)
  8. en.wikipedia.org en.wikipedia.org
    Model theory - Wikipedia
    1
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    en.wikipedia.org/wiki/Model_theory
  9. www.namics.nysaes.cornell.edu www.namics.nysaes.cornell.edu
    Cootie, Candyland or Chutes and Ladders: Solving a Parent's Dilemma with Monte Carlo Simulation
    4
    1. chrisaldrich 20 Mar 2021
      This article demonstrates how Monte Carlo simulation can be used to solve a real-world, every day problem: Of these three games, which one will provide entertainment for my four-year-old yet let me retain my sanity? If your child is inflexible regarding changing the rules, choose Cootie or Chutes and Ladders which have similar average game lengths. Of the two, Chutes and Ladders is probably the more interesting because of the possibility of moving both forward and backward. If your child insists on Candyland, consider changing the rules as suggested above. An alternative strategy, of course, is simply to let your child cheat. This not only shortens the games, but has the additional incentive that it usually causes the child to win and puts them in a better mood (though it certainly doesn't teach much about ethics). On the bright side, in the few weeks it has taken to complete this study, we have progressed from board games to card games, specifically Uno, which are much more interesting for adults and children. Perhaps there is a God after all.

      The most awesome set of conclusions I've read in a paper in years!

      mathematics conclusions games
    2. chrisaldrich 20 Mar 2021
      In each of the games moves are entirely determined by chance; there is no opportunity to make decisions regarding play. (This, of course, is one reason why most adults with any intellectual capacity have little interest in playing the games for extended times, especially since no money or alcohol is involved.)

      The entire motivation for this study.

      probability theory games mathematics
    3. chrisaldrich 20 Mar 2021
      Monte Carlo simulation is used to determine the distribution of game lengths in number of moves for three popular children's games: Cootie, Candyland and Chutes and Ladders. The effect of modifications to the existing rules are investigated. Recommendations are made for preserving the sanity of parents who must participate in the games.

      And people say math isn't important...

      Monte Carlo simulation mathematics games
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    namics.nysaes.cornell.edu/news15/cootie.html
  10. www.lscheffer.com www.lscheffer.com
    Mathematical Analysis of Candyland
    1
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    lscheffer.com/CandyLand.htm
  11. scholarphi.org scholarphi.org
    ScholarPhi
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    scholarphi.org/
  12. www.coursera.org www.coursera.org
    Differential Equations for Engineers
    1
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    coursera.org/learn/differential-equations-engineers
  13. kids.frontiersin.org kids.frontiersin.org
    The Waiting-Time Paradox
    1
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    kids.frontiersin.org/article/10.3389/frym.2020.582433
  14. math.stackexchange.com math.stackexchange.com
    What is the difference between equation and formula?
    2
    2. TylerRick 10 Mar 2021
      An equation is any expression with an equals sign, so your example is by definition an equation. Equations appear frequently in mathematics because mathematicians love to use equal signs. A formula is a set of instructions for creating a desired result. Non-mathematical examples include such things as chemical formulas (two H and one O make H2O), or the formula for Coca-Cola (which is just a list of ingredients). You can argue that these examples are not equations, in the sense that hydrogen and oxygen are not "equal" to water, yet you can use them to make water.
      distinction mathematics easy to confuse (mix up) terminology
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    math.stackexchange.com/questions/38155/what-is-the-difference-between-equation-and-formula
  15. Feb 2021
  16. arxiv.org arxiv.org
    Coupled Contagion: A Two-Fears Epidemic Model
    1
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    arxiv.org/abs/2102.11045
  17. osf.io osf.io
    Mathematically aggregating experts' predictions of possible futures
    1
    1. zoe_ikeotuonye 23 Feb 2021

      Hanea, A., Wilkinson, D. P., McBride, M., Lyon, A., Ravenzwaaij, D. van, Thorn, F. S., Gray, C. T., Mandel, D. R., Willcox, A., Gould, E., Smith, E., Mody, F., Bush, M., Fidler, F., Fraser, H., & Wintle, B. (2021). Mathematically aggregating experts’ predictions of possible futures. MetaArXiv. https://doi.org/10.31222/osf.io/rxmh7

      is:preprint lang:en structured expert judgement elicitation protocol IDEA probability elicitation aggression mathematically mathematics expert prediction
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    osf.io/preprints/metaarxiv/rxmh7/
  18. en.wikipedia.org en.wikipedia.org
    Mathematical structure - Wikipedia
    1
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    en.wikipedia.org/wiki/Mathematical_structure
  19. qz.com qz.com
    The Quartz guide to bad data
    1
    1. chrisaldrich 12 Feb 2021
      Benford’s Law is a theory which states that small digits (1, 2, 3) appear at the beginning of numbers much more frequently than large digits (7, 8, 9). In theory Benford’s Law can be used to detect anomalies in accounting practices or election results, though in practice it can easily be misapplied. If you suspect a dataset has been created or modified to deceive, Benford’s Law is an excellent first test, but you should always verify your results with an expert before concluding your data has been manipulated.

