Richard Feynman's Math Books

for those of you that don't know Richard Feynman was a Nobel prize-winning physicist he is super famous and probably one of the most famous physics people in history right in in history of the world he is extremely famous he's written several books he's written a physics book which I have which I should totally make a video on and just amazing so here in this video I'm going to show you some books that he used but what makes these books even more interesting is that he used these books to actually teach himself mathematics these are books that he used for self-study in varying degrees also one of the books I have here is the most expensive math book I own I believe I believe the most expensive math book I have is sitting here in a pile I'm not positive but but I'm pretty sure in fact later on in the video I'll actually go online and I'll check the price just to see how expensive it is just to see if it's really the most expensive one I have and I only paid like ten dollars for it but I bought it you know over over a decade ago so let's start with this one trigonometry for the Practical man so before reading this one Richard Feynman read algebra for the Practical man and he thought it was just easy it was too easy so he picked up this one and he really didn't think it was that uh interesting for some reason he really didn't find it appealing it's called trigonometry for the Practical men it's written by J.E Thompson and we'll we'll come back and we'll take a look at this book in a minute let's go ahead and jump to another book which Richard Feynman read in its entirety and he made careful notes which he kept in a notebook it's called calculus for the Practical man it's also by Thompson and it's also a great book for self-study so this is a book you can use to teach yourself um calculus so this is the one that he really really like used this to learn and then we have a more advanced book here this one is called Advanced calculus and this one was written by Woods this is probably the most expensive math book that I have and it's super old I'm just gonna look it up really quick here on the internet I have access to to a computer and I'm just going to type it in advanced calculus Advanced calculus by woods and I'm just going to see what's available I'm just going to go to like Amazon and just click there that's the first link that came up and looks like there's one copy on Amazon right now for 319.99 oh look oh no never mind there's seven used copies from 199 so very expensive book and it's expensive because Richard Feynman is noted for saying in one of his books that he learned some peculiar methods uh you know from this book so this book is famous because he referenced it this book is also very rare and very out of print and contains some very serious mathematics this is a really really hardcore Advanced calculus book I don't know if there's reprints available sometimes you can find reprints on the internet and you can get for like less than 30 bucks I will look and at the end of this video when I post this video I will go online and I will try to find these books and leave links in the description so why did Feynman use these books in particular these these other books here let's start with the trig one which he didn't find interesting probably because Richard Feynman was I I don't want to use the word genius but we can call him a genius I mean people would consider him a genius despite the fact despite the fact that when he was in I believe when he was in high school and I'm paraphrasing here uh correct me if I'm wrong I believe when Feynman was in high school he took an IQ test and his IQ was 125 which is considered high but you know people think of an IQ of 125 and you think that's high but not high enough for a Nobel prize Well Richard Feynman was a person who had an insatiable curiosity for Learning and that's evidenced by all the things he produced and if you look at his notes you know feynman's actual notes that he took from this book they were meticulous so trigonometry for the Practical men let's open it up and I believe this is a reprint um I think the original one is much older because this is published by uh D Van Nostrand Company Inc see if we can find a copyright on this to see how old it is yeah so this is the reprint so 31 was the newer one then 46 and then 62. this must be the copy from 1962 Third Edition Third Edition let's just take a quick look at the contents here and so this is a book that you could buy this is probably available via reprint or maybe you can find the original one I will look I don't know how readily available this book is it's pretty hard to get I think so content angles circles and triangles so basic trigonometry okay more basic trig functions of 45 functions of 30 degrees and 60. so all those basic um trig function angles and the values whoops I want to really jump to that and see what that's about but let's keep going through the content solution of problems by means of right triangles functions of any angle properties and formulas of oblique triangles oblique triangle calculations Solutions of problems involving oblique triangles really interesting layout relations among the trigonometric functions and the best thing about this book is that there are answers to exercises and problems on page 179 um well I don't know if it's the best thing this book is actually extremely good despite Feynman um claiming that it wasn't very interesting but you see here you have answers to all of the problems in the back of the book and that's really nice that's one of the nice things about uh this these books for the Practical man the trigonometry for the Practical man algebra for the Practical man um they have I believe have geometry for the Practical man and they also have calculus for the Practical man so you can check your answers which makes this a wonderful book for for self-study here's the introduction the branch of mathematics which is called trigonometry is preeminently a subject devoted to measurement and numerical calculation cool yeah it's it's very computational in this book angles circles and triangles so it starts from the very beginning if you took a trig class today in college like trigonometry in college um you could use this book to supplement what you learn and I think it would turn you into a mathematics monster because it's presented differently so you're going to get a different treatment and anything you learn via self-study is it's golden I mean Richard Feynman was a fan of self-study and he used this book