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Zach L.
12-11-2004, 11:24 PM
I present you an entirely worthless and random question... Perfect for GD.
Who do you think the best mathematical authors are?

I've got two nominations:

1 - Serge Lang - Sure, some of his books are nearly incomprehensible, but there packed full of information. Sure, he may redefine the term "obvious", but I'm still rather fond of his style. I particularly like his book, Algebra.

2 - Klaus Jänich - A truly remarkable author. He presents complex topics with great clarity, and in a manner that truly helps the reader learn. A quote from the preface of his book, Vector Analysis (the English edition): "An elegant author says in two lines what takes another a full page. But if a reader has to mull over those two lines for an hour, while he could have read and understood the page in five minutes, then - for this particular reader - it was probably not the right kind of elegance." Almost like he was talking directly to Lang in that passage. :)

SMurf
12-12-2004, 09:31 AM
Euler?

I've never read any of his books, as they come in volumes and would melt my brain, but I've heard he's quite important in this field... :rolleyes:

Zach L.
12-12-2004, 10:04 AM
I was thinking more along the lines of math books one would normally read, not necessarily who has contributed the most. :)

I have no doubt that Euler's works are impressive to read, though.

SourceCode
12-12-2004, 12:34 PM
Michael Spivak

Zach L.
12-12-2004, 07:07 PM
Thanks. I'll have to look into his books. For some reason, all four copies of his Calculus on Manifolds are checked out of the library right now, so it looks like I'm gonna have to wait a couple weeks to check it out. :)

iain
12-12-2004, 07:38 PM
Grassman and Tremblay - "Logic and Discrete Mathematics - a computer science perspective"

http://www.amazon.co.uk/exec/obidos/ASIN/0135012066/qid=1102901891/sr=1-8/ref=sr_1_8_8/202-3649571-4041445

SourceCode
12-12-2004, 10:08 PM
Thanks. I'll have to look into his books. For some reason, all four copies of his Calculus on Manifolds are checked out of the library right now, so it looks like I'm gonna have to wait a couple weeks to check it out. :)
Np, the book I have from him is called Calculus, it is his most famed book. It was used at Harvard years ago I believe. The explanations are incredibly clear yet the problems are extremely rigourous. In the preface to the second edition, he comments that several people have told him the book should be called "An Introduction to Analysis." Some schools in Europe also use the book, but it is used in courses where students already have knowledge of the mechanical aspects of Calculus. Personally I am reading the book even after taking 3 semesters of Calculus just so I can refresh my knowledge. I am finding his explanations clear and it is a good refresher for Advanced Calculus and further math courses I have yet to take. The way book is written makes you want to keep reading on and on, he words things so carefuly and he makes Calculus seem more exciting than ever. He has written the book to be a "first real encounter with mathematics" as he states in the introduction, and it truly does become an encounter, the problems are just so complex. The comments on amazon.com about the book speak for themselves. I would recommend buying this as well as the answer book, it is extremely useful considering the problems are so difficult.

Here is the link http://www.amazon.com/exec/obidos/tg/detail/-/0914098896/qid=1102910606/sr=8-4/ref=pd_csp_4/103-7586419-6045408?v=glance&s=books&n=507846

His books on Differential Geometry and Calculus on Manifolds are also highly regarded but I have not read them yet personally.

Other good writers I can think of are Courant and Apostol, they are however more formal and more difficult to read. Algebra by Michael Artin is a very good book also as it covers so much information very clearly.

Zach L.
12-12-2004, 10:30 PM
Ah yes... I've heard of Artin's Algebra. He still teaches it, so I plan on taking it from him next fall. :cool:
From what I've seen of his book, he had a very interesting approach... somewhat of a linear algebra approach running throughout the book (though, I've just glanced over it in the book store).

From how you describe Spivak's work, he sounds to be a good bit like Jänich. While his Topology, which I am currently working through, doesn't have any formal exercises, he makes sure to point out the key facts that the reader really needs to understand, and suggests proofs which would be useful to work out. It is very clear, and intended to be a book from which one can actually learn. To date, it is the only book I have found that treats topology both abstractly and understandably.

Lang's books, while very good, I have found to contain the following passage far too often: "Proof: Obvious". His Undergraduate Algebra was fairly good, but Algebra is a beast to work through (though, still one of my favorite books).

Looks like Spivak's Calculus is out of the library too, but his differential geometry book is there. Also one called, The Joy of TEX. :cool: I think I'll stick to the differential geometry.

There are really rather few math authors I have found to be universally comprehensible (that is, good authors as well as mathematicians), at least in the domain of math text books. There are some other quite good books out there that'd more properly go in some category like, "Popular Mathematics", or some such. Two good examples that come to mind are Gödel's Proof by Ernest Nagel and James Newman, and Abel's Proof by Peter Pesic.

Jez
12-13-2004, 09:34 AM
Ken Stroud's "Engineering Mathematics" series is a brilliant tutorial using his Programmed Learning technique.