      This is a relatively good explanation of Benford's law.

      I've come across the theory in advanced math, but I'm forgetting where I saw the proof. p-adic analysis perhaps? Look this up.

      Benford's law mathematics data analysis
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    qz.com/572338/the-quartz-guide-to-bad-data/
  20. Jan 2021
  21. www.quantamagazine.org www.quantamagazine.org
    Topology 101: The Hole Truth
    1
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    quantamagazine.org/topology-101-how-mathematicians-study-holes-20210126/
  22. www.quantamagazine.org www.quantamagazine.org
    How I Learned to Love and Fear the Riemann Hypothesis
    1
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    quantamagazine.org/how-i-learned-to-love-and-fear-the-riemann-hypothesis-20210104/
  23. Dec 2020
  24. cims.nyu.edu cims.nyu.edu
    Index of /~gromov
    1
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    cims.nyu.edu/~gromov/
  25. www.aier.org www.aier.org
    Professor Sunetra Gupta on the Perils of Disease Modelling
    3
    1. MinorityReports 03 Dec 2020
      In trying to capture the essence of a system through a minimum of unambiguous symbols, scientists and artists are driven by a similar concern for beauty and symmetry, a similar thirst for light. What makes mathematics special is its promise of prophecy, the promise that it will help us understand all mysteries and all knowledge.

      We all want desperately to know what the future holds.

      prophecy revelation mathematics
    2. MinorityReports 03 Dec 2020
      But something about the comforting rigidity of the process, its seductive notation, but perhaps mostly its connotations of intellectual privilege, has drawn a diverse selection of disciplines to the altar of mathematical reasoning. Indeed, the widespread misappropriation of the language of mathematics in the social and biological sciences has to be one of the great tragedies of our time.

      The deliberate misappropriation of the language of mathematics.

      appeal to authority propaganda mathematics
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    aier.org/article/professor-sunetra-gupta-on-the-perils-of-disease-modelling/
  26. Nov 2020
  27. en.wikipedia.org en.wikipedia.org
    List of mathematical jargon - Wikipedia
    2
    1. TylerRick 25 Nov 2020
      the adjective strong or the adverb strongly may be added to a mathematical notion to indicate a related stronger notion; for example, a strong antichain is an antichain satisfying certain additional conditions, and likewise a strongly regular graph is a regular graph meeting stronger conditions. When used in this way, the stronger notion (such as "strong antichain") is a technical term with a precisely defined meaning; the nature of the extra conditions cannot be derived from the definition of the weaker notion (such as "antichain")
      precision of terms/words mathematics stronger property
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    en.wikipedia.org/wiki/List_of_mathematical_jargon
  28. forum.artofmemory.com forum.artofmemory.com
    Jan Zoń - A New Revolutionary Cards Method
    1
    1. chrisaldrich 19 Nov 2020
      Jan Zoń - A New Revolutionary Cards Method

      This highlights a question I've had for a while: What is the best encoding method for very quickly memorizing a deck of cards while still keeping a relatively small ceiling on the amount of space to memorize and work out in advance.

      I want to revisit it and do the actual math to maximize the difference between the methods.

      Memory speed cards combinatorics Mathematics
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    forum.artofmemory.com/t/jan-zon-a-new-revolutionary-cards-method/57009
  29. Oct 2020
  30. www.ams.org www.ams.org
    AMS :: Feature Column :: How to Differentiate with a Computer
    1
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    ams.org/publicoutreach/feature-column/fc-2017-12
  31. qz.com qz.com
    A mathematician has created a teaching method that’s proving there’s no such thing as a bad math student
    2
    2. chrisaldrich 10 Oct 2020
      “Many thought, okay to get from A to B there are these three steps, but it turns out there are really five or six,”

      Sounds a lot like the mathematicians who came after Perelman to show that his proof of Poincare was correct--they needed help in getting from A to B too.

      Mathematics pedagogy
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    qz.com/901125/a-mathematician-has-created-a-method-of-teaching-that-is-proving-there-is-no-such-thing-as-a-bad-math-student/
  32. danmackinlay.name danmackinlay.name
    The Dan MacKinlay family of variably-well-considered enterprises
    1
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    danmackinlay.name/
  33. gowers.wordpress.com gowers.wordpress.com
    Mathematical Research Reports: a “new” mathematics journal is launched
    1
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    gowers.wordpress.com/2020/05/20/mathematical-research-reports-a-new-mathematics-journal-is-launched/
  34. www.aft.org www.aft.org
    Developing Mathematical Mindsets
    6
    3. chrisaldrich 10 Oct 2020
      Unfortunately for low achievers, they are often identified as struggling with math and therefore given more drill and practice—cementing their beliefs that math success means memorizing methods, not understanding and making sense of situations. They are sent down a damaging pathway that makes them cling to formal procedures, and as a result, they often face a lifetime of difficulty with mathematics.
      Mathematics
    4. chrisaldrich 10 Oct 2020
      Unfortunately, many classrooms focus on math facts in isolation, giving students the impression that math facts are the essence of mathematics, and, even worse, that mastering the fast recall of math facts is what it means to be a strong mathematics student. Both of these ideas are wrong, and it is critical that we remove them from classrooms, as they play a key role in creating math-anxious and disaffected students.

