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Videos uploaded by user “3Blue1Brown” for the 2017
How secure is 256 bit security?
 
05:06
Supplement to the cryptocurrency video: How hard is it to find a 256-bit hash just by guessing and checking? What kind of computer would that take? Cryptocurrency video: https://youtu.be/bBC-nXj3Ng4 Thread for Q&A questions: http://3b1b.co/questions Several people have commented about how 2^256 would be the maximum number of attempts, not the average. This depends on the thing being attempted. If it's guessing a private key, you are correct, but for something like guessing which input to a hash function gives a desired output (as in bitcoin mining, for example), which is the kind of thing I had in mind here, 2^256 would indeed be the average number of attempts needed, at least for a true cryptographic hash function. Think of rolling a die until you get a 6, how many rolls do you meed to make, on average? ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 708041 3Blue1Brown
But what *is* a Neural Network? | Chapter 1, deep learning
 
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Subscribe to stay notified about new videos: http://3b1b.co/subscribe Support more videos like this on Patreon: https://www.patreon.com/3blue1brown Special thanks to these supporters: http://3b1b.co/nn1-thanks For any early-stage ML entrepreneurs, Amplify Partners would love to hear from you: [email protected] Full playlist: http://3b1b.co/neural-networks Typo correction: At 14:45, the last index on the bias vector is n, when it's supposed to in fact be a k. Thanks for the sharp eyes that caught that! For those who want to learn more, I highly recommend the book by Michael Nielsen introducing neural networks and deep learning: https://goo.gl/Zmczdy There are two neat things about this book. First, it's available for free, so consider joining me in making a donation Nielsen's way if you get something out of it. And second, it's centered around walking through some code and data which you can download yourself, and which covers the same example that I introduce in this video. Yay for active learning! https://github.com/mnielsen/neural-networks-and-deep-learning I also highly recommend Chris Olah's blog: http://colah.github.io/ For more videos, Welch Labs also has some great series on machine learning: https://youtu.be/i8D90DkCLhI https://youtu.be/bxe2T-V8XRs For those of you looking to go *even* deeper, check out the text "Deep Learning" by Goodfellow, Bengio, and Courville. Also, the publication Distill is just utterly beautiful: https://distill.pub/ Lion photo by Kevin Pluck Music by Vincent Rubinetti: https://soundcloud.com/vincerubinetti/ ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 1894914 3Blue1Brown
Ever wonder how Bitcoin (and other cryptocurrencies) actually work?
 
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Bitcoin explained from the viewpoint of inventing your own cryptocurrency. These in-depth videos are made possible by patreon: https://patreon.com/3blue1brown Protocol Labs: https://protocol.ai/ Interested in contributing? https://protocol.ai/join/ Special thanks to the following patrons: http://3b1b.co/btc-thanks Some people have asked if this channel accepts contributions in cryptocurrency form as an alternative to Patreon. As you might guess, the answer is yes :). Here are the relevant addresses: ETH: 0x88Fd7a2e9e0E616a5610B8BE5d5090DC6Bd55c25 BTC: 1DV4dhXEVhGELmDnRppADyMcyZgGHnCNJ BCH: qrr82t07zzq5uqgek422s8wwf953jj25c53lqctlnw LTC: LNPY2HEWv8igGckwKrYPbh9yD28XH3sm32 Supplement video: https://youtu.be/S9JGmA5_unY Music by Vincent Rubinetti: https://soundcloud.com/vincerubinetti/heartbeat Here are a few other resources I'd recommend: Original Bitcoin paper: https://bitcoin.org/bitcoin.pdf Block explorer: https://blockexplorer.com/ Blog post by Michael Nielsen: https://goo.gl/BW1RV3 (This is particularly good for understanding the details of what transactions look like, which is something this video did not cover) Video by CuriousInventor: https://youtu.be/Lx9zgZCMqXE Video by Anders Brownworth: https://youtu.be/_160oMzblY8 Ethereum white paper: https://goo.gl/XXZddT ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 2039856 3Blue1Brown
Derivatives of exponentials | Chapter 5, Essence of calculus
 
