A quick trick for computing eigenvalues | Essence of linear algebra, chapter 15 0 (0)

From 3Blue1Brown. How to write the eigenvalues of a 2×2 matrix just by looking at it. Thanks to Tim for the jingle: https://www.youtube.com/acapellascience Help fund future projects: https://www.patreon.com/3blue1brown​ An equally valuable form of support is to simply share the videos. Special thanks to these supporters: https://3b1b.co/quick-eigen-thanks Introduction to eigenvectors and eigenvalues: https://youtu.be/PFDu9oVAE-g Lockdown math lecture…

How (and why) to raise e to the power of a matrix | DE6 0 (0)

From 3Blue1Brown. General exponentials, Love, Schrödinger, and more. Home page: https://www.3blue1brown.com Brought to you by you: https://3b1b.co/thanks —————— The Romeo-Juliet example is based on this essay by Steven Strogatz: http://www.stevenstrogatz.com/essays/loves-me-loves-me-not-do-the-math The book shown at the start is Vladimir Arnold’s (excellent) textbook on ordinary differential equations. https://amzn.to/3dtXSwj Need a review of ordinary powers of e? https://youtu.be/m2MIpDrF7Es…

The medical test paradox: Can redesigning Bayes rule help? 0 (0)

From 3Blue1Brown. Bayes factors, aka Likelihood Ratios*, offer a very clear view of how medical test probabilities work. Home page: https://www.3blue1brown.com Brought to you by you: https://3b1b.co/bayes-factor-thanks The book by my friend Matt Cook about paradoxes mentioned at then end: https://amzn.to/3aBrEzg On the topic, I can’t help also mentioning another paradox book I’m rather fond…

Hamming codes part 2, the elegance of it all 0 (0)

From 3Blue1Brown. Part 1: https://youtu.be/X8jsijhllIA Watch Ben Eater’s video: https://youtu.be/h0jloehRKas Viewer-supported: https://3b1b.co/hamming-thanks A cleaner perspective on Hamming error correction codes. You can read Hamming’s own perspective on his discovery of these codes in chapter 12 of "The Art of Doing Science and Engineering". https://amzn.to/3lwcnmh Heavily related is the chessboard puzzle I did with Matt Parker:…

Hamming codes and error correction 0 (0)

From 3Blue1Brown. A discovery-oriented introduction to error correction codes. Part 2: https://youtu.be/b3NxrZOu_CE Ben Eater:’s take: https://youtu.be/h0jloehRKas Many thanks to these supporters: https://3b1b.co/hamming-thanks Heavily related is the chessboard puzzle I did with Matt Parker: https://youtu.be/as7Gkm7Y7h4 You can read Hamming’s own perspective on his discovery of these codes in chapter 12 of "The Art of Doing Science…

Group theory and why I love 808,017,424,794,512,875,886,459,904,961,710,757,005,754,368,000,000,000 0 (0)

From 3Blue1Brown. An introduction to group theory, and the monster group. Paid for by viewers, like you: https://3b1b.co/monster-thanks Minor error corrections below↓↓↓ 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 impossible chessboard puzzle 0 (0)

From 3Blue1Brown. An information puzzle with an interesting twist Solution on Stand-up Maths: https://youtu.be/as7Gkm7Y7h4 Paid for by viewers, like you: https://3b1b.co/chess-thanks Home page: https://www.3blue1brown.com —————— 0:00 Introduction 3:58 Visualizing the two-square case 5:46 Visualizing the three-square case 12:19 Proof that it’s impossible 16:22 Explicit painting of the hypercube —————— Thanks to everyone who endured me…

Tips to be a better problem solver [Last lecture] | Lockdown math ep. 10 0 (0)

From 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…

Intuition for i to the power i | Lockdown math ep. 9 0 (0)

From 3Blue1Brown. i^i, visualized and explained. 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 Mistakes: At 1:06:20, when changing r to equal 0.69*i, I said "this is what we might think of as (2i)^x", but that is not correct. It’s what we’d think of as [Exp(ln(2)*i)]^x for whatever complex number Exp(ln(2)*i)…

Does contact tracing necessarily sacrifice privacy? (via Nicky Case) 0 (0)