      This article uses the word "unfortunately quite a lot.

      Mathematics
    6. chrisaldrich 10 Oct 2020
      The hippocampus, like other brain regions, is not fixed and can grow at any time,15 but it will always be the case that some students are faster or slower when memorizing, and this has nothing to do with mathematics potential.
      Mathematics
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    aft.org/ae/winter2018-2019/boaler
  35. blogs.ams.org blogs.ams.org
    The Hungarian Approach and How It Fits the American Educational Landscape
    2
    1. chrisaldrich 10 Oct 2020
      Moreover, the teacher repeatedly asks, “Did anyone get a different answer?” or “Did anyone use a different method?” to elicit multiple solutions strategies. This highlights the connections between different problems, concepts, and areas of mathematics and helps develop students’ mathematical creativity. Creativity is further fostered through acknowledging “good mistakes.” Students who make an error are often commended for the progress they made and how their work contributed to the discussion and to the collective understanding of the class.
      Mathematics pedagogy
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    blogs.ams.org/matheducation/2015/01/10/the-hungarian-approach-and-how-it-fits-the-american-educational-landscape/
  36. www.dpmms.cam.ac.uk www.dpmms.cam.ac.uk
    2cultures.pdf
    5
    1. chrisaldrich 10 Oct 2020
      This result of Erd ̋os [E] is famous not because it has large numbers of applications,nor because it is difficult, nor because it solved a long-standing open problem. Its famerests on the fact that it opened the floodgates to probabilistic arguments in combinatorics.If you understand Erd ̋os’s simple argument (or one of many other similar arguments) then,lodged in your mind will be a general principle along the following lines:if one is trying to maximize the size of some structure under certain constraints, andif the constraints seem to force the extremal examples to be spread about in a uniformsort of way, then choosing an example randomly is likely to give a good answer.Once you become aware of this principle, your mathematical power immediately increases.
      Mathematics probability Paul Erdős
    2. chrisaldrich 10 Oct 2020
      Once again, Atiyah writes very clearlyand sensibly on this matter (while acknowledging his debt to earlier great mathematicianssuch as Poincar ́e and Weyl). He makes the point (see for example [A2]) that so muchmathematics is produced that it is not possible for all of it to be remembered. The processesof abstraction and generalization are therefore very important as a means of making senseof the huge mass of raw data (that is, proofs of individual theorems) and enabling at leastsome of it to be passed on. The results that will last are the ones that can be organizedcoherently and explained economically to future generations of mathematicians. Of course,some results will be remembered because they solve very famous problems, but even these,if they do not fit into an organizing framework, are unlikely to be studied in detail by morethan a handful of mathematicians.

      bandwidth in mathematics is an important concept

      We definitely need ways of simplifying and encoding smaller cases into bigger cases to make the abstractions easier to encapsulate and pass on so that new ground can be broken

      Memory Mathematics
    5. chrisaldrich 10 Oct 2020
      many clever techniquesinvented. Some of these can again be encapsulated in the form of useful principles. Oneof them is the following, known to its friends as Concentration of Measure:if a functionfdepends in a reasonably continuous way on a large number of smallvariables, thenf(x) is almost always close to its expected value.
      Mathematics combinatorics
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    dpmms.cam.ac.uk/~wtg10/2cultures.pdf
  37. nautil.us nautil.us
    Why Mathematicians Should Stop Naming Things After Each Other
    3
    1. chrisaldrich 10 Oct 2020
      their name gives no mnemonic boost whatsoever. Whatever faint associations it might once have held fade away, especially when the discover was neither famous nor narrow, and the reader is several generations removed.

      This might be debatable as many of the names in the example are relatively famous names. Any associations they provide might also extend to the dates of the mathematician which also then places the ideas historically as well.

      More often I see the problem with some of the bigger greats like Euler and Cauchy who discovered so many things and everything is named after them.

      The other problem is mis-attribution of the discovery, which happens all-too-frequently, and the thing is named after the wrong person.

      Mathematics naming Memory history
    2. chrisaldrich 10 Oct 2020
      The average number of coauthors on math papers has gone up since 1900. So has the number of working mathematicians in the world, which raises the odds of independent rediscoveries, separated in time or space. These two trends have opened the door to triple and even quadruple hyphen situations, as in the Albert-Brauer-Hasse-Noether Theorem and the Grothendieck-Hirzebruch-Riemann-Roch Theorem.

      But this also gets rid of naming quirks for multiple people like the Cox-Zucker Machine.