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What is e? And why are exponentials proportional to their own derivatives? Full series: http://3b1b.co/calculus Series like this one are funded largely by the community, through Patreon, where supporters get early access as the series is being produced. http://3b1b.co/support Special thanks to the following patrons: http://3b1b.co/eoc5-thanks ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 327083 3Blue1Brown
Essence of calculus, chapter 1
 
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I want you to feel that you could have invented calculus for yourself, and in this first video of the series, we see how unraveling the nuances of a simple geometry question can lead to integrals, derivatives, and the fundamental theorem of calculus. Full series: http://3b1b.co/calculus Series like this one are funded largely by the community, through Patreon, where supporters get early access as the series is being produced. http://3b1b.co/support Special thanks to the following supporters: http://3b1b.co/eoc1-thanks ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 1013370 3Blue1Brown
The hardest problem on the hardest test
 
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A difficult geometry puzzle with an elegant solution. Practice more problem-solving at https://brilliant.org/3b1b Solution to the puzzle mentioned at the end: https://brilliant.org/3b1bindicator/ Special thanks to the following patrons: http://3b1b.co/putnam-thanks These videos exist thanks to Patreon: https://www.patreon.com/3blue1brown A different write-up of this solution: http://lsusmath.rickmabry.org/psisson/putnam/putnam-web.htm 1992 Putnam with this problem: http://kskedlaya.org/putnam-archive/1992.pdf A problem with a similar flavor came up on the 2005 Putnam A6. Give it a try! In the solutions for that problem, by the way, the that Calvin Lin is a friend of mine who works at Brilliant. http://kskedlaya.org/putnam-archive/2005.pdf http://kskedlaya.org/putnam-archive/2005s.pdf Music by Vincent Rubinetti: https://soundcloud.com/vincerubinetti/ ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 2410445 3Blue1Brown
Backpropagation calculus | Appendix to deep learning chapter 3
 
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This one is a bit more symbol heavy, and that's actually the point. The goal here is to represent in somewhat more formal terms the intuition for how backpropagation works in part 3 of the series, hopefully providing some connection between that video and other texts/code that you come across later. Find the full playlist at http://3b1b.co/neural-networks Thanks to everyone supporting on Patreon. http://3b1b.co/nn3-thanks http://3b1b.co/support For more on backpropagation: http://neuralnetworksanddeeplearning.com/chap2.html https://github.com/mnielsen/neural-networks-and-deep-learning http://colah.github.io/posts/2015-08-Backprop/ Music by Vincent Rubinetti: https://soundcloud.com/vincerubinetti/ ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe, and click the bell to receive notifications (if you're into that): http://3b1b.co/subscribe If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 293370 3Blue1Brown
Fractals are typically not self-similar
 
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What fractal dimension is, and how this is the core concept defining what fractals themselves are. Patreon page: https://www.patreon.com/3blue1brown Special thanks to the following Patrons: http://3b1b.co/fractals-thanks Check out Affirm careers here: http://affirmjobs.3b1b.co Music by Vince Rubinetti: https://soundcloud.com/vincerubinetti/riemann-zeta-function One technical note: It's possible to have fractals with an integer dimension. The example to have in mind is some *very* rough curve, which just so happens to achieve roughness level exactly 2. Slightly rough might be around 1.1-dimension; quite rough could be 1.5; but a very rough curve could get up to 2.0 (or more). A classic example of this is the boundary of the Mandelbrot set. The Sierpinski pyramid also has dimension 2 (try computing it!). The proper definition of a fractal, at least as Mandelbrot wrote it, is a shape whose "Hausdorff dimension" is greater than its "topological dimension". Hausdorff dimension is similar to the box-counting one I showed in this video, in some sense counting using balls instead of boxes, and it coincides with box-counting dimension in many cases. But it's more general, at the cost of being a bit harder to describe. Topological dimension is something that's always an integer, wherein (loosely speaking) curve-ish things are 1-dimensional, surface-ish things are two-dimensional, etc. For example, a Koch Curve has topological dimension 1, and Hausdorff dimension 1.262. A rough surfaces might have topological dimension 2, but fractal dimension 2.3. And if a curve with topological dimension 1 has a Hausdorff dimension that *happens* to be exactly 2, or 3, or 4, etc., it would be considered a fractal, even though it's fractal dimension is an integer. ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: https://www.youtube.com/playlist?list=PLZHQObOWTQDPHP40bzkb0TKLRPwQGAoC- Various social media stuffs: Twitter: https://twitter.com/3Blue1Brown Facebook: https://www.facebook.com/3blue1brown/ Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 718706 3Blue1Brown
What is backpropagation really doing? | Chapter 3, deep learning
 
