Am posting this topic for the assistance/help fellow Gaussians can give so as we can ahve a reference in the development of curriculum, research topics we're working on, or materials to browse in relation to the lessons we teach or study...

Uhm.. If you are a new-comer to dynamical systems then the book by Steven Strogatz called "Nonlinear Dynamics and Chaos" .. =) And then when you are done with that you can go on to the classic by Guckenheimer & Holmes...

what are some good books on abstract algebra?

Have anybody read John Penrose: Introduction to reality? Is it a good book?

Here are some classic math books

1.What Is Mathematics?  by Richard Courant 

"A lucid representation of the fundamental concepts and methods of the whole field of mathematics...Easily understandable." -Albert Einstien

2.Principles of Mathematical Analysis by Walter Rudin

3.On Formally Undecidable Propositions of Principia Mathematica and Related Systems by Kurt Gödel

revolutionary paper available here

4. A Mathematician's Apology by G.H. Hardy

People who like graph theory, nice proofs and chess may want to get Across The Board. It's a chess-related math book answering questions about for example knight tours on (generalized) chess boards, mostly with nice proofs.

Drknownothing, my information is rather old, but I am still confident in saying that for a graduate text on abstract algebra, Serge Lang's "Algebra" stands out, and is elegant and concise. However, the level of abstraction would make it difficult to use as an first look at most of the topics covered, but better after having done a first degree with several algebra courses in it, or for looking again at any particular topic studied in another text aimed at first courses.

I recommend "Men of Mathematics" by E.T. Bell. I read that John Nash read that book and that's what got him into mathematics.

Thank You, I didn't remember the right name. Perhaps I try to read it.

Best greeting,

kataikkola alias Martti Turunen

Hei!

I'm looking for a good book on statistics, following these criteria:

• Nice format, loads of pictures and examples.
• Not too heavy, around 300 is good, >500 is not so good.
• Entry level, it should be advanced but not expecting too much pre-knowledge of statistics.
• It would be nice if it was programming-oriented, but it is not necessary.

Thanks

Here we use John B. Fraleigh's book...You can also use Thomas Hungerford's..