      Mathematics
    3. chrisaldrich 10 Oct 2020
      The worst answer I can imagine is the one Pope Gregory VII gave for refusing to let the Holy Scripture be translated out of Latin: “... [I]f it were plainly apparent to all men, perchance it would be little esteemed and be subject to disrespect; or it might be falsely understood by those of mediocre learning, and lead to error.”

      I'd push back on this a bit by saying that there are huge swaths of people looking at English translations, of Latin translations, of Greek, Hebrew, and Aramaic translations. Not only is there some detail lost in the multiple levels of translation, but many modern Christians are actively mis-applying the stories in the Bible to apply to their modern lives in radically different ways than was intended.

      translations Bible Mathematics naming semantics
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    nautil.us/issue/89/the-dark-side/why-mathematicians-should-stop-naming-things-after-each-other
  38. www.nytimes.com www.nytimes.com
    To the Mathematician Eugenia Cheng, There’s No Gap Between Art and Science
    1
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    nytimes.com/2020/08/13/books/review/eugenia-cheng-by-the-book-interview.html
  39. fs.blog fs.blog
    Einstein: Combinatory Play is the Essential Feature of Thought
    1
    1. chrisaldrich 10 Oct 2020
      In 1945 Jacques S. Hadamard surveyed mathematicians to determine their mental processes at work by posing a series of questions to them and later published his results in An Essay on the Psychology of Invention in the Mathematical Field.

      I suspect this might be an interesting read.

      Mathematics want to read
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    fs.blog/einstein-productive-thought-combinatory-creativity/
  40. projecteuclid.org projecteuclid.org
    AOS023.dvi
    1
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    projecteuclid.org/download/pdf_1/euclid.aos/1035844977
  41. Local file Local file
    Design for Cognitive Bias
    1

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  42. katmat.math.uni-bremen.de katmat.math.uni-bremen.de
    Abstract and Concrete Categories - The Joy of Cats
    2
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    katmat.math.uni-bremen.de/acc/acc.pdf
  43. myscript.com myscript.com
    Apps & Demos | MyScript
    1
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    myscript.com/technology/technical-demonstrations/
  44. Sep 2020
  45. www.scientificamerican.com www.scientificamerican.com
    Can an Algorithm Help Solve Political Paralysis?
    1
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    scientificamerican.com/article/can-an-algorithm-help-solve-political-paralysis/
  46. Jul 2020
  47. en.wikipedia.org en.wikipedia.org
    Abelian group - Wikipedia
    1
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    en.wikipedia.org/wiki/Abelian_group
  48. twitter.com twitter.com
    Olivier Lacan on Twitter: "Without checking in IRB, tell me what you think this code returns: [1,2,3,3] - [3]" / Twitter
    2
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    twitter.com/olivierlacan/status/1084930269533085696
  49. ncatlab.org ncatlab.org
    nLab
    1
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    ncatlab.org/nlab/show/HomePage
  50. www.youtube.com www.youtube.com
    Net-COVID Session4A: Math Models of Epidemic Spreading in the Time of COVID-19 by Ginestra Bianconi
    1
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    youtube.com/watch
  51. Jun 2020
  52. thinkmath.edc.org thinkmath.edc.org
    "Puzzling through problems” as a habit of mind | Think Math!
    2
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    thinkmath.edc.org/presentation/puzzling-through-problems”-habit-mind
  53. thinkmath.edc.org thinkmath.edc.org
    Practicing Skills Video | Think Math!
    1
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    thinkmath.edc.org/video/practicing-skills-video
  54. www.nature.com www.nature.com
    Has Twitter just had its saddest fortnight ever?
    1
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    nature.com/articles/d41586-020-01818-3
  55. www.humblebundle.com www.humblebundle.com
    Humble Book Bundle: Fun with STEM by Adams Media
    1
    1. TylerRick 01 Jun 2020

      PAY $1 OR MORE TO ALSO UNLOCK!

      Star Wars Vs. Star Trek

      Everything Everyday Math Book

      Everything Guide to Pre-Algebra

      100 Things to See in the Night Sky

      Simple Acts to Save Our Planet

      Weather 101

      1,001 Facts That Will Scare the S#*t Out of You

      Why Didn't I Think of That?

      What's Your STEM?

      Dad's Book of Awesome Science Experiments

      Psych 101

      PAY $8 OR MORE TO ALSO UNLOCK!

      Everything Guide to Algebra

      Math Geek

      Anatomy 101

      Physics of Star Wars

      Facts From Space!

      100 Things to See in the Southern Night Sky

      Everything STEM Handbook

      Architecture 101

      Nature is the Worst

      Ultimate Roblox Book: An Unofficial Guide

      The Everything Astronomy Book

      Everything Psychology

      PAY $15 OR MORE TO ALSO UNLOCK!

