Using Statistics To Beat Wordle RandomMathsInc 2022-01-15 | This is a video on how we can use concept of probability and expected values to create an almost perfect Wordle player. I also make a simple proof of concept to show how good the method is, and do some analysis on why some guesses are better than others (spoiler: "lares" is apparently a very good first guess).I don't claim this idea to be unique or anything, but I still do want to give the problem a go myself regardless. If you haven't played Wordle, check it here (I am not the developer of the game): powerlanguage.co.uk/wordleSlight disclaimer: 99.9% win rate is only true for the game's easy mode. It's a slight caveat but it's still quite impressive the solver worksGitHub repository with the codes I wrote (as a Jupyter notebook, currently a bit untidy): github.com/thecheesynachos/word-game-solver. I try my best to check for bugs, and I don't think there are any. If there are though, do let me know. Many improvements to the code can still be made (e.g. use approximation techniques, optimise code, judging words with a different objective, etc.), so I encourage anyone else to build on what I did if you want.For the record, I don't use the solver when I actually play the game, since it kind of ruins the fun that way (lol).Chapters0:00 - Introduction1:36 - The game5:12 - Making the game work8:52 - Setting up the problem13:58 - How the variables relate to each other19:03 - What should we try to optimise?23:28 - The mathematical details30:29 - Which words should be checked?34:10 - Comparing the methods37:31 - Some demo40:15 - Words that are good (or bad) first guesses44:29 - Some details on the implementation45:21 - Other ways to potentially approach the problem46:19 - Outro and a bit of rambling
Conservation of Momentum RandomMathsInc 2020-05-02 | Extra bit: youtu.be/7-toe229pfUSome points - the argument I made for the conservation of momentum in this video is a bit simplistic (e.g. that the forces during the collision is a constant throughout, or that we restrict ourselves to collisions of objects), but just as a simple "proof" this works well enough. The extra bit (linked above) should provide a good enough generalisation to deal with these points.
Real Analysis: 12 Classes, Episode 12 RandomMathsInc 2020-01-05 | The final episode of the series, where I talk about a very proof-heavy maths classes. I ended on a maths class because, well, this channel is called RandomMathsInc after all.12 Classes playlist: youtube.com/playlist?list=PLBzCYlA4J3e58YH6o73Na3EeVDIO4Y5zO
Optimisation: 12 Classes, Episode 11 RandomMathsInc 2020-01-04 | What do you study in an Optimisation class, and why is it so useful?12 Classes Playlist: youtube.com/playlist?list=PLBzCYlA4J3e58YH6o73Na3EeVDIO4Y5zO
Statistical Mechanics: 12 Classes, Episode 10 RandomMathsInc 2020-01-03 | Probably my favourite physics class, all about describing the big world by considering things on the small scale.Fun fact: because of how I don't make the videos in this series in order, this is the last video I filmed and edited.12 Classes playlist: youtube.com/playlist?list=PLBzCYlA4J3e58YH6o73Na3EeVDIO4Y5zO
Machine Learning: 12 Classes, Episode 9 RandomMathsInc 2020-01-02 | If there was ever a trending page for computer science classes this one would be leading the chart. Featuring a picture of my friend (singular).12 Classes Playlist: youtube.com/playlist?list=PLBzCYlA4J3e58YH6o73Na3EeVDIO4Y5zOAndy's channel for random contents (NSFW warning probably appropriate): youtube.com/channel/UCyxKz0Boqiv6NjLXoc7aBiA
Quantum Mechanics & Atomic Physics: 12 Classes, Episode 8 RandomMathsInc 2020-01-01 | Three of the most difficult physics classes I have ever taken. 12 Classes Playlist: youtube.com/playlist?list=PLBzCYlA4J3e58YH6o73Na3EeVDIO4Y5zO
Discrete Maths: 12 Classes, Episode 7 RandomMathsInc 2019-12-31 | A maths class that talks about probability, logic, proofs, counting things, and a whole lot more.12 Classes playlist: youtube.com/playlist?list=PLBzCYlA4J3e58YH6o73Na3EeVDIO4Y5zO
Data Structures and Algorithms: 12 Classes, Episode 6 RandomMathsInc 2019-12-30 | One of the more difficult computer science class people will encounter.12 Classes Playlist: youtube.com/playlist?list=PLBzCYlA4J3e58YH6o73Na3EeVDIO4Y5zO
Numerical Methods: 12 Classes, Episode 5 RandomMathsInc 2019-12-29 | Sometimes you can't find answers of maths problems exactly. You have to approximate it. This is what this class is for. Also featuring me trying to do stuff with the Taylor series.12 Classes Playlist: youtube.com/playlist?list=PLBzCYlA4J3e58YH6o73Na3EeVDIO4Y5zOAdditional note for 5:44 that I should have mentioned: Taylor series, in the simplest explanation, says that you can turn any (continuous) function into a polynomial with infinitely many terms. However, if you take a few first terms of that polynomial, you can get a good approximation of the function around a certain point. We use that to calculate the error of our approximation. I haven't explained that too well.
