Learn ALL THE MATH IN THE WORLD from START to FINISH

in this video we are going to go over every single area of mathematics so what have done is have created eight categories and you can take any math subject in the world and you can fit them into one of these categories now there are different categorizations of mathematics typically people do it by saying okay this is pure math and this is applied math decided not to do that for couple reasons one the stacks of books would be huge and they would reach the ceiling two think this gives you better idea of the different subject areas and that's my goal of making this video lot of people when they first see math they're frustrated by it because it is challenging right math is hard and when things are hard well it's hard right we want to give up but it's okay once you realize that math is hard and that there's different types of math well that kind of makes you like it more and people tend to like what they're good at so if you like math and you're really interested in it then chances are you can become very very good at it so this video will give you an overview of the specific subjects so under each category like for example here is foundations of mathematics like under this category there's bunch of subjects okay there's all kinds of math that falls into that category put algebra there as well some basic number Theory logic sets algebra and structures same thing saying bunch of stuff falls under this category you've got like linear algebra that falls under that category as well geometry and topology this one's pretty self-explanatory it's geometry and topology but there's some specific types of topology that are little more advanced like algebraic topology which decided to put in this category here discrete mathematics and combinatorics this is the kind of thing you would see like as computer science major computer science Majors typically have to take discrete math and this is an entire book on common tox which is which is pretty cool by the way I'll leave links to some of these books in the description of this video not all of them it's too many and some of them are rare and stuff you won't be able to find them but I'll leave like some good ones for you in case you want to pick up some books and learn some of these cool topics this is Monumental stack right look at this this is completely ridiculous this is analysis and calculus so the reason it's so high is because decided to put in bunch of good calculus books and then complex analysis is here real analysis is here differential equations 4A series ordinary differential equations so bunch of stuff falls into this Hilbert spaces right tons of stuff applied math and modeling here's where the stat could really reach the ceiling right but got tired of looking for books have thousands of books and they're scattered everywhere they're in Stacks just like this and so basically here put physics and we've got some engineering and some other topics as well probability and statistics this is really useful stuff and don't think think people care about it enough so I've got couple different options here for learning stats some that are just like General stats and some are for engineers and some are for mathematicians so different stats books with different audiences Advanced topics and Frontiers could have put lot of these books in this pile but decided no let me just pick two really weird books that these are things you've never ever heard of probably it's like super Advanced and on the bottom here have hidden that super secret book which want to show you at the end of this video because it's awesome it's really really awesome and if you've watched my videos before I'll tell you interviewed the author here on the channel and he's he's super awesome so yeah his book is down there we'll talk about that at the end all right so guess we're going to get started now I'm going to go through here and just go through each stack I'm going to start with foundations of mathematics and then just keep going so feel free to fast forward this video like you know Skip ahead if you want to jump to specific area but yeah after watching this you should have really really good idea of you know the different areas and and I'll also give you the pr Rex as go through all right let's go ahead and get started right away all right let's start with foundations of mathematics so we're just going to go through each book and I'm just going to give you the pre Rex and what think about the subject all right so foundations of mathematics so the first book we have here is one on logic it's called introduction to logic it's by Patrick Subs so this is book that in theory you could use to learn logic so logic in mathematics is really important proof writing is based on logic and so typically in foundational math you do lot of logic you learn about sets which are you know collections of objects and then you do lot of baby proofs like easier proofs with sets and stuff so book like this will teach you logic this is book on logic there aren't that many books on logic compared to like calculus books and logic books vary from one book to the other so one logic book can be very different from another logic book it just depends on the book next up we have book on arithmetic and actually have several books on arithmetic but wanted to show you there's that's topic right modern arithmetic through Discovery so feel like this is not class course that's taught in college today there's not really like arithmetic courses wanted to include this one because this is an amazing book so if you have to get one foundational book think this is the one that will affect your life in the most positive way ever this one's called how to prove it structured approach and it's written by Daniel velman the reason feel that this book will be more life-changing for you than any of these books here actually than probably any book here except maybe that book at the end this will teach you to write proofs once you know how to write proofs you can do lot more of the advanced stuff like that you see here in these other you know more advanced categories right so very good book he explains things really well and yeah can't can't say enough good things about this book this book bought because people kept leaving comments about it and did not want to buy it cuz remember at the time was like really got to stop buying books don't have any room they're all over the floor it's ridiculous and then people were like