It's Time to Stop Recommending Rudin and Evans...

Ever been in a situation where you needed help and some mathematician gave you the most technical book on whatever that subject was you needed help with? Join the club! Today we're going to be addressing this issue as well as some tips you can employ when the mathematicians do their thing. Feel free to ask for help here in our community, our members should be very inviting and welcoming.

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[railgap]

Speaking as a retired "polymath" who worked in many technical careers... (and I can't speak to textbooks or math theory references)
but when it comes to doing practical work using math in non-math fields, it has been my experience there is always That One Reference Book. Math for electronics, math for machinists, math for chemists, whatever technical work that you do, there is always That One Book. Thus if you work in any technical field, there is mostly likely a math book for you that is accessible and useful. You just gotta ask the non-mathematicians what the titles are for your field. :)

I once worked with a very, very smart mathematician plus a couple of coders and an algorithms guy. I often felt like the dumbest guy in the room even tho I knew I wasn't dumb... but when we went to lunch or dinner or whatever, I had to figure out the tabs and tips. Mathematicians don't do arithmetic, as a general rule. >_<

Math geek joke!
Q: what's gray and proves the uncountability of the reals?
A: Cantor's Diagonal Elephant.

I'll show myself out.

[seanhunter]

Couldn’t agree more. I think with Rudin in particular there is a certain sort of person who deliberately recommends it knowing that the person they are supposedly recommending it to will struggle. It’s like they’re showing off saying “I’m smart enough to not find Rudin hard”, and get a kick out of making other people look/feel dumb. I remember when I worked in finance I had a trader who had been a math professor come over to my desk and pick up my copy of “The Volatility Surface” by Gatherall and say (with a sneer) “What’s the point of *you* owning this book?”

[BhrantoPathik]

Rudin is of course written in a poor way, it's not written for theory. It's mainly a problem book but along the way you will also see some slickest ways of doing things, for which it's definitely worthy to read it along with some other good books

[royalfinest]

The best books out there IMHO are the ones that offer clarity and EMPHASIS instead of depth and quantity. For example, I saw many people still struggling to understand the true nature of Least Upperbound (Supremum) and Infimum because most books do not give enough emphasis on the “progressive discovery” of terms. Second example, many Calc 2 students are put on “what method to use” mode when given simple questions on Limits. The reason being calculus books do not give enough emphasis that Direct Substitution is the primary technique used to find the limit, but may take a slight detour before coming back again to Direct Substitution. Calc books often generally mention D.S. just as like any other techniques, no emphasis given.

[jloiben]

I think the Long Form Math book is one of the best for learning analysis on your own (ie - not as part of a university course). That book gets some recognition, but that should be recommended as a starting point way more often than it actually is

[shrihansuchit]

Pedagogy of teaching has evolved for many good reasons. Earlier people used to have dense textbooks which used compact language with few amount of hard problem sets. But now knowledge is accessible to all and not only to some genius students attending lecture in some top institutions and then reading such harder texts for further intuition.

I have realised that books should be meant to read with joy and motivation to read further and not worship it necause someone great read from it.
Yes I love any new/updated text provided by Springer UTM series or GTM series (which contain many known works like Abbott, Ross, Pugh, Laczkovich and Sós, Sheldon Axler etc...).

[timeslices]

There seems to be a cult of pride among mathematicians that rewards abstrusity. This might be because psychologically, mathematics is fun because it is abstract. Hence the value system of mathematics rewards such exclusionary behavior.

[markborz]

The last year I changed my tactics: Instead of reading books, I'm watching first YT videos on this specific topic and afterwards use books to go into more details, after I already understood main parts.
That saves a lot of time and nerves.

[SabrinaMarquez-rwxb]

If someone asked for a recommendation for a first analysis book I would probably say Understanding Analysis by Abbott or Elementary Analysis by Ross. The former if they want more motivation and exposition and the latter if they want a bit more of a challenge but not be completely overwhelmed. Yes, some would probably consider those books “rigorous calculus books”. In fact, some MAA reviews of Ross’s book refer to it that way as if to say it isn’t a “real” analysis book like Baby Rudin. Which is just elitist.

And I don’t even hate Baby Rudin. I would definitely pick up a copy and go through it right now if I could afford to because I love analysis. But if I didn’t absolutely love analysis I would probably find the book off putting because of how it’s pushed on people as almost like a hazing sort of thing.

[trivialqed]

imo this culture is slowly changing, the new younger profs that hated going through rudin and other similar traditional references are ditching them for newer and better books

in my analysis and linear algebra courses both profs hated rudin and hoffman textbooks respectively, they werent even included as references in their syllabus. i remember one of them saying "dry" textbooks with no examples, no motivations behind theory and with concise proofs were great for quick searches at a time when google didnt exist. now they're obsolete even for mathematicians

[CrazyShores]

Spot on as always. Someone had to say this out loud and clearly!