ODEs & PDEs: 12 Classes, Episode 4 RandomMathsInc 2019-12-28 | A fun maths class, but also a very important concept you find in physics and other fields of science.12 Classes Playlist: youtube.com/playlist?list=PLBzCYlA4J3e58YH6o73Na3EeVDIO4Y5zO
Electricity and Magnetism: 12 Classes, Episode 3 RandomMathsInc 2019-12-27 | An interesting physics class where we learn about one of the four fundamental forces of nature.12 Classes Playlist: youtube.com/playlist?list=PLBzCYlA4J3e58YH6o73Na3EeVDIO4Y5zO
Linear Algebra: 12 Classes, Episode 2 RandomMathsInc 2019-12-26 | In a video where I try to discuss vectors, matrices and other things in linear algebra.12 Classes Playlist: youtube.com/playlist?list=PLBzCYlA4J3e58YH6o73Na3EeVDIO4Y5zO
Classical Mechanics: 12 Classes, Episode 1 RandomMathsInc 2019-12-25 | In the first episode, I talk about the physics class that started it all. Extra footage I had: youtu.be/GqjfCDIq_TI12 Classes Playlist: youtube.com/playlist?list=PLBzCYlA4J3e58YH6o73Na3EeVDIO4Y5zO
The Introduction: 12 Classes, Episode 0 RandomMathsInc 2019-12-24 | TL;DR: New series about 12 classes I have taken at university. First episode in 24 hours.Check it out at youtube.com/playlist?list=PLBzCYlA4J3e58YH6o73Na3EeVDIO4Y5zO
The YouTuber Dilemma (Dynamic Programming, Part 2) RandomMathsInc 2019-08-18 | We use dynamic programming to help our YouTuber friend get more profit from his videos. A very interesting problem indeed.Traditionally (or at least in CLRS), this would be the pipe cutting problem. But honestly, that's a bit boring isn't it?Part 1: youtu.be/Dn601s2-4Oc Extra part (how to actually chop the videos up?): youtu.be/c5y_CpC9W4k
Dynamic Programming (Part 1) RandomMathsInc 2019-08-11 | What is dynamic programming? You have came to the right place. In this video, we use principles in dynamic programming to speed up the process of finding Lucas numbers.Part 2: youtu.be/RaKBxwIPsBAThe top down implementation: youtu.be/yeUxWw9vwl0Whatever this is: youtu.be/uHOuLgC3Dvo
I Made A Flows Solver (Graph Problems and Linear Programming) RandomMathsInc 2019-07-30 | In this video I show you how I made a solver for a mobile game called Flows. This video is also an excuse for me to talk about linear programming, graph theory, maximum flow problem and also to make some terrible jokes. Hope people don't mind that it's a bit long!I was not sponsored by any mobile game in this video.Sections:0:09 - Flows Puzzle Problem3:05 - Graphs6:29 - Linear Programming (LP)11:11 - Maximum Flow Problem16:28 - Solving Maximum Flow Problem With LPs25:48 - Finally, the Flows Solver!36:28 - Results and ConclusionLink to code on GitHub: github.com/thecheesynachos/flows_solver (need Julia 1.0 and a few packages on the computer)Found a mistake somewhere in the video? Tell me and I'll put them down here in the description.