you should get it and got it and read chapter or two and was like wow wow so good number Theory know number Theory can go you know maybe in some other categories but wanted to include it here so you know the basics of numbers and the theory of divisibility stuff like that prime numbers felt like that should be foundational set theory this is probably the most famous set theory book ever written it it's the one by Felix hos dorf so if you know topology you know about hos dworf spaces this is the same Felix hos dorf after which hos dorf spaces also known as T2 spaces are named have to smell it I'm sorry this is first edition set the it's little bit hardcore the prere for this one by the way think you really should know how to write proofs before jumping into this same thing with number the sorry forgot to tell you so proof writing right that's going to be big prere for lot of things okay for lot of things the logic book you can just jump into this you can jump into right you can just get this and read it and learn you don't need really any PRX other than like an amazing willpower because it is it is hard it is hard that one's mistake have book there that is not supposed to be in that pile college algebra by Blitzer decided to include algebra and Foundations because you do need algebra in order to you know progress right you have to learn algebra so that you can take calculus this is book that I've used to teach college algebra in college for years so it's great book and you can use it for self-study it's got answers in the back of the book so this is mainly like you know quadratic equations graphing parabas you know you've got some stuff with polinomial so systems of equations here's some graphs as you can see yeah got to smell this I'm sorry smells amazing if you're really just getting started pre-algebra mean this is foundational this is basic stuff like you know converting fractions to decimals stuff like that really basic mathematics is pre-algebra Intermediate Algebra this one comes after pre-algebra but before college algebra the order is pre-algebra intermediate College all algebra though they're all algebra books and yet another algebra book in foundations and you need to know algebra this is actually pre-calculus book this is book I've used to teach pre-calculus to teach trigonometry and to teach combined course pre- tri combo course which is way harder in college and this is great book this basically has all the information that the Lesser books have like that the pre-algebra books this whoops whoops this has everything the college algebra book has mean so you can just basically books are falling here in if you already know some algebra you can skip Blitzer and just and just get this one that's just my my take anyways that's the foundational stuff right so you can see it's just mostly algebra little number Theory proof writing sets that's like the foundations of mathematics and could have included more books on proof writing have tons don't know why did was more focused on making sure everything went in the right category and are these the best categories right because again you can categorize things differently and there is lot of overlap let's go to one of my favorite categories which is algebra and structures next this is actually really fun to go like not in order cuz like we have like Advanced books then we have easy books so algebra and structures this is great category this book here teaches you abstract algebra this is more advanced book this is an Incredible Book because it contains so much content bought this as reference my biggest regret is buying it used because look my copy is is is not is not in good condition really I'm going to buy new copy someday look look see it's falling apart but it's wonderful book this has things in it that are just Priceless for example even in graduate school was using this when was studying semi-direct products so very useful you can use it to learn abstract algebra the prere for this is knowing how to write proofs but don't think that this is the best beginner book but it's book worth having if you're serious about learning abstract algebra so that's subject that covers groups Rings Fields modules you're looking at algebraic structures then you have linear algebra here you dealing with matrices linear Maps systems of equations also this book here is computational based so it's going to have some proofs but it's not like proof-based linear algebra book so usually usually you have two types of linear algebra books you've got like the computational ones and then you've got the proof-based ones but it's all inine your algebra and it falls under algebra and structures an actual book called algebraic structures and matrices galwa Theory So This falls under the again the algebra and structures Cate galwa theory is more advanced you have to know some field Theory to get there field Theory you learn in book like this this actually has galwa theory in it as well this is this is an amazing book again for the content so am going to buy one at some point another legendary book survey of modern algebra by burkoff and mlan my favorite abstract algebra book this is the one learned abstract algebra algebra with read this entire book and my only complaint about this book is that it didn't have enough information got to smell it so good so good so good but it's great little book super begner friendly highly recommend getting this one if you're going to get one this is probably the easiest one linear algebra book that is proof-based this is the one by Friedberg so this is very similar to the one we looked at earlier the one here it's glare Sorry by Larson and Edwards but this this is harder okay this has proofs it's way more rigorous so so this is usually used for second course okay in linear algebra kind of nice great book it's like feel like it's like necessary evil like it's it's it's good book but it's hard like it just don't know don't know had really hard time in that class when was student but it's good book used it even as grad student as reference and I've looked up stuff really good for beginners though this one this one's better for beginners than any of the ones I'm shown you it's another linear algebra book by Anton and then we have one here that just has more information look how thick that is by shenan con Kade so basically this category is just algebra and you know linear algebra so let's let's just can scoot this over and let's take look here at this category here this is