The book entitled “Intro to Topological Manifold” is pretty clear indeed. This is a result of seeing so many other books on AT that offers nothing about major concept of manifold. This is the missing book that I have been looking for so far.
However, I was also looking for problems solutions books for Algebraic Topology [...]
Lee?
Homotopy and fundamental group?
I just come across some information that shed more light on this subject of homotopy and fundamental group on Wikipedia. The connection to a French website with a flash animation is excellent. It points out something that I have never thought about it. It is the requirement that the pointer on the loop must finish [...]
Topology again
What a pain when I reviewing the Fundamental group part of the topology. There are so many BASIC thing that I have missed the first time I read this subject. It appears to be a little clearer now this time I have them reviewed and with many books at hand to compare with each others.The [...]
The description and proof of Pi(circle)=Z
http://en.wikibooks.org/wiki/The_fundamental_group
This is most confusing description that I have seen so far. The given information is never clearly stated. All the symbols and notations are ambiguous. The argument is esoteric. So far I have a hard time following it.
This is because the author tries to prove that map from is a isomorphic. This sounds [...]
New link for math
http://www.siam.org/news/news.php
Well this is a new link for math articles. This was thought to be a site that would charge the visitor for information. But it is not.
This is not a very helpful site for the technical thing. The web is not good for math information. Many of the site about math is either too advanced [...]
Lie derivative
This is a very general kind of derivative. I read the Lovelock and Rund book, especially the appendix part of it. This is a very esoteric subject. But it is widely used in theoretic physics. This book has a very good motivation and derivation of all the characteristics of the Lie derivative. This information [...]
Google
What is the major point of the Stoke Theorem is that the surface integral sometime is so hard to calculate. So instead of doing the surface integral, the Stoke theorem provides a different way to do it.
It is the using of the right hand side of the equation of Stoke, i.e., using the path integral [...]
Stoke theorem intricacy
I try to write my impression about the Stoke theorem and then I run into problem with a differential form of the same forum and more looking up on the web.
The end result is a bunch of confusions that is distracting me from my main task to write my impression about the Stoke theorem.
The [...]
Mind game, vector bundle and manifold musing
The idea of there’s a limit to the scale that further probing would not making any more sense is a very philosophical one. The Planck scale level is not needed for the unifying effort of four forces in the universe according to Greene. So there is no need for the incorporation of the Planck [...]
Line integral of a vector field
Line integral of a vector field
This is a site that deals with the concept of line integral. The concept of line integral in 2-d is innocuous looking. It is not many different from any other plane geometry integral at all. It is when the geometry change from 2-d to 3-d that we see the [...]
The idea of divergence and curl*
The idea of divergence and curl*
http://www.math.umn.edu/~nykamp/m2374/readings/divcurl/ this web site is so unbelievable in its effort to make the concept of curl of a vector field understood. The 3-D image of curl and div of a vector field is clearly explained and shown with 3-d image.
This is much better than those image on the flat 2-D [...]
