Recent content by pswongaa

I've learned some complex analysis from the book written by James Brown and Ruel Churchill, but I forget almost everything about complex analysis. Would there be any problem if I study adult rudin directly?

if lebesgue integral of f^2 over an interval equal 0, must f=0 a.e on that interval?

the integrals themselves are not important, I just want to find a way to improve my integration skill

My integration skill is very poor, there a many integral that I can't solve, for example: $$\int_{0}^{\infty}\frac{\sin^{2n+1} x}{x} dx$$ $$\int_{0}^{\infty}\frac{\cos ax-\cos bx}{x} dx$$ but my friend could solve them very quickly, so may I wonder if there are any books about technique for...

could you suggest some abstract algebra books? I only have artin's algebra, it is enough?

I want to study algebraic geometry and differential geometry, what should I learn beforehand what is the relation between abstract algebra and homological algebra:confused:

Let L_{\theta} be the line passing through the point z(\theta)=(\cos\theta,\sin\theta) on the unit circle at angle \theta and with slope \frac{1}{2}\theta. The mobius band is M={(z,v):z\in S^{1},v\in L_{\theta}} my question is , why M is a mobius band?