the geometry and topology category so let's see what we got this is the general topology book so to learn topology you have to know proof writing and you have to be good at it so like just being okay is not enough right in topology you study continuous functions that take topological spaces to other topological spaces and you have like properties that are preserved under homomorphisms and they're called topological properties and you study those and yeah and you can keep going here's more topology this is topology with an introduction with application an introduction with application of topological groups so this is more specific I've seen topological groups in an online book called topology without tears it's free so yeah and then we have geometry but look how hardcore it's differential geometry so it's not in order right so normally you do like okay step one no no so to do this you have to know calculus you have to know how to write proofs this is tough differential geometry you have to know lot here's lost subject you've probably never seen plain and spherical trigonometry right that's pretty cool so spherical trigonometry is no longer taught so have this Theory think it's it was used lot and it was taught lot during the World War II era and know that during the war think they they used lot of this stuff so it was taught lot back then like what's the copyright on this let's see yeah see 1950 so that was after World War II all the ones have are older don't have any newer books on spherical trigonometry it's like they don't exist so so if anyone out there is really into it and wants to write book there's hole in the market for spherical trigonometry books kind of an interesting fact let's keep going we've got whoops whoops so many books are falling over so here we have lectures in projective geometry this is very Advanced book this came actually from private collection this book belonged to man named Augustus Prince he was the first black radar man in the US Navy and he was nuclear physicist who worked at Brook Haven National Laboratory how do know all this have call collect books I'm collector right so have lot of math books and so like you know the history of the book matters and so was able to pick up some books from his collection he passed away several years ago so really sad yeah really really sad all right geometry an actual book on Geometry and it's it's comprehensive this one's good because it's affordable and you learn lot so that falls into this category another differential Geometry book this one this one is really fun this one has solutions to every proof in the back of the book let me show you check this out this one you can but you might say so it's easy can learn wouldn't go that far just because you have the answers doesn't mean it's easy so it's still really tough again for topology you you you really you know ideally you want to have some Advanced calculus and Analysis we haven't even gotten there yet but you want to have like proof writing in other classes like abstract algebra real analysis and then take topology so yeah this one has in the back love this book and it's affordable too it's probably one of the best apology books you can buy right here and it's like not even expensive highly recommend that one very famous book algebraic topology by Alan Hatcher extremely hard and another algebraic topology book again extremely extremely difficult let's keep going here because we still have like bunch of stacks to go through so let's go to this stack here I'm just going to set the camera down and let's keep going so this stack here it's not big stack even though have zillion books on discret math so discrete math is something that computer science Majors take so if you go to college today and you get computer science degree this is what class you would take okay and combinatorics is also Class math major could take as well and then graph Theory so those that's what that's what you have here discrete math combinatorics and graph Theory that's what falls under here so applied combinatorics this is one of the few books have on actual just combinatorics there's not that many that that exist right so that's the thing this is fun one discreet mathematics in computer science love the name and the cover so discrete math covers bunch of Topics by the way so let me just let me just show you what it covers so you kind of get an idea and the preck for this so the prere for discreet math at most colleges they'll say you have to take Cal 2 before you take discret math right and think they do that just because they want you to like be decent at math not because there's actually anything you need from those classes although sometimes there's examples that use calculus but not many so it starts with logic which which again this could have this could have fallen under foundational right could have done that there is some overlap so you know if you take the intersection of of these categories you know in many cases that intersection is not empty that's because there's lot of relationships in mathematics between between Fields right so it's really impossible to break them to break them up into categories like that binary relations functions infinite sets algebras yeah this one doesn't have as much as some of the other ones here's book on common toic this's really hardcore and then this book this one has more content than the ones this is the best one for beginners right here this is the best discrete math book for beginners and you can use this for graph Theory course combinatorics course or discrete math course took course that was called combinatorics and graph Theory and use one of these books so you could use it for one of those but let me look at the topics here to show you because if you're into computer science you'll want to see it's got number Theory we talked about that already so this stuff this is really foundational stuff right induction but wanted to give it separate category because it's important computer science is important right I'm I'm you know I'm using technology to make this video like yeah computer science is extremely important see there's the graph Theory yeah it deserves think it deserves its own category at this point right it really does it really does all right let's keep going both of these stacks of books contain analysis and calculus books so that's lot of books right and the reason there's so many books and could have added so many more is that there's lot of different subjects that live