The Shadowy World of Umbral Calculus

Comments · 455

• KR

  @krhino42 · 4 years ago

  “By rearranging the question, we get the answer.”  Imma use that

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• AL

  @al.7744 · 4 years ago

  You explained the topics enough to understand what was going on and showed barely enough for us to be intrigued and interested in this without us getting really spoiled or you being tiresome. I am fully convinced to at least attempt and learn more from these fields eventually because of this video. I cannot help but praise you

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• EL

  @elkinmontoya9640 · 4 years ago

  There is so much mystique in this area. I feel like there is a mystery that is just lurking, waiting to be discovered. I see little tidbits of group theory conjugation, analytical combinatorics, probability density functions, so many paths begging to be traversed. From a personal point-of-view, so many potential application to physics

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• LE

  @lego7set · 2 years ago (edited)

  Umbral calculus is truly a shadow of school calculus. I played around with umbral calculus and discovered that the sequence 2^n is its own difference. Therefore, 2^n is a shadow of e^x. Really cool.<br><br>EDIT: If you apply newton&apos;s forward difference formula to 2^n, you get something that is disturbingly similar to the maclaurin series for e^x

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• TH

  @therealjordiano · 4 years ago

  The part at <a href="https://www.youtube.com/watch?v=D0EUFP7-P1M&amp;t=455">7:35</a> when you introduced the main idea I near enough leapt out of my chair and yelled &apos;holy shit!&apos; from the bottom of my lungs (not rly but still), amazing stuff and very nice explanation

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• TH

  @TheRationalPi · 4 years ago

  Oooh, this seems like it could have lots of utility in digital audio processing, since you&apos;re regularly moving between the discrete and continuous domains.

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• LE

  @lexinwonderland5741 · 4 years ago

  this is SO much better than the wiki page. It left me fascinated (even moreso than Dr. Michael Penn&apos;s talks on the matter), and honestly someone should REALLY add the homomorphism between discrete and infinitesimal calculus you described here to the wiki AT THE MINIMUM. thank you so much for the contribution to math education!!

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• DI

  @DivineMuffiN0 · 4 years ago

  Absolutely fantastic video. The Newton difference formula derivation was simply amazing, i used it before but never knew where it came from and this was just the cherry on top. Can&apos;t wait for the follow up!

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• CO

  @corbinsmith5015 · 4 years ago

  I love umbral calculus and generating functions. Ive been reading George Boole’s book on the calculus of finite differences, and I really appreciate videos like these which make the ideas more accessible to the general public

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• FA

  @fabiant.2485 · 4 years ago (edited)

  In the sci-fi rouge like rpg &quot;Caves of Qud&quot; dark calculus is a forbidden field of mathematics, because it&apos;s study opens a path into a transcending layer of reality inhabited by an infinite ocean of psionic minds...<br>After watching this i am impressed by how accurate to real life the devs made their lore.

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• JO

  @joda7697 · 2 years ago

  Umbral Calculus is just the best when you&apos;re deep in some special functions, like Bessel, Laguerre, and so on.

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• 魏寅

  @魏寅生 · 4 years ago

  I&apos;ve been struggling with abstract algebra and your video presents a perfect example for why isomorphisms are useful! Really appreciate it!

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