to self-study but again he found it on interesting uh perhaps again because it was it was too easy maybe um he did say the algebra book was too easy and he found this one uninteresting that's really all we know so trigonometry for the Practical man this is the book that he read in its entirety it's called mathematics for self-study and it's called sorry it's called calculus for the Practical practical man this book here is part of this series so if you look at older copies of this book they also say mathematics for self-study I actually have an older copy of this book I'm just going to grab it really quick why not it's actually right here so here's my older copy of um trigonometry uh for the Practical Man by Thompson so this one this one has a different let's just take a quick look at the copyright on this one oh look at this look at this in the manufacturer of this book The Publishers have observed the recommendations of the war production board and any variation from previous printings of the same book is the result of this effort to conserve paper and other critical materials as an aid to war effort wow wow the country was at War right the United States was that war and there were issues with paper um that's pretty crazy trigonometry for the Practical man I mean imagine living during that time that's just really nuts so yeah look this one's 1931 this must be uh the first printing or maybe not it says here first published in 31 and then it's been reprinted a gazillion times look how many times it's been reprinted look at that that's just insane to me so wildly popular book uh despite Feynman not thinking it was very interesting um so yeah same book as uh this one the size is a bit different but this is this is the reprint and uh this is also a reprint but I guess it's still like the first edition perhaps I I'm yeah I'm not perhaps it's just like a different printing so I'm gonna put these down let's look at this one so this is the one on calculus this is the one that fireman actually uh pretty much read in its entirety and took meticulous notes associate professor of mathematics School of Engineering Pratt Institute J.E Thompson it's kind of cool he just sat down with this book and his notebook and I think what what really helps and I'm I'm just I'm not claiming to read feynman's mind here but I'm assuming I'm assuming that what really helped him was that he had answers to all of the problems right you have answers to all of the problems in this book which is on let's just check those three 26. let's check those first because yeah look at that those are just integrals those aren't the answers should have answers back here there we go here are the answers to the problems which is really nice you see one two three four five six seven eight nine ten you have all of them there it smells incredible I'm sorry I just got to give it a whiff here just ah it smells like an old comic book it's just a really incredible smell let's take a look at the contents of this book to see what type of calculus you actually get is it you know single variables a multivariable this book on simplified calculus is one of the series designed by the author and publisher for the reader with an interest in the meaning and simpler technique of mathematical Science And for those who wish to obtain a practical Mastery of some of the more usual and directly useful branches of the science without the aid of a teacher right so these books are actually meant for self-study this mathematics for self-study series and so it was around and in print during feynman's Lifetime and so it makes sense that Feynman picked it up and successfully used it and learned enough math and and continue to learn math and physics and eventually won a Noble Prize fundamental ideas rates and differentials functions and derivatives differentials of algebraic functions so differential of the square of a variable differential of the square root of a variable the product and the quotient so very basic but notice we're only on page 22 right so this book has a lot of information and it's really broken down into tiny little subsections which make it really easy to self-study you know you've got these tiny little sections you can sit down for half an hour to an hour read it do a couple exercises you can check your answer and you can learn calculus Like Richard Feynman did I think that's pretty awesome so differentials of trigonometric functions velocity acceleration and derivatives interpretation of functions and derivatives by means of graphs maximum and minimum values problems in Maxima and Minima differentials of logarithmic and exponential functions cool stuff do we have a summary of differential formulas reversing the process of differentiation integral formulas how to use integral formulas interpretation of integrals by means of graphs graphical applications of integration and then use of integrals and solving problems while population increase the laws of falling bodies I bet Feynman didn't know he was going to win the Nobel Prize when he was reading from this book that's pretty incredible the natural law of growth and the number e I I the fireman story to me is one that is of great interest because you know I believe that effort is very important in mathematics and I think that Richard Feynman um just had an insatiable curiosity and effort towards math and physics and that's how he was able to learn uh so much I mean he just really cared about it fundamental ideas rates and differentials rates the most natural illustration of a rate is that involving motion and time if an object is moving steadily as time passes its speed is the distance or space passed over in a specified unit of time cool as for example 40 miles per hour one mile per minute 32 feet per second Etc then he goes on and explains some more of that let's look at some of the exercises let's just jump to like a random page here we go what do we have here let's look at some of the we have some illustrative examples okay we have so the differential so super easy x squared minus two X plus three it's a really easy derivative it's just going to be 2x minus two so pretty pretty easy they go through they do it with differential notation so they find differentials okay that's three examples look at that four five six oh that one's harder that's a lot harder you have a product rule here there look they show all the work they go through all the steps carefully they explain everything so like if you didn't have a teacher that's what this book is for if you didn't have a teacher and you were