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What's actually happening to a neural network as it learns? Training data generation + T-shirt at http://3b1b.co/crowdflower Crowdflower does some cool work and addresses a meaningful need in machine learning, so I was pretty excited that they agreed to sponsor this video. Find the full playlist at http://3b1b.co/neural-networks The following video is sort of an appendix to this one. The main goal with the follow-on video is to show the connection between the visual walkthrough here, and the representation of these "nudges" in terms of partial derivatives that you will find when reading about backpropagation in other resources, like Michael Nielsen's book or Chis Olah's blog. Thanks to everyone supporting on Patreon. http://3b1b.co/nn3-thanks http://3b1b.co/support For more on backpropagation: http://neuralnetworksanddeeplearning.com/chap2.html https://github.com/mnielsen/neural-networks-and-deep-learning http://colah.github.io/posts/2015-08-Backprop/ Music by Vincent Rubinetti: https://soundcloud.com/vincerubinetti/ ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 528796 3Blue1Brown
Implicit differentiation, what's going on here? | Chapter 6, Essence of calculus
 
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Implicit differentiation can feel weird, but what's going on makes much more sense once you view each side of the equation as a two-variable function, f(x, y). Full series: http://3b1b.co/calculus Series like this one are funded largely by the community, through Patreon, where supporters get early access as the series is being produced. http://3b1b.co/support Special thanks to the following Patrons: http://3b1b.co/eoc6-thanks ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 274971 3Blue1Brown
All possible pythagorean triples, visualized
 
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Can we describe all right triangles with whole number side lengths using a nice pattern? Check out Remix careers: https://www.remix.com/jobs Regarding the brief reference to Fermat's Last Theorem, what should be emphasized is that it refers to *positive* integers. You can of course have things like 0^3 + 2^3 = 2^3, or (-3)^3 + 3^3 = 0^3. Special thanks to the following patrons: http://3b1b.co/triples-thanks Music by Vincent Rubinett : https://soundcloud.com/vincerubinetti/heartbeat ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 589732 3Blue1Brown
Higher order derivatives | Footnote, Essence of calculus
 
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A very quick primer on the second derivative, third derivative, etc. Full playlist: http://3b1b.co/calculus ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 122340 3Blue1Brown
Taylor series | Chapter 10, Essence of calculus
 
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Taylor polynomials are incredibly powerful for approximations, and Taylor series can give new ways to express functions. Early access to future series: https://patreon.com/3blue1brown Full series: http://3b1b.co/calculus Series like this one are funded largely by the community, through Patreon, where supporters get early access as the series is being produced. http://3b1b.co/support ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 487261 3Blue1Brown
Tattoos on Math
 
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After a friend of mine got a tattoo with a representation of the cosecant function, it got me thinking about how there's another sense in which this function is a tattoo on math, so to speak. One month free audible trial: http://www.audibletrial.com/3blue1brown ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 262138 3Blue1Brown
What does area have to do with slope? | Chapter 9, Essence of calculus
 
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Integrals are used to find the average of a continuous variable, and this can offer a perspective on why integrals and derivatives are inverses, distinct from the one shown in the last video. Full series: http://3b1b.co/calculus Series like this one are funded largely by the community, through Patreon, where supporters get early access as the series is being produced. http://3b1b.co/support Special thanks to the following supporters: http://3b1b.co/eoc9-thanks ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 215039 3Blue1Brown
Visualizing the chain rule and product rule | Chapter 4, Essence of calculus
 
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A visual explanation of what the chain rule and product rule are, and why they are true. Check out Brilliant: https://brilliant.org/3b1b Full series: http://3b1b.co/calculus Series like this one are funded largely by the community, through Patreon, where supporters get early access as the series is being produced. http://3b1b.co/support Special thanks to the following Patrons: http://3b1b.co/eoc4-thanks ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 283194 3Blue1Brown
Hilbert's Curve: Is infinite math useful?
 
