I am starting to learn Real Analysis and I have come across the generalised definition of the derivative for higher dimensions. I realise that the derivative being a linear transformation nicely accommodates the one dimensional case where the derivative is just a constant at any point. I also und...
I was just wondering if anybody knows of any good books or articles that study rings (and algebras) without (or not necessarily with) identity. I have gone through Thomas Hungerford's Algebra textbook (and loved it), but every book I have read afterwards on noncommutative algebra (Farb and Dennis...
I have seen this question on the internet and was interested to know the answer. Here it is : Calculate $\lim\limits_{n\to\infty}(1+\sqrt[2]{2+\sqrt[3]{3+\dotsb+\sqrt[n]n}})$? Edit : I really tried doing it but wasn't able to get somewhere. I know how to do questions like $ y = (1+\sqrt{1+\...
Let $X$ be a complex manifold and $Y\subseteq X$ a submanifold. I define $TX_{|Y}$ as the restriction bundle of $TX$. How I can prove that $$d \iota: TY\longrightarrow TX_{|Y}$$ ($\iota:Y\longrightarrow X$ is the canonical inclusion) is injective?
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