Thread: Books

Originally Posted by Guitarist

I make no claims that my attempts to explain manifolds is in any way thorough. Rather my intention was to give my friend, and other interested readers, just enough of a feel for the subject that, should they wish to dig deeper in textbooks (good Heavens - what are those?) or on sites like Wolfram or PlanetMath, they will at least have a fighting chance.

I understand that. Basically this is my way of seeing some stuff like this until I'm able to get my hands on some good books or take courses or whatever, and then, as you said, I'll have some foundation for the material and won't be going in blind.

I've just discovered that there are some pretty cheap books on amazon, so I'd like to post some in case anyone has had experience with them and can give a thumbs up or thumbs down. Any recommended books are most welcome too (preferably under about $20...)

Differential Topology: An Introduction, David B. Gauld
Elementary Real And Complex Analysis, Georgi E. Shilov
Elementary Functional Analysis, Shilov

A concern that I have is that one may describe a book as 'easy' or 'beginner level,' but then that person may have a degree in mathematics or at least have taken advanced courses...it's all relative.

I need to go for now but I'll do some hunting when I have time and post more.

DrRocket, I see you just made some suggestions in our other thread, thank you.

Originally Posted by Chemboy

Originally Posted by Guitarist

I make no claims that my attempts to explain manifolds is in any way thorough. Rather my intention was to give my friend, and other interested readers, just enough of a feel for the subject that, should they wish to dig deeper in textbooks (good Heavens - what are those?) or on sites like Wolfram or PlanetMath, they will at least have a fighting chance.

I understand that. Basically this is my way of seeing some stuff like this until I'm able to get my hands on some good books or take courses or whatever, and then, as you said, I'll have some foundation for the material and won't be going in blind.

I've just discovered that there are some pretty cheap books on amazon, so I'd like to post some in case anyone has had experience with them and can give a thumbs up or thumbs down. Any recommended books are most welcome too (preferably under about $20...)

Differential Topology: An Introduction, David B. Gauld
Elementary Real And Complex Analysis, Georgi E. Shilov

I need to go for now but I'll do some hunting when I have time and post more.

Go take a look at the books that I listed in my post in the manifolds forum. That post might have been better here, but it is too late and I was responding to the information that you provided in response to my questions there.

I don't know the Gauld book. For differential topology I recommend the book by Morris Hirsch. But before you take on differential topology you need some basic topology. For that I recommend something like Kelley's

Shilov's book is an old one, I think probably pretty, but I do not own it and am always a bit leery of the style of Russian authors. I would personally recommend Rudin's book Real and Compex Analysis, but either of those books really needs something like Rudin's Principles of Mathematical Analysis or Bartle's Elementa of Real Analysis (inexpensive on the used book market) as a prerequisite. General Topology or Topology by Hocking and Young. Lew Wards Topology:An Outline for a First Course is an interesting and inexpensive option (used book market) if you want to experience the pleasure of a Moore Method course where you do all of the proofs yourself.

For inexpensive used book look on Alibris as well as Amazon. Sometimes older books, particularly older editions, are available at a fraction of the cost of new ones, and older editions of most math books are as good as the new editions, unless you need to follow and instructor page by page in a formal class.

Here are some of my favorite advanced math books, all classics. Most can be found, in an appropriately old edition, at reasonable prices on the used book market.

Calculus on Manifolds -- Michael Spivak (for some reason this little paperback seems to be unreasonably expensive at the moment)
Elements of Real Analysis -- Robert Bartle
Principles of Mathematical Analysis -- Walter Rudin
Real and Complex Analysis -- Walter Rudin
Functional Analysis -- Walter Rudin
Algebra -- Michael Artin (a gentle introduction)
Algebra -- Serge Lang (not for the faint of heart)
Group Theory -- Marshall Hall
Topology -- Dugundji
General Topology -- Kelley
Algebraic Topology, An Introduction -- Massey

Thank you for the suggestions. The one thing that I'll stress is just price... But I suppose I'll just have to accept that a lot of things I won't be able to find cheaply.

Might go ahead and buy The Elements of Real Analysis by Bartle sometime... It was in your post so I'm guessing you think it's a good one to read?

Found this free e-book for you, looks a pleasant read on topology

Thank you, it looks good. Might work through it and post the exercises as I do them to see if they're correct.

Originally Posted by Chemboy

Thank you for the suggestions. The one thing that I'll stress is just price... But I suppose I'll just have to accept that a lot of things I won't be able to find cheaply.

Might go ahead and buy The Elements of Real Analysis by Bartle sometime... It was in your post so I'm guessing you think it's a good one to read?

That book by Bartle is excellent.

AbeBooks.com, and Play.com are very often cheaper for textbooks than Amazon. Abe, in particular, sells International Editions of expensive textbooks.