The Second Law of Thermodynamics RandomMathsInc 2019-04-04 | So this is a video I have wanted to make for a while now. I know that its production quality is not as good as other videos I have made in the past, and honestly, it may not give the Second Law the justice it deserves for the video. I might remake this in the future, we shall see. However, I felt the argument is interesting enough that it had to be told.Paper by Schroeder and Moore: arxiv.org/pdf/1502.07051.pdfThe video on the presentation I gave (which wasn't that good): youtu.be/CADqG4S8E2YExtra part on sticks and stones method: youtu.be/8ERONDNqYHk
Magnetic Field - Maxwells Equations, Pt. 5 RandomMathsInc 2018-09-09 | Now that we looked at electric fields, we look at the other field we have to consider - magnetic fields.The series: youtube.com/playlist?list=PLBzCYlA4J3e7B1Vi9PJ44igHftCPpP7NK
Gauss Law - Maxwells Equations, Ep. 4 RandomMathsInc 2018-09-02 | The first of the Maxwell's Equations!The series: youtube.com/playlist?list=PLBzCYlA4J3e7B1Vi9PJ44igHftCPpP7NK
Electric Fields - Maxwells Equations, Ep. 3 RandomMathsInc 2018-08-26 | Quick introduction into electric fields and what they are.The series: youtube.com/playlist?list=PLBzCYlA4J3e7B1Vi9PJ44igHftCPpP7NK
Divergence - Maxwells Equations, Ep. 2 RandomMathsInc 2018-08-19 | We look a bit deeper into the maths and talk about divergence and the divergence theorem.The series: youtube.com/playlist?list=PLBzCYlA4J3e7B1Vi9PJ44igHftCPpP7NK
Flux - Maxwells Equations, Ep. 1 RandomMathsInc 2018-08-12 | We begin our journey of Maxwell's equation by looking at vector fields, then working out how to calculate the flux of such field.The series: youtube.com/playlist?list=PLBzCYlA4J3e7B1Vi9PJ44igHftCPpP7NK
Actual Rocket Science - 12 Integrals, Ep. 12 RandomMathsInc 2018-01-05 | This is not a clickbait, as we will actually be deriving Tsiolkovsky's Rocket Equation in the finale of 12 Integrals.For the whole series: youtube.com/playlist?list=PLBzCYlA4J3e6zirZf7gu9vQgkJ_H1S0Fc
Another Trig Trick - 12 Integrals, Ep. 11 RandomMathsInc 2018-01-04 | If you haven't realised already, this whole series is just a lot of weird integration tricks. And here's another one for you.For the whole series: youtube.com/playlist?list=PLBzCYlA4J3e6zirZf7gu9vQgkJ_H1S0Fc
This Integral? Its Nothing - 12 Integrals, Ep. 10 RandomMathsInc 2018-01-03 | It's really nothing. I'm not joking.For the whole series: youtube.com/playlist?list=PLBzCYlA4J3e6zirZf7gu9vQgkJ_H1S0Fc
Gabriels Horn - 12 Integrals, Ep. 9 RandomMathsInc 2018-01-02 | A peculiar shape. A peculiar shape indeed.For the whole series: youtube.com/playlist?list=PLBzCYlA4J3e6zirZf7gu9vQgkJ_H1S0Fc
Length Of A Line - 12 Integrals, Ep. 8 RandomMathsInc 2018-01-01 | We look at how we can calculate the length of some line.For the whole series: youtube.com/playlist?list=PLBzCYlA4J3e6zirZf7gu9vQgkJ_H1S0Fc
Area Of A Circle - 12 Integrals, Ep. 7 RandomMathsInc 2017-12-31 | You are familiar with this equation. But can you prove it using integration?Link to the other method: youtu.be/YliEmHvxnvMFor the whole series: youtube.com/playlist?list=PLBzCYlA4J3e6zirZf7gu9vQgkJ_H1S0Fc
Two More Similar Integrals - 12 Integrals, Ep. 6 RandomMathsInc 2017-12-30 | It's very similar to yesterday's trick. It really is.For the whole series: youtube.com/playlist?list=PLBzCYlA4J3e6zirZf7gu9vQgkJ_H1S0Fc
Two Similar Integrals - 12 Integrals, Ep. 5 RandomMathsInc 2017-12-29 | It's another integral involving functions of trig, but with an interesting trick.For the whole series: youtube.com/playlist?list=PLBzCYlA4J3e6zirZf7gu9vQgkJ_H1S0Fc
Leibnizs Rule - 12 Integrals, Ep. 4 RandomMathsInc 2017-12-28 | Today we show you Feynman's favourite trick.Here's the video of the proof I was talking about: youtu.be/SrufNRtvgZwFor the whole series: youtube.com/playlist?list=PLBzCYlA4J3e6zirZf7gu9vQgkJ_H1S0Fc
The Integral Test - 12 Integrals, Ep. 3 RandomMathsInc 2017-12-27 | Here's an application of integration - to test the behaviours of infinite series.For the whole series (no pun intended): youtube.com/playlist?list=PLBzCYlA4J3e6zirZf7gu9vQgkJ_H1S0Fc
Some Complex Integrals - 12 Integrals, Ep. 2 RandomMathsInc 2017-12-26 | Euler would have been proud of this.For the whole series: youtube.com/playlist?list=PLBzCYlA4J3e6zirZf7gu9vQgkJ_H1S0Fc
Just Some Trigs - 12 Integrals, Ep. 1 RandomMathsInc 2017-12-25 | For the next 12 days, I will upload random videos all about integration. Today, we start with a simple warm up involving a lot of trigonometry.For the whole series: youtube.com/playlist?list=PLBzCYlA4J3e6zirZf7gu9vQgkJ_H1S0Fc
The Gaussian Integral RandomMathsInc 2017-08-26 | In this video, we try to evaluate the Gaussian integral. Featuring some multi-variable calculus, some graphs and my Paint illustrations.Little background:I first came across this integral in my quantum mechanics class a couple of months ago (see D. Griffiths' Introduction to Quantum Mechanics, 2nd Ed., Problem 1.3). I thought the way to solve this integral was rather cool, and had it in my list of to-make video for a while now. And here it is.