[liver-b]

Guenther and Lee was used at my school for the applied pde... it's pretty readable. And, Ablowitz and Fokas for complex variables with an applications bent.

[Djentstructer]

3rd year MecE student here. Currently taking a PDE course. The course textbook (Applied Partial Differential Equations by Logan) is great. The professor's notes, on the other hand, are absolute gibberish. I would've expected that it would be the other way around but waddaya know?

This wouldn't be a problem if the course material was confined to the stuff in the textbook. But sadly, prof has special topics sprinkled into his notes.

[vukstojiljkovic]

I am a m.s.c student and a self-learning researcher in operator inequalities. I have read multiple books and what I can say is that deeper and longer the book and harder it is, the less you get at the end when you eventually read it. Now I prefer smaller books with concrete topics. For example, I've read some book on functional analysis which was around 700 pages long and when I've finished I questioned myself what did I really learn at the end?
In my opinion, a book with >=300 pages is just useless. It's better to write multiple smaller editions of at most 100 pages where you explain stuff in great detail.

What I can suggest is to learn certain things from master's thesis and b.s.c thesis if possible. I find a thesis a great way to learn as they must be written nicely due to the nature of a thesis in the first place and they will recommend stuff that is needed/not included/properly cite. Some books don't even cite stuff or blatantly state without evidence.

Let me know what do you think about my suggestion and my opinion!

[mstrawblay]

Lakatos en su libro "proof and refutations" ya critico a rudin de como presenta el libro, creo que la manera correcta de leerlo es complementarlo con libros y aplicaciones en otras ramas y hacer una resumen historico leyendo a hardy, emile picard, Camille Jordan, Kolmogorov, Diedonne, landau, Courant, ludwig wittgenstein, etc.Saludos

[economicist]

Just waiting to see who recommends Baby Rudin here in the comments before they watch the video or even look at the thumbnail...

[icybrain]

"written by Riddler" made me do a double-take, lol

[eetuhalme]

Interesting video, I essentially agree but I would like to offer some differing prespective to consider. In my experience, most mathematicians I have worked with are keenly aware how difficult these books are and would not recommend them without proper context and background of the reader. If you are a scientist or engineer learning PDE's for applications the first time or a hobbyist interested in dipping their toes, then Evans is clearly the wrong book to recommend.

However if you are interested in learning the theory of PDE's at a graduate level with enough background in vector analysis, measure theory and functional analysis, then for this purpose Evans is simply the best source available. It is the standard recommendation for this audience at this level for a good reason. There are other options at graduate level like Taylor's trilogy of books, but I find them much more demanding (and comprehensive). Rudins PMA is less defendable, as there are more clearly written books at that level as you state in the video. However Rudins Real and Complex analysis is excellent as a graduate book.

Okay but why do these books get recommended so much, esp. in online communities? I believe one reason could be that when you are missing the critical background information, it is easy to just recommend the standard reference like Evans. For Rudin's PMA, I think that is a victim of it's own popularity and "mythical" status. People see it recommended online and that the book is popular, so they recommend it futher when given the opportunity. I suspect that most who recommend PMA online, have not used it as the first primary learning source themselves.

I find it really important that when recommending books and asking for recommendations, enough background is provided. What's the existing knowledge, what are the (true) prerequest of the book and what is the goals of the reader. I would like to believe that there are no bad books, only wrong audiences for them. Altought in some cases the size of the correct audience might be tending 0...

[jakubzielinski]

Hello, undergraduate here. I share with all you here my deep hatred towards the style in which both of the books are written - recently I've read Functional Analysis by Rudin (which is written in the same manner as all of his books). To be frank, I'd say it's one of the worst mathematical textbooks I've ever laid my fingers onto. While reading it all the time I felt like the author assumes that I already know everything and he just puts the least effort possible, only to remind me about facts that I already should have known. It's trash and unreadable. Of all the content only the exercises can be sometimes teaching. In my field of interest, which is the number theory, there are these books titled "Introduction to Analytic Number Thoery" by Kowalski and Iwaniec and "Opera de Cribro" by Friedlander and Iwaniec - both of them are impenetrable but always recommended by specialists. I respect Friedlander and Iwaniec as researchers in number theory, they've done an amazing progress in recent years, but all their books and papers are just unreadable.

[ricecake]

I saw someone on Reddit try to recommend Baby Rudin to an engineering student who has no idea what real analysis is. lol