inside this analysis and calculus category so what is calculus people will say that calculus is the mathematics of change and that's pretty true statement typically in calculus you start by learning what's called limits and basically it's the idea of getting infinitely close to something but never actually getting there and limit kind of kind of you know that's what it defines it allows you to get close to something allows functions to get really close to numbers when values get really close to numbers you know what happens to the function value you know when gets really close to two right you know what happens to the function value when gets infinitely close to two right that's the idea of limit so that's defined precisely via definition with inequalities and stuff and so once you have limits you can Define derivatives derivatives basically describe rates of change so like if you have function that tells you the temperature well the derivative of that function is the rate of change of the temperature right or if you have graph the derivative is going to be the slope at that particular point where you find the derivative assuming it exists so all kinds of stuff can talk about it forever but this book this book is wonderful because this book does not require any trigonometry I've used this book to teach certain class in college and the prct for that class is only college algebra so this is very special book because there's not many books like this in the world that allow you to learn calculus without knowing trig now you should know trig but it's just book worth getting if you can get if you can get copy I'll leave link in the description so you can check it out this is calculus book called calculus and was written by man named Michael spivac now this book is very famous it has cult following because it has beautiful explanations it does not have as much material though as some of the modern books partial differential equation equations it's all out of order so this is basically partial differential equations in order to learn this you have to know ordinary differential equations and in order to learn that you have to know calculus so the order is calculus differential equations and then partial differential equations they're called partial because they involve partial derivatives remember earlier said derivatives describe the rate of change of function so partial derivatives are very similar but you just look at the rate of change with respect to one of the variables in multivariable fun function that was lot of information hopefully did not misspeak then we have complex analysis so when you study calculus you deal with real numbers right you have functions that have real numbers so here it's very similar except all of sudden you have complex numbers but lot of the same rules apply right like all your derivative rules are the same all the series stuff is the same there's some really cool new stuff like harmonic functions and Koshi integral theorem it's one of the really cool subjects in order to get into this you have to know calculus and it helps to know some proof writing wonderful book by the way worth every penny love this book this is probably my favorite calculus by James Stewart definitely the most popular calculus book in the world because it's used mean definitely in the US and Canada this is the most popular one for sure many schools use this book used different version of this book when took calculus you could use this to learn Calculus 1 calculus 2 and calculus 3 so in calc 1 you learn the basics of limits and integrals and derivatives and you learn lot of the key theorems like the mean value theorem the intermediate value theorem the First Fundamental Thea calculus the second funomenal theor calculus calc 2 you do more stuff you do some applications infinite series more integration calc 3 it's multivariable Cal so functional analysis this is graduate level graduate level course here you need analysis for this you need algebra you need topology you need to know lot of mathematics before you do functional but it's really really fun threw this in just for fun this is great calculus workbook that you can use to learn calculus like right away Advanced calculus so this is like real analysis this is basically calculus with proofs so we talked about how calculus has limits and stuff like that so here you prove everything so this is something that requires knowledge of calculus and proof writing okay and this is probably the hardest subject on undergraduate studies in the US like some people might say it's algebra some people might say it's topology think that advanced calculus is by far the hardest subject and undergraduate math major has to get through it's also called real analysis by the way another complex variables book this is one of the first ones ever purchased another analysis book this is the one by Apostle this one's really hardcore numerical analysis here we go different subject so numerical analysis is like analysis basically but you're doing approximation so you can take whole course on this stuff you do little bit of numerical analysis and differential equations but you do lot more when you take an entire course another book on partial differential equations what's this Hilbert space yeah you need to know topology analysis all that stuff for that 4A series same thing you want to know lot of calculus you want to know how to prove things it's just messy this is This falls under like applied math by the way know didn't break it up into pure and applied so very famous book it's called principles of mathematical analysis was written by Walter Ruden so this is an analysis book or an advanced calculus book but people call it an analysis book it is called mathematical analysis in any case smell it this book has really hard examples and really hard exercises and it's very famous like the book by Buck better because it has more examples regular differential equations right so I'm going out of order so regular differential equations you can learn that after you know calculus and then once you know this you can learn differential equations so differential equations you basically study these equations like this one here let me show you and you have to solve for dydx dydx is the derivative of the function so you sorry you have to solve for which is the function misspoke so you have an equation involving an unknown function and one or more of its derivatives that's the definition of differential equation dyd is the