just trying to teach yourself calculus on your own this would work obviously it's better if you have a teacher right you know as much as I love self-study and I think it's great uh having a teacher having a lecture is is much much easier having a course however a book is kind of like a course right because it gives you the structure wow look at that 12 examples so you've got 12 examples that's ridiculous and then you have exercises uh you have 20 exercises with answers to them in the back of the book Let's just check it says art 1931 so it's page 30 31. let's go let's go to the back of the book and let's just see just to make sure it's there right because we want to know so so it's going to be 19. so there it is right there there are the 20 answers to the first set of exercises you get 12 examples and then you get 20 exercises with answers to all of them so it makes it really really good for self-study the biggest problem with this book is its availability I I didn't really look to see if it was available um you know before making this video but I'm pretty sure you can get it and I will do my best to find these for you in case you want to check them out integral formulas wow wow what a great book to think that a young Richard Feynman sat down with his little notebook and you know he worked through this and he he learned calculus so a more advanced Richard Feynman uh Richard Feynman who knows how to write proofs is much more mathematically mature so now we're looking at a Richard Feynman here who um you know he's he's learned a significant amount of mathematics he knows math and this is the book he uses Advanced calculus by Woods this is the one that's really expensive it's probably the most expensive book I have I have a lot of math books but I've been collecting for a lot of years and so some of them I've bought new but you know they're math books not that many people in the world collect them so a dollar fifty so someone paid that that was not me I know I paid uh not much for this I bought this over a decade ago Advanced calculus a course arranged with special reference to the needs of students of Applied Mathematics by Frederick s Woods professor of mathematics in the mathematics Massachusetts Institute of Technology we could rename MIT call it the Mathematics Institute of Technology so there's a copyright on this one I think this is the first printing copyright 1926 I think this is the first one I think this is the first edition this course in advanced calculus contained the course in advanced calculus contained in this book so it is a course it's kind of like what I was saying earlier right like these books you can you can get a course out of it has for many years been given by the author to students in the Massachusetts Institute of Technology so that's MIT so this book was used at MIT for many years which is an incredible School so you know that says something about the book the choice of the subject matter and the arrangement of the material are the result of the experience thus gained the students to whom the course has been given have been chiefly interested in the applications of the calculus and have felt the need of a more extensive knowledge than that gained in the elementary courses but they have not been primarily concerned with theoretical questions nice this is a course one in analysis very nice so it's basically an intro course but it's still very tough tough um you know if you compare this to other analysis books um this is so much more advanced just to throw out some names if you compare this to understanding analysis uh by Abbott which I actually have here let me just grab it actually I think I know where it is I'm back here we go I've got it this is understanding analysis uh by Abbott so if you compare um this old book uh by you know Woods to a modern book by Stephen Abbott understanding analysis you would see that the woods book has significantly more content and is significantly more advanced does that mean that the woods book is better than the analysis book absolutely not Steven Abbott has done a great job on this newer book and this is a book for beginners this is much more Elementary uh in his presentation than a book like this one so this is something that I mean I'm a collector of math books right so to me this is like super valuable and super Priceless and incredible so you get different knowledge in this book you're going to find things in this book that you're not going to find in this one so it's just a nice way to satisfy your curiosity so if you're curious like Feynman was then maybe this is a book to check out contents so functions continuity the derivative composite function rowley's theorem no I'm kidding it's called Rawls but I always wanted to say Rollies theorem of the Mean Taylor series with the remainder so we've got some indeterminate form zero over zero Infinity over infinity you can apply l'hopitals to those it talks about other forms infinitesimals fundamental theorems on infinitesimals it's interesting it's got that in the book right it talks about infinitesimals you pick up a modern book on analysis it's not going to do that right it's just not going to be in there and then power Series in chapter two look page 38 we're discussing power series who does that right who does that Woods does definitions comparison tests for convergence the ratio test for convergence region of convergence uniform convergence this is really good stuff I really like this stuff hyperbolic functions we should look at some of the stuff in a minute partial differentiation to me this is the most interesting of the books that I've shown you here because it's the most advanced and it's got a lot of interesting topics implicit functions applications to Geometry the definite integral the gamma and beta functions then we have line surface and space integrals this is calc 3 type stuff except you're going to see a rigorous treatment here right so people often ask what's a proof-based multi-variable calculus book well here you go right here's one that has a lot Vector notation differential equations of the first order differential equations of a higher order it's got DES in here which is pretty incredible and there's more look at this bezel functions partial differential equations calculus of variations functions of a complex variable wow elliptic integrals like OMG right and it has answers let's look at those 387 so page 387 that's what we can find answers in this book and you can see there are quite a few answers in this book it doesn't have everything right we can