The Monte Carlo Method RandomMathsInc 2017-08-14 | RandomMathsInc is back after a long break, and today we talk about approximations using the Monte Carlo Method. Featuring random numbers and coding with Python.Footnotes:1 - If you want to know more about Monaco, wait until Geography Now makes a video about them (they're a great channel, you should check them out if you haven't already).2 - Most of the time, rather than using truly random numbers, computers will use pseudorandom numbers (see en.wikipedia.org/wiki/Pseudorandom_number_generator). They aren't actually random, but looks random enough to us and is random enough for the Monte Carlo Method.3 - Have you seen our Pi Day video this year? That problem was solved with the Monte Carlo Method: youtu.be/9r45ADGHK5sSome pictures I used:upload.wikimedia.org/wikipedia/commons/thumb/f/f8/Whole_Monaco.jpg/1200px-Whole_Monaco.jpgupload.wikimedia.org/wikipedia/commons/thumb/b/b6/Monaco_location_map.svg/2000px-Monaco_location_map.svg.pngupload.wikimedia.org/wikipedia/commons/thumb/4/42/France-monaco-map.svg/2000px-France-monaco-map.svg.pngupload.wikimedia.org/wikipedia/commons/b/ba/Monte-Carlo01.gifupload.wikimedia.org/wikipedia/commons/5/5f/RREA_Monte_Carlo_simulation.png
Calculating Pi Experimentally (Buffons Needle Problem) RandomMathsInc 2017-03-13 | It's Pi Day again. And here's a video to celebrate it.Featuring toothpicks, pies and Buffon's Needle Problem.Me throwing a toothpick: youtu.be/9-nc8pGBiu4Link to Wikipedia article on this: en.wikipedia.org/wiki/Buffon's_Link to that excel spreadsheet: dropbox.com/s/1nouq6d79fkca3z/toothpick%20simulation.xlsx?dl=0Links to photos I used that aren't public domain: commons.wikimedia.org/wiki/File:Gianluigi_Buffon_(31815848711).jpgcommons.wikimedia.org/wiki/File:Dice-111.svg
One Channel Called RandomMathsInc (12 Days of Christmas) RandomMathsInc 2017-01-05 | This is the end of our 12 day series.It is also the channel's THIRD birthday. Isn't that cool?But seriously guys, thanks for all the support. Even though our channel is very small and hardly anyone follows us, it's still great. I'll keep making these sorts of videos for you guys to watch. Thanks again for all the support!Song on the outro: "This Ain't The End Of Me" by White ComicFacebook Page: facebook.com/randommathsincAlso, I'll buy an ice-cream for the first person to bump into me in real life and recite a line from a Shakespeare play (very unlikely, but why not).
2 Branches of Calculus (12 Days of Christmas) RandomMathsInc 2017-01-04 | The penultimate episode of our series, and we talk about the two different branches of calculus, and the main cconcept behind each of the branches.Facebook Page: facebook.com/randommathsinc
3 Impossible Straightedge & Compass Constructions (12 Days of Christmas) RandomMathsInc 2017-01-03 | The three problems that fumbled the Greeks.Facebook Page: facebook.com/randommathsinc
4 Arithmetic Operators (12 Days of Christmas) RandomMathsInc 2017-01-02 | We talk about adding, subtracting, multiplying and dividing. It's simple, seriously!Facebook Page: facebook.com/randommathsinc
Why Methanes Bond Angle Is 109.5° RandomMathsInc 2016-12-16 | FACEBOOK PAGE: http://www.facebook.com/randommathsincWe find out why the bond angle of methane is 109.5° using some vectors.Making methane on paint: youtu.be/4yoSocEwTEYSome picture I used:Carbon dioxide molecule: commons.wikimedia.org/wiki/File:Carbon_dioxide_3D_ball.pngSulphur hexafluoride molecule: commons.wikimedia.org/wiki/File:Sulfur-hexafluoride-from-xtal-3D-balls.pngThis question was originally asked by my mechanics teacher a while back. Credits to him.
