Mathematics for Beginners

Key Takeaways

and that is the nature of reality any questions yes well this get me laid yes hello world it's Suraj and learning mathematics will enable you to truly understand not just artificial intelligence but every other scientific discipline as well I'm gonna show you a 10 step process that anyone regardless of their background can use to understand any math equation either in a blog post a textbook or a scientific paper no matter how difficult it may seem then we're gonna use that process to understand an equation that I find particularly interesting a language model capable of generating coherent texts which we can then use to create our own Twitter bot that offers therapeutic advice to people with anxiety if you're new to the channel welcome subscribe to get updated when I release new educational videos math is the science of patterns and we've subdivided it into many different categories for example arithmetic and number theory study patterns of numbers and counting geometry studies patterns of shapes calculus studies the patterns of motion logic studies patterns of reasoning probability it deals with patterns of chance do you see the pattern here meta AF stem stands for science technology engineering and mathematics these topics are all related when we discover mathematical laws be that in physics or in artificial intelligence through the scientific process we can then engineer new types of technology thus the reason we have all the technology we've come to know and love is because we now understand a portion of the consistent patterns in nature which allows us to build these systems be it a rocket a language translation app or a hearing enhancer so if you want to build any new type of technology business or get a job in the field knowing math is crucial and because the language of mathematics is used across every discipline understanding it will help you jump into an entirely new field much faster for example the same techniques from calculus used find the growth rate of bacteria can also be used to find the direction to learn for neural nets and the acceleration of a moving object the calculus is my city it's become so easy to build generic apps and services these days that it's hard to differentiate yourself but if you implement AI in your service in some way something not every programmer knows how to do you can provide your customers with more personalized more accurate and more effective services so let's go through my 10 step process to read any math equation together remember math is a foreign language so we're going to need to work at it to gain literacy the ability to read and write it step one is to find a math equation that sparks joy within us we shouldn't try to read an equation that we don't care about or we won't be able to sustain the motivation necessary to understand it for example when I took some time to study physics the equation I wanted to understand the most was Schrodinger's equation because it caused so much controversy in the physics community around the nature of reality a challenge to so many long-held beliefs but it ultimately ended up becoming a very useful tool to make later discoveries and create all sorts of technologies once we find an equation we care about we need to define its objective what is the equation trying to say what does it represent how is it being used read it in the context of how its presented be it in an article a scientific paper a video or a textbook chances are that there will be some English text before and after the equation that describes it once we've done that it's time to understand the dependencies equations are written with a specific audience in mind be it computer scientists biologists or even laymen we need to ensure that were the intended audience or be willing to do what it takes to become the intended audience all math is cumulative almost everything we do in math will depend on subject we've previously learned for example even the most simple equations from calculus will be difficult to understand unless we've first understood its major dependency algebra the source text that were reading the math equation from will usually mention the math topic involved and if not we can Google some of the mathematical terms it's using to try to discern what branch of mathematics that term is from once we know what branch or branches of math an equation is using we'll write them down then literally Google what math topic do I need to learn X the answers to that question will be spread across sites like Quora and Stack Exchange the upvote functionality on these websites helps us ensure the validity of the answers consider it crowd sourced accreditation once we've understood the mathematical dependencies and have written them down we know exactly what we'll need to learn to understand the equation but are we gonna pause our analytical process to learn these subjects in their entirety no this brings us to the next step pull up the related formula sheets I have several formula sheets that I use for each math subject they condense the entire subject into one or a few pages they're like cheat sheets I went ahead and compiled all of them into a list for you the link to it will be in the video description we're gonna pull up the related formula sheets in two separate tabs on our computer that we can use to help decipher the equation we're trying to understand to truly understand an equation passively staring at it is pretty much worthless we're gonna need to investigate question and probe that brings us to our next step write it out we can use either a pencil pen or whiteboard unlike English the language of math is built to capture ideas perfectly we say things precisely once later sentences will presuppose perfect comprehension of earlier ones so reading it demands our full attention we'll need to fill in the missing steps every variable every symbol needs to be fully understood before moving on to the next one we'll rewrite the equation in our own handwriting then make marks around it to help us describe it in further detail the simple act of writing it with our hands helps ingrain it in our minds much more efficiently and this is backed by several studies the formula sheets will help us roughly piece together