      Psych Experiments https://www.amazon.com/Psych-Experiments-Rorschachs-psychologys-fascinating-ebook/dp/B01M3R7RVN/ 4.6/5 $12/$11

      DNA is You! https://www.amazon.com/DNA-You-Marvelous-One-Kind-ness/dp/1721400176/ 3.8/5 $11/$14 Want: 8/10

      Everything Guide to the Human Brain https://www.amazon.com/Everything-Guide-Human-Brain-Everything%C2%AE-ebook/dp/B00CMVFW62/ 4.3/10 $14/$13 Want: 8/10

      Astronomy 101 https://www.amazon.com/Astronomy-101-Wormholes-Theories-Discoveries-ebook/dp/B00DV1V7LQ/ 4.5/5 $9/$11 Want: 7/10

      Everyday Amazing https://www.amazon.com/Everyday-Amazing-Fascinating-Science-Surrounds-ebook/dp/B07M5VB9FW/ 4.6/5 $15/$13 Want: 7/10

      Everything Kids' Scratch Coding Book https://www.amazon.com/Everything-Kids-Scratch-Coding-Book/dp/1507207972/ 4.4/5 $14/$15 Want: 6/10

      In the Company of Trees https://www.amazon.com/Company-Trees-Honoring-Connection-Sacred/dp/1507209541/ 5/5 $13/$15 Want: 9/10

      Science of Marvel https://www.amazon.com/Science-Marvel-Infinity-Stones-Revealed/dp/1507209983/ 4.6/5 $13/$11 Want: 7/10

      Bizarre World https://www.amazon.com/Bizarre-World-Collection-Creepiest-Traditions-ebook/dp/B07MKDH8XY/ 5/5 $9/$10 Want: 8/10

      Statistics 101 https://www.amazon.com/Statistics-101-Distribution-Determining-Probability-ebook/dp/B078M5FZ1P/ 3.4/5 $11/$10 Want: 3/10

      Everything Guide to Anatomy and Physiology https://www.amazon.com/Everything-Guide-Anatomy-Physiology-Everything%C2%AE-ebook/dp/B00XO0PZAS/ 4.6/5 $16/21 Want: 7/10

      Advanced Roblox Coding Book: An Unofficial Guide https://www.amazon.com/Advanced-Roblox-Coding-Book-Unofficial-ebook/dp/B07GNVRPXW/ 4.6/5 $11/$10 Want: 5/10

      Genetics 101 https://www.amazon.com/Genetics-101-Chromosomes-Cloning-Everything-ebook/dp/B078M5KLXB/ 4.1/5 $11/$10 Needs pictures Want: 5/10

      book bundle science technology education for kids mathematics
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    humblebundle.com/books/fun-with-stem-adams-media-books
  56. May 2020
  57. scholar.harvard.edu scholar.harvard.edu
    kissmillersimontocandindex.pdf
    1
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    scholar.harvard.edu/files/joelmiller/files/kissmillersimontocandindex.pdf
  58. psyarxiv.com psyarxiv.com
    The Global Response to COVID-19 as an Example of a One-Sided Problem Definition in the Absence of General Collective Intelligence
    1
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    psyarxiv.com/emgxc/
  59. wellcomeopenresearch.org wellcomeopenresearch.org
    Estimating the overdispersion in COVID-19 transmission using outbreak sizes outside China
    1
    1. edampf 27 May 2020

      Endo, A., Centre for the Mathematical Modelling of Infectious Diseases COVID-19 Working Group, Abbott, S., Kucharski, A. J., & Funk, S. (2020). Estimating the overdispersion in COVID-19 transmission using outbreak sizes outside China. Wellcome Open Research, 5, 67. https://doi.org/10.12688/wellcomeopenres.15842.1

