Papers better than books?

Question

Not so long ago I took a class called "Discrete analysis". I remember that I couldn't find any "novice" level material on Mobius functions in combinatorics. So then I went to the roots and read Rota's original paper "On the foundations of combinatorial theory I" and it really impressed me. So I wonder is there other mathematical subjects that it would be better for novice to get started with by reading rather original papers than actual books?

ADDED: Thanks for your answers. That's really interesting!

I would call Stanley's book on combinatorics an amazingly good introduction to Moebius functions... — Mariano Suárez-Álvarez, Sep 01 '13 at 09:24
A somewhat related question http://mathoverflow.net/questions/28268/do-you-read-the-masters — , Sep 01 '13 at 09:48
Rota was a master expositor. Not all originals are as well thought out. — Benjamin Steinberg, Sep 01 '13 at 17:18

score 45 · Accepted Answer · answered Sep 01 '13 at 12:56

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Very recently I and Misha Sodin had a strong incentive to learn the Ito-Nisio lemma (which, roughly speaking, says that weak convergence in probability of a series of symmetric independent random variables with values in a separable Banach space implies almost sure norm convergence to the same limit). The textbooks we could find fell into 2 categories: those that didn't present the proof at all and those presenting it on page 2xx as a combination of theorems 3.x.x, 4.x.x, 5.x.x, etc. The original paper is less than 10 pages long, essentially self-contained, and very easy to read and understand.

The moral is the same as Boris put forth: the books are there to optimize the time you need to spend to learn the whole theory. However, for every particular implication A->B the approach they usually take is something like E->F->G, G->F, (F and Q)->B; since A->E, then A->G; once we know G, we have F, so it suffices to prove that A->Q to show that A->B; we show that Q,R,S,T,U are equivalent, with the trivial implication S->Q left to the reader as an exercise; finally, we prove that A->S. So if all you need is A->B, you may be much better off reading the paper whose only purpose is to prove exactly that.

answered Sep 01 '13 at 12:56

fedja

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+1 for the personal experience as well as for devising such a mischievous scheme of demonstration. – Jonathan Chiche Sep 01 '13 at 13:13
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Alas, I cannot take the credit for devising the scheme without running the risk of plagiarism lawsuits from many textbook authors and copyright lawsuits from their publishers. So, let's say, I just made "fair use" of it :). – fedja Sep 01 '13 at 13:38
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Thanks! That's a very good answer. As always, examples make our life simplier. – Charlie Kilo Sep 01 '13 at 15:57
fedja's description is a caricature. It applies only to the worst among books. There are many excellent books for studying and learning mathematics (at research level), very well written by Fulton, Mumford, Serre , Arnold, Vinberg, Bott, Postnikov,Samuel, Hirsch,Ziegler, etc..., etc ... – Al-Amrani Sep 09 '13 at 09:32
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I would not say that the implication scheme indicated by fedja is necessarily a sign of a bad textbook. I think, it is rather a usual style if you want to present a whole theory. – Lennart Meier Sep 09 '13 at 14:40

score 13 · Answer 2 · answered Sep 01 '13 at 09:27

If you want to learn the theory as a whole (together with generalizations and applications), then you need to read the book. If you want to understand how the author guessed to this theory, then you need to read the original article. In fact one has to do both that and another.

Papers better than books?

2 Answers2