How to Learn Mathematics Fast

Key Takeaways

why'd the chicken cross the Mobius strip to get to the same side hello world it's Suraj and if you're interested in AI you're going to need to brush up on your math skills in this video I'll describe my strategy to learn mathematics as fast as possible math is a specific powerful vocabulary for ideas imagine a cook that only knows the descriptive words yummy and yucky if he makes a bad meal he has no way to describe it is it too sour too dense too spicy that last one is impossible but all of these critiques are hazy variations of yucky his vocabulary shapes what he's capable of thinking of in the same way math vocabulary shapes concepts and ideas that we are capable of thinking of it uses the rules embedded in our universe to create models and relationships and the process of learning what these rules are has been iteratively refined over millennia take counting for example first there was the unary system which was like drawing lines in the sand then came Roman numerals which had shortcuts for large numbers then decimals and binary than scientific notation and you can bet that in the future we'll have an even better system for counting or take the word quantity for example we understand this concept it's considered common sense but this understanding includes concepts refined over millennia like base-10 notation zero decimals and negatives now imagine improving your vocabulary for structure shape change and tense that's where algebra geometry calculus and statistics come in all math concepts build on other math concepts multiplication and division used to elude geniuses millennia ago and now they are homework for primary school kids newer concepts require them has prerequisites if you're like me you were likely taught math in a very boring way involving blind memorization and speed testing it did improve my ability to fall asleep fast AF though actually memorizing math facts is just a small part of mathematics and being fast at math doesn't necessarily mean you're good at math there's this widespread myth that some people are math people and some people aren't there's so much fear and boredom involved in introductory math curriculums with very little real-world application and if you don't believe you're good at math it will definitely affect your performance neuroscience research shows that there is a strong connection between the attitude that students hold about their own learning ability and their academic performance so the first step before starting to learn any math subject is to believe that you can learn it your brain is adaptable AF it can learn anything if you have the right motivation don't worry if you don't get a concept right away research shows that when you make a mistake in math your brain grows it's that period when our brains struggle to understand a concept that real learning occurs you got worked it out like a muscle like any athlete would to complete a task no pain no gain right when it comes to picking a math topic think the subjects that interest you don't waste your time learning subjects you don't care about like C sharp development just cause if you're like me and are interested in AI linear algebra probability theory calculus and statistics are crucial concepts to understand the field each with a depth of knowledge to learn there are a wealth of great learning resources available to you to learn about any of these textbooks however rarely focus on developing real understanding they're mostly about solving problems with a plug and chug formula for example the Pythagorean theorem isn't just about triangles it's about the relationship between similar shapes the distance between any set of numbers and more math is not a spectator sport while memorizing concepts is useful in order to actually learn you need to be solving problems and you should be solving problems that you actually enjoy solving for it to be fine right for the memorization part just use a cheat sheet for any subjects you want to learn about as a helpful guide as you solve problems I've linked to several in the video description in terms of gamifying problem solving brilliant org has done a great job of making an aging content to learn about different math subjects with a big variety of styles I highly recommend checking that website out you can also find video games that help you learn about a math subject variant for example lets you learn calculus by using it to solve puzzles while playing a young woman who tries to save a planet from imminent destruction while true learn is a game that lets you play the life of a machine learning developer using visual programming to make a living use the internet to find enjoyable ways of learning whatever subject you are interested in that's the best way to motivate yourself to actually learn it make your own curriculum no need to follow existing courses if you don't want to you can use them for inspiration but develop a learning path that works for you on your time that fits your goals whatever subject you're learning make sure to take notes when you're taking notes think of it as a teaching guide for someone who knows nothing about the subject the practice of explaining is the best way to learn any concepts a great methodology to follow for creating explanations for a concept is called adept or analogy diagram example fine English and technical definition this is how you can teach yourself a difficult concept or explain one to others the first part analogy asks the question what else is this concept of light most new concepts are variations of what we already know we've encountered millions of objects and experiences as we've aged surely one of them is vaguely similar to this new topic then make a diagram which engages the other half of your brain dedicated to vision processing if we can create a diagram of imaginary numbers we can see that it lets us rotate around the number line not just move side to side then give an example like what happens after four turns on these axes describe it in plain English once you have an example and lastly use a technical description this final step converts our personal understanding into formal notation it's like sharing a song you made you can hum it but other people need sheet music puppet to play it let's use this method in the context of studying the popular machine learning course by Professor aim on Coursera who also liked a tweet that mentioned me I see you Aang I see you love you when studying if we see an idea that makes sense we can write it down in language that we ourselves would understand if it doesn't we can still write it down and then use the Adept method to decompose it we can write down one sentence explanations for ourselves of any core concept that makes sense to us and then later use these concepts as our own personal cheat sheet to understand later material the course is chock full of formulas that most people have never encountered under advanced optimization for example if we're unclear why the negative sign is used in the formula we can make a note effect then focus on concepts we already understand like derivation it turns out that in derivation the natural log is expected to be negative and sometimes the terminology can get confusing like using the word cost instead of error if we take the time to write out explanations for each term we don't understand we can see that cost captures things outside the model like complexity which error alone doesn't encapsulate it's important to continuously try and create brief easily understandable explanations for everything we learn we could try and summarize the course by saying machine learning is all about creating models with linear algebra then improving them with calculus embrace your confusion it's ok to forget things your notes are meant for you to record what you don't understand what you do understand in the process of how you come to understand eventually eventually you can make technical content for the public based off of your notes and that will improve your understanding even more by making your vocabulary more broadly accessible math is awesome and so is hard work don't let anyone tell you otherwise let your curiosity guide your learning have goals and don't be afraid to be confused it's all a part of the learning process want to become a math genius hit the subscribe button and I will show you the way for now I've gotta solve vehicles and B so thanks for watching [Music]