      is:article lang:en COVID-19 overdispersion superspreading branching process transmission dynamics mathematics modeling branching process model secondary transmission R
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  60. www.nature.com www.nature.com
    Modelling COVID-19
    1
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    nature.com/articles/s42254-020-0178-4
  61. ai.googleblog.com ai.googleblog.com
    Understanding the Shape of Large-Scale Data
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    ai.googleblog.com/2020/05/understanding-shape-of-large-scale-data.html
  62. en.wikipedia.org en.wikipedia.org
    Lattice (order) - Wikipedia, the free encyclopedia
    1
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  63. en.wikipedia.org en.wikipedia.org
    Necessity and sufficiency - Wikipedia
    1
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    en.wikipedia.org/wiki/Necessity_and_sufficiency
  64. www.bmj.com www.bmj.com
    Response to 'Modelling the pandemic': reconsidering the quality of evidence from epidemiological models
    1
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    bmj.com/content/369/bmj.m1567/rr-0
  65. Apr 2020
  66. en.wikipedia.org en.wikipedia.org
    Pseudocode - Wikipedia
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    en.wikipedia.org/wiki/Pseudocode
  67. en.wikipedia.org en.wikipedia.org
    Up to - Wikipedia
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    en.wikipedia.org/wiki/Up_to
  68. en.wikipedia.org en.wikipedia.org
    Isomorphism - Wikipedia
    1
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    en.wikipedia.org/wiki/Isomorphism
  69. arxiv.org arxiv.org
    Hate multiverse spreads malicious COVID-19 content online beyond individual platform control
    1
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    arxiv.org/abs/2004.00673
  70. arxiv.org arxiv.org
    1907.11162.pdf
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    arxiv.org/pdf/1907.11162.pdf
  71. www.vox.com www.vox.com
    Why it’s so hard to see into the future of Covid-19
    1
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    vox.com/science-and-health/2020/4/10/21209961/coronavirus-models-covid-19-limitations-imhe
  72. www.nature.com www.nature.com
    How you can help with COVID-19 modelling
    1
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    nature.com/articles/s42254-020-0175-7
  73. jamanetwork.com jamanetwork.com
    Predictive Mathematical Models of the COVID-19 Pandemic: Underlying Principles and Value of Projections
    1
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    jamanetwork.com/journals/jama/fullarticle/2764824
  74. en.wikipedia.org en.wikipedia.org
    Polymorphism (computer science) - Wikipedia
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    en.wikipedia.org/wiki/Polymorphism_(computer_science)
  75. Jan 2020
  76. en.wikipedia.org en.wikipedia.org
    Closure operator - Wikipedia
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    en.wikipedia.org/wiki/Closure_operator
  77. en.wikipedia.org en.wikipedia.org
    Partially ordered set - Wikipedia
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    en.wikipedia.org/wiki/Partially_ordered_set
  78. en.wikipedia.org en.wikipedia.org
    Ordered set operators - Wikipedia
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  79. math.stackexchange.com math.stackexchange.com
    Is there a symbol for "dependent"?
    1
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    math.stackexchange.com/questions/702191/is-there-a-symbol-for-dependent
  80. en.wikipedia.org en.wikipedia.org
    List of mathematical symbols - Wikipedia
    1
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  81. www.amazon.com www.amazon.com
    Norbert Wiener-A Life in Cybernetics (The MIT Press): Norbert Wiener, Ronald R Kline: 9780262535441: Amazon.com: Books
    1
    1. TylerRick 29 Jan 2020

      Norbert Wiener was a mathematician with extraordinarily broad interests. The son of a Harvard professor of Slavic languages, Wiener was reading Dante and Darwin at seven, graduated from Tufts at fourteen, and received a PhD from Harvard at eighteen. He joined MIT's Department of Mathematics in 1919, where he remained until his death in 1964 at sixty-nine. In Ex-Prodigy, Wiener offers an emotionally raw account of being raised as a child prodigy by an overbearing father. In I Am a Mathematician, Wiener describes his research at MIT and how he established the foundations for the multidisciplinary field of cybernetics and the theory of feedback systems. This volume makes available the essence of Wiener's life and thought to a new generation of readers.

      AI mathematics cybernetics
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    amazon.com/Norbert-Wiener_A-Life-Cybernetics-Mathematician/dp/0262535440
  82. en.wikipedia.org en.wikipedia.org
    List of logic symbols - Wikipedia
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  83. en.wikipedia.org en.wikipedia.org
    Universal quantification - Wikipedia
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    en.wikipedia.org/wiki/Universal_quantification
  84. en.wikipedia.org en.wikipedia.org
    Functor - Wikipedia
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    en.wikipedia.org/wiki/Functor
  85. en.wikipedia.org en.wikipedia.org
    Category theory - Wikipedia
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    en.wikipedia.org/wiki/Category_theory
  86. mathoverflow.net mathoverflow.net
    MathOverflow
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    mathoverflow.net/
  87. en.wiktionary.org en.wiktionary.org
    ∃! - Wiktionary
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  88. en.wikipedia.org en.wikipedia.org
    Duality (mathematics) - Wikipedia
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  89. www.red-gate.com www.red-gate.com
    Divided We Stand: The SQL of Relational Division - Simple Talk
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    red-gate.com/simple-talk/sql/t-sql-programming/divided-we-stand-the-sql-of-relational-division/
  90. Dec 2019
  91. hybridpedagogy.org hybridpedagogy.org
    Why OERs are Important for Critical Pedagogues — Hybrid Ped
    1
    1. sboyce1 16 Dec 2019
      “The pupil is thereby ‘schooled’ to confuse teaching with learning, grade advancement with education, a diploma with competence, and fluency with the ability to say something new. His imagination is ‘schooled’ to accept service in place of value.” (1)

      I think this issue is particularly important in mathematics. One of the seminal researchers in my field, Les Steffe, distinguishes "school mathematics" from the mathematics of students as a modeling construct; others have conceptualized situated cognition; informal mathematics,

      mathematics of students versus school mathematics
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    hybridpedagogy.org/why-open-educational-resources-oers-are-important-for-critical-pedagogues/
  92. Oct 2019
  93. en.wikipedia.org en.wikipedia.org
    Determinacy - Wikipedia
    1
    1. TylerRick 31 Oct 2019
      Determinacy is a subfield of set theory, a branch of mathematics, that examines the conditions under which one or the other player of a game has a winning strategy, and the consequences of the existence of such strategies. Alternatively and similarly, "determinacy" is the property of a game whereby such a strategy exists.
      determinacy mathematics
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  94. www.youtube.com www.youtube.com
    Harvard Science of Psychedelics Club: The Hyperbolic Geometry of DMT Experiences - YouTube
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    youtube.com/watch
  95. Feb 2019
  96. neuralnetworksanddeeplearning.com neuralnetworksanddeeplearning.com
    Neural Networks and Deep Learning
    4
    1. siva82kb 05 Feb 2019
      And so it makes most sense to regard epoch 280 as the point beyond which overfitting is dominating learning in our neural network.