derivative of and so basically you have to solve this for so there's usually procedures that you have to do in order to do that not like you just like use algebra to solve because you have to get rid of the dydx right so you learn techniques this one's beri differential equation those are really fun yeah have some videos here on my channel of beri differential equations and then analysis another book on analysis wanted to include this one this one has less content than the other analysis books you've seen so far in this video but it has better explanations and it's easier so it's really good for beginners all right let's keep going we've got three more categories to go through here's an area that feel doesn't get much love from people it's probability and statistics feel like most math Majors I've known aren't really into this and the people who are into it are very much into it keep in mind you can get an entire degree in statistics right so it is almost like separate field but it is part of mathematics so wanted to include it so probability and statistics is our next category and you know have way more books than this but these cover pretty much the core things so here's mathematical statistics book this is something you would take as math major or as stats major as statistics major in college this is probably the hardest course you take so mathematical statistics is basically statistics where you prove everything right and everything's little more rigorous and what is statistics by the way well in statistics you basically you go out right and you're you're trying to say something about population this is just one example and what you do is you take sample which is subset of that population and then you can do things with that sample right you can estimate the population mean or you can ask questions about the population mean you know is the average age of people in this area greater than 40 and you can do like hypothesis test so there's different ways of applying statistics to the real world and think that's really really cool and think people should care more about it but think now data science is the thing but yeah that uses statistics here's another mathematical statistics book excellent book as this one used and then here is an easier one this is good one this is one that actually used to teach in college long time ago so used this one for few semesters and then we switched books but this is the one by brass and Brass it's solid book and this one has really good explanations like it'll teach you statistics it'll explain you know what is confidence interval how do you interpret confidence intervals how do you interpret hypothesis test you know and all the other basic stuff like probability and stuff like that by the way these book this book has probability in it right so probability is another subject another basic stats book very similar to the brass and Brass one mathematical statistics book and again this also has probability in it this one again would be for math Majors whereas these two here would be just like the general public so like if you just know basic algebra you can you can you can jump into these books whereas the whereas these mathematical statistics ones they do require some basic proof writing and some knowledge of calculus however you could in theory jump into this and then like you know when you get to the calculus you just skip it so not everything requires calculus and this one again it's more probability statistics but this one is specifically for engineers so very similar to the mathematical statistics books these books and these are typically used in college by people who are studying engineering okay typically they are required to take some course called like statistics for engineers and most courses are okay but the better course is the math course like the usually the one by the math department is more rigorous because it's taught by statistician or mathematician lot of times think the people who teach these are just like mean I'm not nothing against Engineers but they're not math people right so don't want to get any hate in the video but just think it's little bit harder like this is harder class like if you take if you take mathematical statistics in college it's going to be harder than stats for engineer it's going to be this is going to be way harder this is way harder know took took took two semesters of it and I've seen I've seen what's taught in this because have I've had students who have taken this class and it's hard so level of difficulty would be in case you're curious so easiest and then harder hardest right that that's that's that's my view on the stats hierarchy there feel free to disagree all right let's go to the next subject Li mathematics modeling so this this could really fill an entire room of books because there's so much applied math out there and there's so much modeling so decided to throw physics in here thought physics let me throw this in here because it's applied math mean people might say well it's physics it's not math you use lot of math and it's applied so decided to throw in physics and this book here is wonderful this is the one by holiday and Resnik great physics book The prere is calculus by the way you got to know calculus an advanced engineering mathematics book so this book actually contains linear algebra differential equation calculus complex variables it has lot of material it gives you rough overview of everything but it's Advanced engineering mathematics wanted to throw it in with this stack here wonderful book the worst thing about this book is the price it's never cheap because it's always in demand that's true for lot of books some books are just like always expensive because people want them thought would throw in an electrical engineering book mean sure it's different field but it is an application of mathematics right we use math in all areas mean math is so prevalent right so physics engineering mean they all use math right cryptography actually uses for course yeah our teacher went through the entire book we went through the entire book it was completely insane remember being so lost because we were covering so much it wasn't hard you it takes effort there's lot of like algorithms and procedures you have to learn but when you go through the whole book that that's pretty intense but beautiful subject the prere for this is smells great guess it's nothing thing mean it helps if you know how to write per and you had some other math in your