see that obviously things are missing but we do have some things right we do have some answers and that is better than no answers in my opinion so this book is extremely hardcore let's let's see how it starts starts with very basic Advanced calculus chapter 1 preliminary functions a quantity Y is said to be a function of a quantity X if the value of y is determined when the value of x is given someone wrote In the book that was not me Elementary examples are the familiar algebraic trigonometric logarithmic and exponential functions by means of which Y is explicitly given in terms of X such explicit formulation however is not necessary to the idea of a function so here we have some examples and it talks about continuity it's got some graphs it's pretty good from a book from the 20s right 19 I believe it was 1926 yeah 19 26. wow that's a long time ago that's this is a this is a pre-World War II era book I mean this is old this is all the derivative here's the definition a function f of x is said to have a derivative for x equals a if the expression approaches a limit as H approaches 0 in any manner whatever this limit is called the derivative for x equals a and is denoted by F Prime of a we write in order that the derivative should exist it is necessary that f of x should be continuous when x equals a for otherwise the fraction one would not approach a limit this condition is not sufficient as may be seen by considering the function defined by the equations x times sine pi x when X is down that's the example they give as X approaches 0 sine of pi over X oscillates infinitely between plus and minus 1. but X sine of pi over X approaches zero hence the function is continuous for zero yep and then using this function in the fraction one so up there okay we get this expression here so and it's you get sine of pi over H and that does not approach a limit as H approaches zero hence the function has no derivative when x equals zero so you could you could justify that a little bit more rigorously but it's pretty clear that that is not going to exist which you could probably give a proof there with Epsilon and stuff but not uh not really necessary in 1872 ystros gave the explicit statement of a function which has for all values of X the property which X sine pi over X has for x equals zero so it is known now that a continuous function does not necessarily possess a derivative hence when a new function appears in analysis it is necessary to inquire first whether it is continuous and secondly whether it has a derivative so it explains everything fairly well it's got good pictures I don't like this let me show you what I don't like and this is going to sound silly but I'm just going to come out and say it I'm not a fan of that variable Zeta or Ada I can't do it I just I've given up on it I took a functional analysis class once and the teacher would use those because the book was using those the krizzic book on functional analysis uses those variables and it was very painful I just used X and Y so this is what a teacher would write that down I'd put X or something you know because I couldn't do the variables but you can see here tons tons and tons of mathematics in a book like this just so much indeterminate forms infinitesimals I think we're getting to the end now uh of this chapter differentials here's some exercises really nice exercises what do we got let's see by division find an expression okay find an expression for wow find the limits we've got some limits here it's pretty tough and pretty have some pretty tough stuff here right it's not like necessarily like the easiest exercises and that kind of says something about Feynman right I mean the guy really really really studied hard I mean this is pretty tough stuff I wonder who wrote all this this wasn't me Blast from the Past power series Power series are really really cool um for me series are one of the things that initially got me interested in mathematics you first learn about series by the way in a course called calculus 2. so if you take calculus 2 that's when you would see series but this is a you know proof-based hyperbolic functions there's cosinch and cinch you could think of cosinch as the average of e to the X and e to the negative X because you're averaging them right you're adding up and dividing by two and cinch is half the difference you're subtracting and dividing by two just fun extra knowledge I figured I'd share yeah pretty cool pretty cool stuff here really really Incredible Book so I just wanted to show you some books that Richard Feynman used because I think that um it's just good to see them you know and I have a lot of math books and I think that this this makes these math books special to me so here we have understanding analysis I'll give that a shout out um great book for beginners right probably better than the one by Woods for beginners but the one by Woods has significantly more content and then this is the one um that Feynman actually read in its entirety we know because I'm pretty sure they found his notebook and he had um you know detailed detailed notes that he took uh from from this book he he created like a chapter uh you know like everything right he he went through it carefully and he created his own notes from this book and I I probably worked out almost every single problem so you know back then there was no internet so this this is it this is all he had you know books were all he had and Mathematics for self study calculus for the Practical Man by Thompson is the book that he read in its entirety and then this one uh the trigonometry for the Practical man this is the one that he um didn't really find that interesting and he thought the algebra one was too easy so kind of an interesting look I think at some books that a legend used to learn mathematics if you have any comments on Richard Feynman or the books he used do you have any of these books have you used these books what do you think of these books do you think these books are outdated sometimes people will ask is it outdated math does not get outdated what I will say about this one though is that it's a tough book but it's also a very beautiful book and it's very well written so if you can get a copy it's worth it I will leave links in the description to all of these if I can find them yeah until next time good luck take care thanks for being a subscriber

Channel: The Math Sorcerer

Views: 146,017

Keywords: feynman, math, books, richard, richard feynman, learn math

Id: 5rTAs5dvI4M

Length: 27min 34sec (1654 seconds)

Published: Mon Mar 13 2023