Real Analysis Book for Self Study

This is a book that seems to be not so popular but it's still available today. It is called Real Analysis A Historical Approach and it wasw ritten by Saul Stahl. In this video we take a close look at this book. You can use this to supplement a course you are taking in college or for help during your math self-study sessions. I hope you enjoy this video:)

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Thank you:)

[madisonseay]

I have been watching your videos for almost four years straight. You are an inspiration to me and others who have had a passion for math since we were little bitty. I'm double majoring in Mathematics and Physics. Never stop making videos!!

[bargainbincatgirl]

I would like this book more for the historic angle. I find pretty interesting the discussions in how the fields of mathematics come to being, because nowadays math is treated like "revealed truth, don't question it" but its past has being more rugged, inexact, and weird.

[Taylor-rxyb]

What a cool book! I saw when you had the back of the book showing that there is a historical one for algeba? That sounds like something that would have been very helpful to be when I was first learning algebra

[odysseushuxley]

Would you be willing to do a video demonstrating your math note-taking strategies? I'm not sure if you already have a video on this subject, but if you don't, it would be very useful and interesting to see how you take notes from a math textbook.

[daniellejdevlin]

I wish I could train my brain to understand analysis. I have tremendous respect and admiration for people that can do this kind of math. Math proofs have always been the bane of my existence, but I'm still hopeful one day I'll get it :)

[markgrindol]

I took a class at the University of Kansas that was taught by Saul Stahl. It was a one credit Math class that was a fun class on knots. The class didn't have a textbook. I enjoyed the class.

[xaviergonzalez]

Wow, what a book! One more in my list! Thank you Sir

[dimitrioskalfakis]

beautiful to self-study but intense when taken as a subject in college. it is only afterwards with hindsight and having the experience that you may appreciate its essence.

[demongeminix]

When I took Real Analysis, I had to do it as a self study, as it wasn't being offered as a class the year before my graduation (small college, small population... upper level classes weren't offered every semester. They had an every-other-year schedule for a bunch of upper level classes. I took Abstract Algebra before I got to Analysis. Go figure). I had to see the instructor at a weekly appointment that lasted close to an hour and we would cover 2 to 3 sections a week. I ran through 3 5-subject college ruled notebooks for this class alone. I think I slaughtered a small forest for the class. If Greta Thunberg was alive back then, she probably would have burned me at the stake. I used the Bartle & Sherbert book, but it would have been nice to have something like this. Any way, it was tough, but I still got an A. Since I've left college, I've obtained 3 or 4 more Real Analysis books. I'll be adding this one to my collection as well. Thanks for the heads up.

[vnever]

Really amazing book! A similar one is _Analysis by its History_ by Hairer and Wanner

[WaelAjam]

Thanks for the recommendation. The table of contents seems very interesting. I 'll buy for sure.

[douglasstrother]

What makes Real Analysis so challenging?

I'm a Physics Geek, so my exposure to Real Analysis is limited to the elementary exposure in a Calculus text (Marsden & Weinstein, in particular) showing that derivatives and integrals make sense.

[Nyihm]

Great video, do you have any recommendations for books for history of math/applied math? Your videos are great to see timepieces of textbooks and topics

[vegenzohrabian]

there is also modern algebra book by stahl

[hrenhrenov]

Thanks for the video! It looks like a VERY interesting book, I new nothing about it and Saul Stahl before! By the way, quick search shows that Saul Stahl also wrote books on introductory abstract algebra, geometry, and even game theory. Might be interesting, too. If an author wrote one good book, other books from him are likely to be good. (Not always works, of course. Queen Victoria asked for other books of Lewis Carrol after reading Alice in Wonderland, and was disappointed to learn that Carrol wrote on math :-)

[sicko_the_ew]

Your "Gowse" is right for Gauss. ("Goass" would be more "French", I think.)

For German, "W" sounds like "vee" (and "V" sounds like, "eff"). It looks like a lot of mathematicians from the English speaking world just ignore that, and use the English form. (A word is only proper English when it has been pronounced as if written in English. It's a very old tradition, so I don't expect it to change any time soon. Going right back to kids who would shout, "Watch out!" in school Latin, that sounded like "Cavey, !" - where Cicero ("Kickero" to his family, not "sissero") would have said, "Cah-veh!" before rolling over in his grave again. Naughty boys used to "Keep Cavey". Keep a lookout for grown ups, while getting up to mischief. And every time he heard them say that, from beyond the grave, poor Kickero would die all over again. :D )

So maybe the correct English for Weirstrass would actually be something like "Wire Struss", not "Vyre Struss". I suppose it depends on who you speak to. I had teachers who called "Oiler" "Yewler" for instance. Took me many years to make the connection between his "Eu" and the "eu" in Deutschland.

(And poor old Bach's name is a lost cause for most English speakers. That "ch" sound is lost from English. Has been missing for several hundred years, now.)

[BboyKeny]

I saw that there is a second edition of this book from 2011. So I imagine it's still in print.

[αηομαλψ]

This is the only source I could find on the history of analysis :(

[realnameverified]

I was looking for a book like this just last week (judging from the title).

[rich_in_paradise]

I think it's strange that books like this get withdrawn from libraries. You can imagine a lot of books becoming out of date, in the sciences and history, etc. But this is mathematics! Math doesn't go out of date. I guess there are cases where a better book replaces an old one, but unless they had many copies, why not still keep the old one? Seems strange to me.