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April 19

Chain rule in multi-variable calculus

From Wiki, I found the chain rule of composite functions of several variables with notations in partitions and blocks at The electronic journal of combinatorics 13 (2006), # R1. Since this formula has been used extensively in generalized functions, does Wiki provide any information of this rule in terms of multi-indices? More precisely, let y=f(x) where x,y are vector variables, z=g(y) is a real variable and $m=(m_{1},...,m_{k})$ is a multi-index where $m_{j}$ are integers $\geq 0$ . What is an explicit formula to express $\partial ^{|m|}z/\partial x^{m}$ in terms of partial derivatives of f,g? Thank you in advance. twma 07:11, 19 April 2008 (UTC)[reply]

Thanks to somebody for making

\partial ^{|m|}z/\partial x^{m}={\frac {\partial ^{m_{1}+...+m_{k}}z}{\partial x_{1}^{m_{1}}...\partial x_{k}^{m_{k}}}}

readable. twma 03:04, 20 April 2008 (UTC)[reply]

Don't write it like that; write it instead like this:

\partial ^{|m|}z/\partial x^{m}={\frac {\partial ^{m_{1}+\cdots +m_{k}}z}{\partial x_{1}^{m_{1}}\cdots \partial x_{k}^{m_{k}}}}

I.e. use \cdots, or at least \dots, rather than "...". Michael Hardy (talk) 20:38, 21 April 2008 (UTC)[reply]

female mathematicians

in the world of mathematics,is there any famous female mathematicians?i mean aname related to afamous theory?Husseinshimaljasimdini (talk) 08:26, 19 April 2008 (UTC)[reply]

Probably the greatest female mathematician of all time is Emmy Noether. Aside from her foundational work in abstract algebra, Noether's theorem and the ideas behind it are fundamental to modern physics. Algebraist 11:01, 19 April 2008 (UTC)[reply]

See our list of female mathematicians and this more extensive list; Sophie Germain prime; Noether normalization lemma and Noetherian groups; Cauchy-Kowalevski theorem ... Gandalf61 (talk)

We should not forget Vera Sós, who surprisingly has no article here on wikipedia. –King Bee ^{(τ • γ)} 13:14, 19 April 2008 (UTC)[reply]

Her student László Babai has a page. She should be added to WP:Requested articles/mathematics#Mathematicians. I added several female mathematicians to the list of female mathematicians whose work I had personally encountered. I don't think anyone has seriously gone through and added people to this list. JackSchmidt (talk) 05:15, 20 April 2008 (UTC)[reply]