      I do not get this. Epoch 15 indicates that we are already over-fitting to the training data set, on? Assuming both training and test set come from the same population that we are trying to learn from.

      NeuralNetworks mathematics ML questions
    4. siva82kb 05 Feb 2019
      What is the limiting value for the output activations aLj

      When c is large, small differences in z_j^L are magnified and the function jumps between 0 and 1, depending on the sign of the differences. On the other hand, when c is very small, all activation values will be close to 1/N; where N is the number of neurons in layer L.

      NeuralNetworks mathematics ML
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    neuralnetworksanddeeplearning.com/chap3.html
  97. Nov 2018
  98. iphysresearch.github.io iphysresearch.github.io
    A Paper A Day
    5
    1. Herb 24 Nov 2018
      Stochastic Gradient Descent Optimizes Over-parameterized Deep ReLU Networks

      这个哥们的文章和这个月内好几篇的立意基本一致(1811.03804/1811.03962/1811.04918) [抓狂] ，估计作者正写的时候，内心是崩溃的~[笑cry] 赶快强调自己有着不同的 assumption~

      Generalization Mathematics
    3. Herb 17 Nov 2018
      Learning and Generalization in Overparameterized Neural Networks, Going Beyond Two Layers

      全篇的数学理论推导，意在回答2/3层过参的网络可以足够充分地学习和有良好的泛化表现，即使在简单的优化策略（类SGD）等假定下。（FYI： 文章可谓行云流水，直截了当，标准规范，阅读有种赏心悦目的感觉~）

      Generalization Mathematics
    5. Herb 13 Nov 2018
      A Convergence Theory for Deep Learning via Over-Parameterization

      又一个全篇的数学理论证明，但是没找到 conclusion 到底是啥，唯一接近的是 remark 的信息，但内容也都并不惊奇。不过倒是一个不错的材料，若作为熟悉DNN背后的数学描述的话。

      Optimization Mathematics
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    iphysresearch.github.io/paper_summary/APaperADay.html
  99. Apr 2018
  100. wiki.c2.com wiki.c2.com
    Untitled document
    1
    1. eyefocus 17 Apr 2018
      ConvexHull

      In mathematics, the convex hull or convex envelope of a set X of points in the Euclidean plane or in a Euclidean space (or, more generally, in an affine space over the reals) is the smallest convex set that contains X. For instance, when X is a bounded subset of the plane, the convex hull may be visualized as the shape enclosed by a rubber band stretched around X. -Wikipedia

      convex hull algorithms wikipedia mathematics
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  101. Nov 2017
  102. blog.mrmeyer.com blog.mrmeyer.com
    Dismantling the Privilege of the Mathematical 1%
    1
    1. daveh70 15 Nov 2017

      As Uri Treisman said, “The most common use of algebra in the adult world is helping their kids with algebra.”

      CUNY found that more students went on to graduate when they were allowed to take statistics instead of remedial algebra. And the results were the same regardless of race or ethnicity.

      mathematics education
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    blog.mrmeyer.com/2017/dismantling-the-privilege-of-the-mathematical-1/
  103. Jul 2017
  104. www.pobonline.com www.pobonline.com
    U.S. Survey Feet Versus International Feet
    1
    1. daveh70 06 Jul 2017

      there are two different measurements for the length of a foot in the United States: the International Foot (also commonly called the foot) and the U.S. Survey Foot. The International Foot (which we were all taught in school) is defined as 0.3048 meters, whereas the U.S. Survey Foot is defined as 0.3048006096 meters. The difference of the two equates to 2 parts per million.

      For example, in a measurement of 10,000 feet, the difference would be 0.02 feet (just less than one-quarter of an inch). In a measurement of 1 million feet, the difference is 2 feet.

      science mathematics measurement programming
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  105. Apr 2017
  106. waitbutwhy.com waitbutwhy.com
    Neuralink and the Brain's Magical Future - Wait But Why
    1
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    waitbutwhy.com/2017/04/neuralink.html
  107. Jan 2017
  108. betterexplained.com betterexplained.com
    Math, Better Explained eBook + Video Course
    1
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    betterexplained.com/ebook/math/
  109. Nov 2016
  110. www.scottaaronson.com www.scottaaronson.com
    philos.pdf
    1
    1. fiatjaf 04 Nov 2016
      If you accept this, thenit seems fair to say that untilPversusNPis solved, the story of Hilbert's Entscheidungsproblem|itsrise, its fall, and the consequences for philosophy|is not yet over.