life like you know you have some foundational math but you can see it starts with classical crypto systems and it goes through it just gives you like some simple examples it does talk about digital currencies but this book was written before the existence of Bitcoin so you get pre- Bitcoin introduction to digital currency because Bitcoin didn't exist right people don't realize how big of deal it was when it was created so so this book was created before Bitcoin so it does not cover that but it does have chapter on digital cash so it does cover it but again it's pre- Bitcoin physics again this is specifically modern physics actually use this for course in college called physics 3 really beautiful subject you do stuff you do some of the stuff with Einstein in there like you do like relativity and stuff so time dilation pretty fun and another physics book thought physics deserves another another another book here so threw in physics here as well and there's more specific subjects Within within the you know within the category of Applied math but again you can take any subject any math subject and just it'll fit into this category and you're there but Chaos Theory Etc all kinds of stuff all right let's go to the last category Advanced topics and Frontiers so this is basically things that were Advanced that didn't decide to fit into other categories certainly there were some books and some of the categories that fall into this category there's plenty of books here that were very advanced that one could easily put into this category but decided not to for whatever reason and I've got two really strange books on topics that you've probably never heard of and by Frontiers you could throw in anything new any type of new mathematics would go in here like you know research mathematics any papers you know you could put those in here and that would be an example of Frontiers so combinatorial topology here's really old book on combinatorial topology you've probably never heard of this super advanced stuff right this requires tons of mathematics right topology commor everything you just have to know all the core areas analysis algebra topology counting mean you have to know lot right you have to Le lot of math to do this and then this one here is really weird piecewise linear topology this is probably something you've never seen again super super Advanced what's it say here effects Sub Zero through xar are points and dimensional ukan space either the we say they're linearly dependent in the Ain sense okay yeah yes this is some linear algebra they're reviewing yeah but it does it does mean it just jumps into it as you saw it's pretty hardcore promised you book at the end that covers bunch of topics so have it here and it's called all the math you missed but need to know for graduate school it was written by Thomas gity interviewed him long time ago for the channel here and really like this book lot so you can see here's brief summary of the topics so we covered lot of these topics already in this video right look linear algebra real analysis here's some more math right very specific right differentiating Vector valued functions that's analysis topology analysis analysis analysis geometry accountability and the axim of choice that that would be foundations of mathematics see so there's lots of these are these are subtopics right within these areas like lot of these books cover these things the books I've shown you right so this is cool book and so how it works is me show you look at all that zoom out so you can see better so let me show you how it works how he so you go to the section and basically like look look at Point set topology so the basic object topological spaces basic map continuous functions and he goes through and like he teaches you mathematics right like he teaches you math and he does it in really good way and it's to the point and I'm sure he struggled to make it clean and short because you know he wants to fit all of this in one book that is Monumental task right it's lot of subjects in one book he covers all the key theorems or lot of them right and then you've got some exercises there at the end so mean pretty incredible have to smell it love this book amazing so I'll definitely leave link to this one in the description of this video in case you want to check it out so yeah that's it that's all of mathematics right eight categories and think you can fit every single math subject into one of these categories right we had analysis and calculus we had probability and statistics right what else did we have we had discrete mathematics and combinatorics right that's for like computer science Majors geometry and topology you know you don't you don't do lot of geometry in in college like there geometry course is not course that many people take in college for some reason typically people who take geometry courses are math education Majors that's usually prere for the math education degree all right so we have all the topics we've got analysis and calculus we have advanced topics and Frontiers geometry and topology probability and statistics discrete math and combinatorics foundations of mathematics and then the last one couple more algebra and structures and then Applied Mathematics and modeling so those are the eight categories 1 2 3 four five six 7 eight Yep they're all there so those are the eight categories that was able to create and yeah that's all the areas of math right you can you can throw in anything into one of these categories and if it's really Advanced you can just throw it into the advanced topics and if it's new you can throw it into the Frontiers so yeah that's pretty much everything yeah that's it hopefully you enjoyed this video and you have an idea of all the areas know it's it's lot to fit into one video it's just like can't imagine you know him writing the book yeah really really tough as always subscribe if you want to and all that stuff and if you want to learn math have courses right do have courses they're on you to me but if you get them use my links they're in the description of this video or they're on my website maths sourcer docomomo price I've got courses on trig college algebra Cal 1 Cal 2 calc 3 differential equations abstract algebra have course on analysis have some courses that have some proofs and stuff so yeah check it out check out the links on my website but the key takeaway from this video should be that there's all kinds of math out there right so yeah take care and keep doing math