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Space filling curves, turning visual information into audio information, and the connection between infinite and finite math (this is a reupload of an older video which had much worse audio). Supplement with more space-filling curve fun: https://youtu.be/RU0wScIj36o For more information on sight-via sound, this paper involving rewiring a ferret's retinas to its auditory cortex is particularly thought-provoking: http://phy.ucsf.edu/~houde/coleman/sur2.pdf Alternatively, here the NYT summary: https://goo.gl/qNuc14 Also, check out this excellent podcast on Human echolocation: https://goo.gl/23f4Yh For anyone curious to read more about the connections between infinite and finite math, consider this Terry Tao blog post: https://goo.gl/NZ4yrW Lion photo by Kevin Pluck Music by Vincent Rubinetti: https://soundcloud.com/vincerubinetti/heartbeat ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brownm/r/3Blue1Brown
Views: 302850 3Blue1Brown
The paradox of the derivative | Chapter 2, Essence of calculus
 
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Derivatives center on the idea of change in an instant, but change happens across time while an instant consists of just one moment. How does that work? Check out the Art of Problem Solving: https://aops.com/3blue1brown Note, to illustrate my point for the target audience of a new calculus student, I discussed a hypothetical speedometer that makes distance measurements over a very small time. Interestingly, most actual speedometers in modern cars work by analyzing the induced current of a spinning magnet, which is in some sense the universe implementing the derivative. Full series: http://3b1b.co/calculus Series like this one are funded largely by the community, through Patreon, where supporters get early access as the series is being produced. http://3b1b.co/support Special thanks to the following supporters: http://3b1b.co/eoc2-thanks ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 561592 3Blue1Brown
Euler's formula with introductory group theory
 
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How e to the pi i can be made more intuitive with some perspectives from group theory, and why exactly e^(pi i) = -1. Apply to work at Emerald Cloud Lab: - Application software engineer: http://3b1b.co/ecl-app-se - Infrastructure engineer: http://3b1b.co/ecl-infra-se - Lab focused engineer: http://3b1b.co/ecl-lab-se - Scientific computing engineer: http://3b1b.co/ecl-sci-comp Special thanks to the following Patrons: http://3b1b.co/epii-thanks There's a slight mistake at 13:33, where the angle should be arctan(1/2) = 26.565 degrees, not 30 degrees. Arg! If anyone asks, I was just...er...rounding to the nearest 10's. For those looking to read more into group theory, I'm a fan of Keith Conrads expository papers: http://www.math.uconn.edu/~kconrad/blurbs/ ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 638664 3Blue1Brown
Science YouTubers attempting a graph theory puzzle
 
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A mug with some unexpectedly interesting math. More problem-solving at Brilliant: https://brilliant.org/3b1b https://brilliant.org/3b1bflipping Special thanks to these patrons: http://3b1b.co/mug-thanks Thanks to all the following channels for participating. Standup Maths https://www.youtube.com/user/standupmaths Wendover Productions https://www.youtube.com/user/Wendoverproductions Welch Labs: https://www.youtube.com/user/Taylorns34 MinutePhysics: https://www.youtube.com/user/minutephysics Ben Eater: https://www.youtube.com/user/eaterbc Mathologer: https://www.youtube.com/channel/UC1_uAIS3r8Vu6JjXWvastJg Singing Banana: https://www.youtube.com/user/singingbanana Numberphile: https://www.youtube.com/user/numberphile Looking Glass Universe: https://www.youtube.com/user/LookingGlassUniverse Veritasium: https://www.youtube.com/user/1veritasium Steve Mould: https://www.youtube.com/user/steventhebrave Special thanks to MathsGear for providing the mugs. https://mathsgear.co.uk/ https://mathsgear.co.uk/products/gift-card Music: Vincent Rubinetti: https://soundcloud.com/vincerubinetti/ Divertissement by Kevin MacLeod is licensed under a Creative Commons Attribution license (https://creativecommons.org/licenses/by/4.0/) Source: http://incompetech.com/music/royalty-free/index.html?isrc=USUAN1100256 Artist: http://incompetech.com/ ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 412494 3Blue1Brown
Gradient descent, how neural networks learn | Chapter 2, deep learning
 