      If you accept this bizarre interpretation, then you can suspend the belief in the fact, known to everybody, that \(P \ne NP\), because it hasn't been mathematically proved, and say the question isn't solved yet. Wow, how interesting!

      mathematics idle mathematicians
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  111. Oct 2016
  112. bullshit.ist bullshit.ist
    Stop Selling Math For Its Usefulness
    1
    1. daveh70 31 Oct 2016

      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.)

      math mathematics education K-12
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    bullshit.ist/stop-selling-math-for-its-usefulness-d9143e80d78d
  113. medium.com medium.com
    As a school child, I suffered from dyscalculia. – Medium
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    medium.com/@lilpeck/as-a-school-child-i-suffered-from-dyscalculia-c9e374cf6256
  114. medium.com medium.com
    Eh, I dunno. – Medium
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    medium.com/@cloverneiberg/eh-i-dunno-ed42d4746f6b
  115. Jul 2016
  116. www.quantamagazine.org www.quantamagazine.org
    A Bird’s-Eye View of Nature’s Hidden Order | Quanta Magazine
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    quantamagazine.org/20160712-hyperuniformity-found-in-birds-math-and-physics/
  117. backchannel.com backchannel.com
    My Time with Richard Feynman — Backchannel
    1
    1. Rtalbert 11 Jul 2016
      I always found it incredible. He would start with some problem, and fill up pages with calculations. And at the end of it, he would actually get the right answer! But he usually wasn’t satisfied with that. Once he’d gotten the answer, he’d go back and try to figure out why it was obvious. And often he’d come up with one of those classic Feynman straightforward-sounding explanations. And he’d never tell people about all the calculations behind it. Sometimes it was kind of a game for him: having people be flabbergasted by his seemingly instant physical intuition, not knowing that really it was based on some long, hard calculation he’d done.

      Straightforward intuition isn't just intuition.

      mathematics physics computational thinking
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  118. Jun 2016
  119. www.phdontrack.net www.phdontrack.net
    Phd on track » Co – authorship
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    phdontrack.net/share-and-publish/co-authorship/
  120. Apr 2016
  121. bartoszmilewski.com bartoszmilewski.com
    Category Theory for Programmers: The Preface
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    bartoszmilewski.com/2014/10/28/category-theory-for-programmers-the-preface/
  122. Mar 2016
  123. www.quantamagazine.org www.quantamagazine.org
    Mathematicians Discover Prime Conspiracy | Quanta Magazine
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    quantamagazine.org/20160313-mathematicians-discover-prime-conspiracy/
  124. Feb 2016
  125. www.math-cs.gordon.edu www.math-cs.gordon.edu
    NTIC Number Theory
    1
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    math-cs.gordon.edu/~kcrisman/mat338/NTIC.html
  126. linear.pugetsound.edu linear.pugetsound.edu
    A First Course in Linear Algebra (A Free Textbook)
    1
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    linear.pugetsound.edu/
  127. www.brainpickings.org www.brainpickings.org
    Synesthesia and the Poetry of Numbers: Autistic Savant Daniel Tammet on Literature, Math, and Empathy, by Way of Borges
    1
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    brainpickings.org/2013/08/05/daniel-tammet-thinking-in-numbers/
  128. www.rdmiddlebrook.com www.rdmiddlebrook.com
    Untitled document
    1
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    rdmiddlebrook.com/D_OA_Rules&Tools/
  129. www.complexityexplorer.org www.complexityexplorer.org
    Complexity Explorer
    1
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    complexityexplorer.org/
  130. Jan 2016
  131. www.muslimheritage.com www.muslimheritage.com
    From Alchemy to Chemistry | Muslim Heritage
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    muslimheritage.com/article/alchemy-chemistry
  132. category-theory.mitpress.mit.edu category-theory.mitpress.mit.edu
    Category Theory for the Sciences
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    category-theory.mitpress.mit.edu/toc.html
  133. aimath.org aimath.org
    Approved Textbooks | American Inst. of Mathematics
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    aimath.org/textbooks/approved-textbooks/
  134. www.golf-simulators.com www.golf-simulators.com
    Physics
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    golf-simulators.com/physics.htm
  135. Dec 2015
  136. math.mit.edu math.mit.edu
    CT4S.pdf
    1
    1. bbarker 06 Dec 2015
      All this time, however, category theory was consistently seen by much of the mathe-matical community as ridiculously abstract. But in the 21st century it has finally cometo find healthy respect within the larger community of pure mathematics. It is the lan-guage of choice for graduate-level algebra and topology courses, and in my opinion willcontinue to establish itself as the basic framework in which mathematics is done
      category theory mathematics history algebra topology
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    math.mit.edu/~dspivak/teaching/sp13/CT4S.pdf
  137. May 2015
  138. oxfordstudent.com oxfordstudent.com
    The Madness of Mathematics | The Oxford Student
    2
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    oxfordstudent.com/2012/05/24/the-madness-of-mathematics/