what an equation is saying and we can use these pieces to translate the whole thing into the English language which is the next step in the process long ago mathematicians agreed to follow a set of rules when doing calculations and we call this the order of operations these are components like add subtract and divide if it's not a number it's probably an operation the order is parentheses exponents multiplication division addition and subtraction we can remember this using the acronym PEMDAS using this ordering and the description of symbols we'll get from the related formula sheets we can verbalize an equation in the English language and this will help improve our understanding the next step is to translate the equation into Python code sometimes the equation we view will be in latex format and sometimes it will just be an image if it's an image we'll use the tool I found called image to latex to convert the image of the equation into latex format once it's in latex we'll use this tool I found called latex to symp I which converts the latex format into symbolic Python Python is great because it helps make equations more human readable and also allows us to plug in different variables to see how the equation works in different contexts with instant results right to the command line all hail the green snake the next step is to visualize it there are many tools to help with this simpie has a built-in plotting module which is an easy first step there's also the Wolfram Alpha website input an equation and it will create all sorts of graphs to help us further in grain or understanding of it another is google image search and another that's less well known is google's animation search sometimes an equation describes a continuous process thus animations are even better than images for understanding once we translated it into different mediums it's time to apply it to problems we find interesting math is abstract it's applied to our lives find examples of problems that it's usually applied to and use the Python version of the equation to try to solve a problem in that direction it's important to be patient here it's not unusual to spend an hour or several trying to use a single equation to solve a problem and develop a complete understanding around the entire process remember whoever's work you're reading didn't write it out in a split second they spent lots and lots of time and energy to come up with those solutions so be patient and forgiving with yourself putting the hard mental work now to reap the benefits later that which tastes bitter at first will taste like nectar in the end and the last step in this process is also perhaps the most important one to ensure you've truly understood the equation explain it to another human being able to explain a concept is the true measure of your understanding of it write a blog post join a study group start a study group call up Microsoft support I don't know or slack channel is a great resource to find humans to explain things to everyone is enthusiastic about learning and teaching make the equation your own paraphrase it put it into your own words and if you can do that I promise you you will understand it now let's use this process in practice to understand a simple language model called the unigram model language models assign probability values to sequences of words when you're typing something on your phone those three words that appear right above the keyboard on your phone that try to predict the next word you'll type are all outputs of a language model in this example we're going to go through a book called speech and language processing which is freely available on the web in Chapter three we come upon this equation labeled a unigram model if we can understand this we can use it to implement our own Twitter therapist bot from the textbook it seems like this equation helps predict the next word in a sentence using that prediction over and over again word by word it can help generate an entire sentence that would be in the style of whichever text data set we use it on say a data set of logs from human to human therapeutic conversations there are some terms here like Markov and chain rule and probability that all seem to be related to the field of probability theory so we'll pull up our probability formula sheet and behold each of these terms is in it will now write out this equation by hand and make notes as to what each of these terms mean it's using the chain rule apply to compute the joint probability of words in a sequence it's leveraging something called the markov property that says that the probability distribution of future states of the process depend only upon the present state not on the sequence of events that preceded it in this context that means the probability of the next word can be estimated given only the previous k number of words for example if k equals 1 the probability of the word depends only on the probability of the previous word this Markov assumption lets us formally define n gram models the simplest one would be defined as a unigram model where k equals 1 this can be extended to become a bigram model where k equals 2 or a trigram model and so on using our Python tools we can convert this into Python code pretty easily Google Image Search can help us find a nice visualization of this concept as well and we'll go ahead and apply it to a real world problem by using the Twitter API to create a simple chat bot in a few lines of Python as for the last part of this process the explanation that's everything I've said throughout this video plot twist now we can move on to more cutting-edge language models that involve deep neural networks like what open a I demonstrated recently with its GPT to model the formula sheets are going to be in the video description and there are three things to remember from this video math is the science of patterns and it's useful across every scientific discipline you can use my 10 step technique to understand any math equation and language models play a central role in natural language processing systems what's an equation you want to learn more about let me know in the comments section and please subscribe for more educational videos for now I've got to learn simulated annealing so thanks for watching