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Subscribe for more (part 3 will be on backpropagation): http://3b1b.co/subscribe Thanks to everybody supporting on Patreon. https://www.patreon.com/3blue1brown http://3b1b.co/nn2-thanks For any early stage ML startup founders, Amplify Partners would love to hear from you via [email protected] To learn more, I highly recommend the book by Michael Nielsen http://neuralnetworksanddeeplearning.com/ The book walks through the code behind the example in these videos, which you can find here: https://github.com/mnielsen/neural-networks-and-deep-learning MNIST database: http://yann.lecun.com/exdb/mnist/ Also check out Chris Olah's blog: http://colah.github.io/ His post on Neural networks and topology is particular beautiful, but honestly all of the stuff there is great. And if you like that, you'll *love* the publications at distill: https://distill.pub/ For more videos, Welch Labs also has some great series on machine learning: https://youtu.be/i8D90DkCLhI https://youtu.be/bxe2T-V8XRs "But I've already voraciously consumed Nielsen's, Olah's and Welch's works", I hear you say. Well well, look at you then. That being the case, I might recommend that you continue on with the book "Deep Learning" by Goodfellow, Bengio, and Courville. Thanks to Lisha Li (@lishali88) for her contributions at the end, and for letting me pick her brain so much about the material. Here are the articles she referenced at the end: https://arxiv.org/abs/1611.03530 https://arxiv.org/abs/1706.05394 https://arxiv.org/abs/1412.0233 Music by Vincent Rubinetti: https://soundcloud.com/vincerubinetti/ ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 808204 3Blue1Brown
Some light quantum mechanics (with minutephysics)
 
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Complementary video on minutephysics: https://youtu.be/zcqZHYo7ONs minutephysics channel: https://www.youtube.com/user/minutephysics Learn more through active problem-solving at Brilliant: https://brilliant.org/3b1b Special thanks to these patrons: http://3b1b.co/light-quantum-thanks Huge thanks to my friend Evan Miyazono, both for encouraging me to do this project, and for helping me understand many things along the way. This is a simple primer for how the math of quantum mechanics, specifically in the context of polarized light, relates to the math of classical waves, specifically classical electromagnetic waves. I will say, if you *do* want to go off and learn the math of quantum mechanics, you just can never have too much linear algebra, so check out the series I did at http://3b1b.co/essence-of-linear-algebra Mistakes: As several astute commenters have pointed out, the force arrow is pointing the wrong way at 2:18. Thanks for the catch! *Note on conventions: Throughout this video, I use a single-headed right arrow to represent the horizontal direction. The standard in quantum mechanics is actually to use double-headed arrows for describing polarization states, while single-headed arrows are typically reserved for the context of spin. What's the difference? Well, using a double-headed arrow to represent the horizontal direction emphasizes that in a quantum mechanical context, there's no distinction between left and right. They each have the same measurable state: horizontal (e.g. they pass through horizontally oriented filters). Once you're in QM, these kets are typically vectors in a more abstract space where vectors are not necessarily spatial directions but instead represent any kind of state. Because of how I chose to motivate things with classical waves, where it makes sense for this arrow to represent a unit vector in the right direction, rather than the more abstract idea of a horizontal state vector, I chose to stick with the single-headed notation throughout, though this runs slightly against convention. Music by Vincent Rubinetti: https://soundcloud.com/vincerubinetti/one-two-zeta ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 491159 3Blue1Brown
Derivative formulas through geometry | Chapter 3, Essence of calculus
 