How many Robots are on the Spaceship? RandomMathsInc 2016-09-18 | OH MY WORD - RANDOMMATHSINC IS STILL ALIVE, and he's talking about the German Tank Problem in his latest video.Some links I used:http://www.statisticalconsultants.co.nz/blog/the-german-tank-problem.htmlhttp://www.theregister.co.uk/2014/05/20/german_tank_problem_and_leaky_datahttp://wikieducator.org/Point_estimation_-_German_tank_problemen.wikipedia.org/wiki/German_tank_problemWas a bit busy in the past month or so. I filmed a video explaining what I was up to, but that's still being edited. So stay tuned.
The e Song RandomMathsInc 2016-08-22 | Contains some explicit lyrics (not much though).Presenting to you, the song about Euler's constant.Extras: youtu.be/h4C-Bk1xxWgGet it on iTunes: http://bitly.com/1H9DQSzLyrics:There is this constant you oughta knowNamed after some dude who came from BaselIts value's just short of three, that's what I'm told.The constant sets the world alightIt gives students a mare at nightIts decimals, well, would take a while to write.The fifth letter of the alphabetAll thought out into a certain limitOne and one over x, to the power of x, as x turns infinite.Or if you don't like thoughts of things approachingThere's also an option of endless addingInvolving factorials, if that's more your thing.We're dealing with e, 'bout 2.7183.We're talking with e,Well who the fuck came up with this, with this constant e.(Talking: Well apparently Jacob Bernoulli came up with e, but Napier made earlier references to it.)Well e can be found in almost every placeWhen things are growing or if it decaysIn interest rates or half-life of toxic wasteDescribe complex numbers in a different notationOr discuss the normal distributionyou'll find that e just joins in the fun.e's part of Euler's identityThe most elegant thing in maths you'll seeIt's got zero, and one, and pi, and e.If you want something better than sexThen raise e to the power of xAnd its derivative will just be itself.We're dealing with e, 'bout 2.7183.We're talking with e,Well when the fuck will we use something like this, use this constant e.[Solo]We're dealing with e, 'bout 2.7183.We're talking with e,Well who the fuck would write a song about this, about this constant e.
How Bookmakers Make Money RandomMathsInc 2016-07-24 | We look at how bookmakers set their odds so that they would make money off the bettors.A bit more on decimal and fractional odds: support.skybet.com/app/answers/detail/a_id/37/~/fraction-and-decimal-pricingIf you're too lazy to watch the whole thing, you can go to;- 0:00 for dice analogy (introduction),- 1:53 for dice analogy (trying to make money),- 3:08 for dice analogy (adjusting odds),- 7:12 for start on part about bookmakers,- 9:20 for implied probability and over-rounding, and- 13:25 for why bookmakers have to adjust odds.Sources I used:en.wikipedia.org/wiki/Mathematics_of_bookmakinghttp://www.pinnacle.com/en/betting-articles/educational/how-bookmakers-make-moneyhttp://www.oddsportal.com (where I took sports odds from)http://www.mirror.co.uk/sport/row-zed/how-odds-leicester-winning-premier-7736523en.wikipedia.org/wiki/2015%E2%80%9316_Leicester_City_F.C._season
A Problem Involving Circles RandomMathsInc 2016-07-06 | A problem involving a string and a ball, where your intuition may fool you.For maximum effect, sit back and don't bother calculating anything. Just have a guess!
Transmitting Data Over the Internet Safely RandomMathsInc 2016-06-03 | A video where we talk about the RSA Algorithm, and how it works.Links I used:en.wikipedia.org/wiki/RSA_(cryptosystem)http://www.di-mgt.com.au/rsa_theory.htmlhttp://www.di-mgt.com.au/rsa_alg.htmlhttp://stackoverflow.com/questions/10214463/how-safe-and-secure-is-rsaPhotos I used:;By Erik Tews (Own work) [CC BY-SA 3.0 (http://creativecommons.org/licenses/by-sa/3.0)], via Wikimedia CommonsBy len adlmen (by mail from len adlman) [CC BY-SA 3.0 (http://creativecommons.org/licenses/by-sa/3.0)], via Wikimedia CommonsBy Ronald L. Rivest (Own work) [CC BY-SA 4.0 (http://creativecommons.org/licenses/by-sa/4.0)], via Wikimedia CommonsUPDATE (April 2018) - For those who see this: I just won FameLab Thailand 2018 with this very topic!Also "Secret Life of Codes" by Kjartan Poskitt (a very good book by a very good author, do check him out).
