The book From Calculus to Cohomology by Madsen looks a nice book. Well, it’s the first time I saw an introduction to topology from CALCULUS so I believe it amazing. Maybe I am too ignorant in mathematics.
I’m studying Commutative Algebra and Topology recently. As far as I’m concerned, categories are fundamental in mathematics so I’m particularly fond of algebra in favor of the concept of category. I saw some one says geometry and topology structures are much more interesting than algebra structures. I don’t understand it very much. Maybe in my mind all structures are algebraic. Well, maybe when we adopt measures and Cauchy sequences we are entering the field of Analysis, Geometry and Topology? Actually in my heart it is still algebraic. I think continuity doesn’t mean non-algebra.
Huh…The above seems almost all stuff. At my level of mathematics I’m not likely to understand much of them. I even used to reject algebra because at that time I think algebra is a boring collection of axioms. I also used to reject categories when I first knew them.
The society in China is weird. Teenagers need to study a lot of things neither interesting nor important in order to survive. As a result they do not have time to do things they like. Students with high grades are expected to be talents, but most of them do not have dreams to live for. All they do is to study for higher grades and to play. Most of them do not have their view in politics, culture, etc.
Because of these, I start to feel that I don’t really have friends. I am in a serious lack of emotions. Actually I don’t think anyone around me really has friends. I impute it to the weird society. It doesn’t allow people to dream, to love. So the lack of friends are natural.
The blog is desolate. Perhaps no one will see this post. But I believe one day here will be crowded, if I will.
By the way, Japan in World History by James L. Huffman is also a good book.