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A few derivative formulas, such as the power rule and the derivative of sine, demonstrated with geometric intuition. Check out Brilliant: https://brilliant.org/3b1b Full series: http://3b1b.co/calculus Series like this one are funded largely by the community, through Patreon, where supporters get early access as the series is being produced. http://3b1b.co/support Special thanks to the following Patrons: http://3b1b.co/eoc3-thanks ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 425042 3Blue1Brown
Who (else) cares about topology?  Stolen necklaces and Borsuk-Ulam
 
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The Borsuk-Ulam theorem from topology solving a counting puzzle. Truly unexpected, truly beautiful. Shirts/posters at DFTBA: http://3b1b.co/store The Great Courses Plus free trial: http://ow.ly/GtbB3083BZc Mathologer's related video: https://youtu.be/7s-YM-kcKME (Seriously, Mathologer is great) VSauce on fixed points: https://youtu.be/csInNn6pfT4 The original 1986 by Alon and West with this proof: https://goo.gl/XeI58w EE Paper using ideas related to this puzzle: https://goo.gl/bPQQpE I first came across this paper thanks to Alon Amit's answer on this Quora post: https://goo.gl/YzFtjf Music by Vince Rubinetti: https://soundcloud.com/vincerubinetti/riemann-zeta-function Special thanks to the following Patrons: http://3b1b.co/borsuk-thanks Apologies for the typos at 3:20 and 17:18. Turns out I was too engrossed with the math to think about spelling! (As a note, for The Great Courses Plus trial, it is currently available to watch through a web browser to almost anyone in the world and optimized for the US market. The Great Courses Plus is currently working to both optimize the product globally and accept credit card payments globally) ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: https://goo.gl/WmnCQZ Various social media stuffs: Website: https://www.3blue1brown.com/ Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown/ Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 333534 3Blue1Brown
Limits | Chapter 7, Essence of calculus
 
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Formal derivatives, the epsilon-delta definition, and why L'Hôpital's rule works. 3Blue1Brown store: http://3b1b.co/store Let me know what you'd like to see in there. Full series: http://3b1b.co/calculus Series like this one are funded largely by the community, through Patreon, where supporters get early access as the series is being produced. http://3b1b.co/support Special thanks to the following patrons: http://3b1b.co/eoc7-thanks ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 224783 3Blue1Brown
Q&A #2 + Net Neutrality Nuance
 
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Questions: http://3b1b.co/questions Answers: https://youtu.be/1nxF19qDBQ0 Full net neutrality video: https://youtu.be/hKD-lBrZ_Gg Ben Eater's channel: https://www.youtube.com/user/eaterbc First Q&A Answers: https://youtu.be/8r5WKpK9-m8 CGPGrey's (excellent) video on Net Neutrality: https://youtu.be/wtt2aSV8wdw ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 120354 3Blue1Brown
Integration and the fundamental theorem of calculus | Chapter 8, Essence of calculus
 
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What is an integral? How do you think about it? Check out the Art of Problem Solving: https://aops.com/3blue1brown Full series: http://3b1b.co/calculus Series like this one are funded largely by the community, through Patreon, where supporters get early access as the series is being produced. http://3b1b.co/support Special thanks to the following patrons: http://3b1b.co/eoc8-thanks ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 256912 3Blue1Brown
Pi hiding in prime regularities
 
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A story of pi, prime numbers, and complex numbers, and how number theory braids them together. Viewer-supported: https://www.patreon.com/3blue1brown The fact that only primes that are one above a multiple of four can be expressed as the sum of two squares is known as "Fermat's theorem on sums of two squares": https://goo.gl/EdhaN2 Special thanks to the following patrons: http://3b1b.co/leibniz-thanks ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 551773 3Blue1Brown
Thinking visually about higher dimensions
 
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How do you think about a sphere in four dimensions? What about ten dimensions? Podcast! https://www.benbenandblue.com/ Problem-driven learning on at https://brilliant.org/3b1b Special thanks to these patrons: http://3b1b.co/high-d-thanks Check out Ben Eater's channel: https://www.youtube.com/user/eaterbc Music by Vincent Rubinetti: https://soundcloud.com/vincerubinetti/heartbeat ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 1423873 3Blue1Brown

Bitcoin client types
Although some companies have good prices, you can need $50,000 to get started. It can be challenging to ascertain a business`s spread policy so the best method to learn is to try several brokers, or speak to other traders who have, not to mention check out the forums. You must take a look at the business`s fine print or e-mail for more information. Businesses are mainly able to prevent fluctuations and easily benefit from the future prices. So, many businesses prefer using ready-made CRM solutions, but a lot of features still require customization and integration to fulfill the particular small business requirements. If your organization is having trouble getting through the proverbial hump, an excellent CRM program system might be the secret to reaching that next level. If you`re a company or private individual wanting to move considerable amounts of money abroad, and you`re therefore seeking to earn a purchase of a huge amount foreign currency, think before going studying the high street bank as your only route to getting that large quantity of foreign money.
When transferring lots of currency you should be careful were you do it to find the best rates. Negotiate hard and receive the very best rate you`re able to. The lower an individual credit rating, the greater her APR interest rate will be.
Some brokers have various spreads for various customers. It`s simpler to stick with the broker you`ve come to know and trust. Regardless of the specific order, brokers must get the finest possible price for their customers. Locating a fantastic broker means finding one that is appropriate for you and your trading style. Brokerage is a price of conducting business and as such you need to always look to reduce your expenses.
Any system that you use for trading has to be operated in a safe encrypted environment and the system has to be fully protected and continuously monitored. As soon as you have a fully tested trading system you`re prepared to trade. Finding the very best forex trading program process isn`t easy and will take you a little bit of time. It`s also simple to manage the computer software. Trading software must for example supply you with a summary of the marketplace so you can spot trends and opportunities as they arise in real time and make it possible for you to focus in and receive in depth info on particular currency pairs with constantly updating real-time rates, along with historic price data. It`s however the major tool of your trade and therefore do not merely accept the very first system you stumble across and work with it, good or bad. Developing an extensive CRM process is complicated and very costly, but its becoming a critical investment.
Utilizing AI algorithms, it will not merely improve itself but can also supply you with precious info about your customers. Understand their terms and legal info, then choose one that you`re comfortable and confident with. Secondly, it`s crucial that you collect as much info and insight as you`re able to.

The miners are interested in finding a nonce which will create a hash with certain characteristics. Lastly, they have to find a random value that they included in the header, which makes the computed hash over that header a value below a particular target. In other words, they do not have to agree to change the protocol. Though there are a few gold diggers attempting to fill their pockets and certain projects that aren`t viable and shouldn`t be encouraged in any way. For users running a complete node, it is a fairly painless procedure to upgrade the software to the newest version. The process of locating a new block to extend the blockchain is known as mining. Proof-of-Work systems utilize cryptographic hashing algorithms to create the action of mining a block a complicated computation. Our software is totally incompatible with altcoins. Changes and modifications to how that it works need to be approved by consensus and every CPU gets a vote. To start with, it`s essential to realize that hardware wallet users control entirely their private keys. Whether you`re bullish or bearish on Bitcoin Gold, you ought not lose your coins as a result of careless mistakes! On the 1 hand, it may result in making a coin that solves all the pending issues. There`s no currency or digital asset named Bitcoin Core. Bitcoin Cash increases the range of transactions that may be processed per block. You could send any quantity of money, any place in the Earth, almost at no cost. You`ve made some great money already on the market, but you want more. For a wealthy individual, BTC`s price premium may be viewed as a plus. For someone without lots of money, BCH`s low price may look like a great deal for Bitcoin. If you have some concerns about the worth of Bitcoin after all forks, you need to be ready for a drop. The distinction is that not all of these suffer the chain split. The primary problem is Bitcoin imposes a hard limit on the magnitude of a block, the location where transaction information becomes stored. The end result is many straightforward wallets, called SPV wallets and very commonly found on your phone, will be quite confused about which chain is Bitcoin. In Bitcoin, the most important reason is known as the network effect.