From 3Blue1Brown. Though many contact tracing apps involve location tracking, they don’t have to. This is a video adaptation of a post by Nicky Case: https://ncase.me/contact-tracing/ New post by Nicky on COVID-19: https://ncase.me/covid-19/ Consider supporting his work: https://www.patreon.com/ncase/ Supporters of this video: https://3b1b.co/ctracing-thanks DP-3T Whitepaper: https://github.com/DP-3T/documents/blob/master/DP3T%20White%20Paper.pdf Full repo: https://github.com/DP-3T Where did the number 60% come…

The power tower puzzle | Lockdown math ep. 8 0 (0)

From 3Blue1Brown. A fun puzzle stemming from repeated exponentiation. 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 Notes by Ngân Vũ: https://twitter.com/ThuyNganVu/status/1261014161464516608?s=20 Play along on Desmos: https://www.desmos.com/calculator/nul32eaaa9 Related videos. Calculus series: https://www.youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr In particular look at: https://youtu.be/CfW845LNObM Numberphile on Grahm’s constant: https://youtu.be/XTeJ64KD5cg —————— Video timeline (thanks to user "noonesperfect") 0:36 Question…

What makes the natural log “natural”? | Lockdown math ep. 7 0 (0)

From 3Blue1Brown. All about ln(x). 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 Beautiful pictorial summary by @ThuyNganVu: https://twitter.com/ThuyNganVu/status/1259288683489849344 Errors: At minute 16, the sum should be written with a "…" to indicate going to infinity. At minute 38, the exponent should have 1/(2s^2) instead of 1/s^2 for s to represent…

Logarithm Fundamentals | Lockdown math ep. 6 0 (0)

From 3Blue1Brown. Back to the basics with logarithms. 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 Triangle of power: https://youtu.be/sULa9Lc4pck Beautiful pictorial summary by @ThuyNganVu: https://twitter.com/ThuyNganVu/status/1258222677573001219 —————— 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…

Imaginary interest rates | Lockdown math ep. 5 0 (0)

From 3Blue1Brown. Compound interest, e, and how it relates to circles. 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 Great Mathologer video: https://youtu.be/-dhHrg-KbJ0 Beautiful pictorial summary by @ThuyNganVu: https://twitter.com/ThuyNganVu/status/1258221677990703105 https://twitter.com/ThuyNganVu/status/1258222002889875457 My other videos on imaginary exponents: https://youtu.be/v0YEaeIClKY https://youtu.be/mvmuCPvRoWQ Mistakes: In the off-handed remarks on quaternions, I mentioned rotation in 4d would…

What is Euler’s formula actually saying? | Lockdown math ep. 4 0 (0)

From 3Blue1Brown. What does it mean to compute e^{pi i}? 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 Beautiful pictorial summary by @ThuyNganVu: https://twitter.com/ThuyNganVu/status/1258220129327800320 https://twitter.com/ThuyNganVu/status/1258220541686628353 —————— Video Timeline (Thanks to user "Just TIEriffic") 0:00:00 Welcome 0:00:20 Ending Animation Preview 0:01:15 Reminders from previous lecture 0:03:30 Q1: Prompt (Relationship with e^iθ=…) 0:05:40…

Complex number fundamentals | Lockdown math ep. 3 0 (0)

From 3Blue1Brown. Intro to the geometry complex numbers. 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 Beautiful pictorial summary by @ThuyNganVu: https://twitter.com/ThuyNganVu/status/1258219199769440257 Errors: – On the first sketch of a complex plane, there is a "2i" written instead of "-2i". – At the end, in writing the angle sum identity, the…

Trigonometry fundamentals | Lockdown math ep. 2 0 (0)

From 3Blue1Brown. Intro to trig with a lurking mystery about cos(x)^2 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 —————– Contents: Introduction  – 0:00 Q1 Graph of (cos θ)²  – 2:14 Q2 Translations of cos θ to (cos θ)²  – 5:34 Q3 f(2x) = f(x)²  – 10:54 Intro to Trig  – 13:14 Q4 sin(3) & cos(3)  –…

The simpler quadratic formula | Lockdown math ep. 1 0 (0)

From 3Blue1Brown. Another view on the quadratic formula. 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 Beautiful pictorial summary by @ThuyNganVu: https://twitter.com/ThuyNganVu/status/1258217451323416577 Po Shen Loh on quadratics: https://www.youtube.com/watch?v=ZBalWWHYFQc Welch Labs on imaginary numbers: https://www.youtube.com/playlist?list=PLiaHhY2iBX9g6KIvZ_703G3KJXapKkNaF Mistakes (there will always be mistakes): At minute 22, I write "b’ / 2" instead of "-b’…