Taylor polynomials are incredibly powerful for approximations and analysis. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/lessons/taylor-series#thanks Home page: https://www.3blue1brown.com/ 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 Timestamps 0:00 - Approximating cos(x) 8:24 - Generalizing 13:34 - e^x 14:25 - Geometric meaning of the second term 17:13 - Convergence issues ------------------ 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

An introduction to group theory (Minor error corrections below) Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: https://3b1b.co/monster-thanks Timestamps: 0:00 - The size of the monster 0:50 - What is a group? 7:06 - What is an abstract group? 13:27 - Classifying groups 18:31 - About the monster Errors: *Typo on the "hard problem" at 14:11, it should be a/(b+c) + b/(a+c) + c/(a+b) = 4 *Typo-turned-speako: The classification of quasithin groups is 1221 pages long, not 12,000. The full collection of papers proving the CFSG theorem do comprise tens of thousands of pages, but no one paper was quite that crazy. Thanks to Richard Borcherds for his helpful comments while putting this video together. He has a wonderful hidden gem of a channel: https://youtu.be/a9k_QmZbwX8 You may also enjoy this brief article giving an overview of this monster: http://www.ams.org/notices/200209/what-is.pdf If you want to learn more about group theory, check out the expository papers here: https://kconrad.math.uconn.edu/blurbs/ Videos with John Conway talking about the Monster: https://youtu.be/jsSeoGpiWsw https://youtu.be/lbN8EMcOH5o More on Noether's Theorem: https://youtu.be/CxlHLqJ9I0A https://youtu.be/04ERSb06dOg The symmetry ambigram was designed by Punya Mishra: https://punyamishra.com/2013/05/31/symmetry-new-ambigram/ The Monster image comes from the Noun Project, via Nicky Knicky This video is part of the #MegaFavNumbers project: https://www.youtube.com/playlist?list=PLar4u0v66vIodqt3KSZPsYyuULD5meoAo To join the gang, upload your own video on your own favorite number over 1,000,000 with the hashtag #MegaFavNumbers, and the word MegaFavNumbers in the title by September 2nd, 2020, and it'll be added to the playlist above. ------------------ These animations are largely made using manim, a scrappy open-source python library: https://github.com/3b1b/manim If you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and it has many other quirks you might expect in a library someone wrote with only their own use in mind. Music by Vincent Rubinetti. Download the music on Bandcamp: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown Stream the music on Spotify: https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people. ------------------ 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: http://3b1b.co/subscribe Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3blue1brown Reddit: https://www.reddit.com/r/3blue1brown Instagram: https://www.instagram.com/3blue1brown_animations/ Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown

Thank you for 2^21 subscribers. Store: http://3b1b.co/store ↓↓Links to things discussed below ↓↓ The Bit Player https://thebitplayer.com/ The Idea Factory https://amzn.to/325PY6W The Information, A History, A Theory, A Flood https://amzn.to/2QhfUtR You can read about Lorenz in "Chaos", also by James Gleick https://amzn.to/3tcXtVF Anthropocene reviewed https://www.wnycstudios.org/podcasts/anthropocene-reviewed Hardcore history https://www.dancarlin.com/ The Numberphile podcast https://www.numberphile.com/podcast Recent Quanta article on the eigenvector discovery https://www.quantamagazine.org/neutrinos-lead-to-unexpected-discovery-in-basic-math-20191113/ Channel supported by http://3b1b.co/thanks ------------------ Animations on this channel are largely made using manim, a scrappy open source python library. https://github.com/3b1b/manim If you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and it has many other quirks you might expect in a library someone wrote with only their own use in mind. Music by Vincent Rubinetti. Download the music on Bandcamp: https://vincerubinetti.bandcamp.com/a... Stream the music on Spotify: https://open.spotify.com/album/1dVyjw... If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people. ------------------ 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: http://3b1b.co/subscribe Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3blue1brown Reddit: https://www.reddit.com/r/3blue1brown Instagram: https://www.instagram.com/3blue1brown... Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown

Tips on problem-solving, with examples from geometry, trig, and probability. Past episodes with integrated quizzes: https://itempool.com/c/3b1b Full playlist: https://www.youtube.com/playlist?list=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev Home page: https://www.3blue1brown.com Brought to you by you: https://3b1b.co/ldm-thanks Huge huge thanks to Ben Eater: https://www.youtube.com/user/eaterbc And Cam Christensen, creator of ItemPool: https://itempool.com/ Notes by Ngân Vũ: https://twitter.com/ThuyNganVu/status/1265480770832855040 Mistakes: 50:35, there should be a dx in the integral 54:40, if you notice the mistake here and are inclined to complain, keep watching ------------------ Video timeline (thanks to user "noonesperfect") 0:34 9-Problem Solving Principles/Tip 1:15 Question 1 (Probability) 2:08 Who is Ben Eater? 4:25 Inscribed angle theorem, θL=2*θs 5:58 Tip-1 7:48 Tip-2 8:16 Question 2 9:34 Answer 2 10:29 Tip-3 15:17 Tip-4 22:48 Question 3 25:56 Answer 3 (Marked incorrectly, Answer: Option D) 26:31 Answer 1 27:28 Explanation for Q1, Floor function 30:38 Tip-5 32:53 Tip-6 33:36 Question 4 34:43 Answer 4 36:37 Question 5 38:10 Answer 5 41:48 Probability graph in Desmos 44:08 Revisiting an alternating series sum for ln(2) 47:29 Tip-7 51:08 Tip-8 55:23 Audience questions through tweets 57:28 Tip-9 58:29 Python programming for various probability question 1:04:31 Arts created using Desmos graph tool with mathematical expressions 1:05:54 Thank you, appreciation to the team and all. ------------------ The live question setup with stats on-screen is powered by Itempool. https://itempool.com/ Curious about other animations? https://www.3blue1brown.com/faq#manim Music by Vincent Rubinetti. Download the music on Bandcamp: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown Stream the music on Spotify: https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people. ------------------ 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: http://3b1b.co/subscribe Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3blue1brown Reddit: https://www.reddit.com/r/3blue1brown Instagram: https://www.instagram.com/3blue1brown_animations/ Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown