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- Mathematics Stack Exchange
Q A for people studying math at any level and professionals in related fields
- Mnemonic for Integration by Parts formula? - Mathematics Stack Exchange
The Integration by Parts formula may be stated as: $$\\int uv' = uv - \\int u'v $$ I wonder if anyone has a clever mnemonic for the above formula What I often do is to derive it from the Product R
- Lie Algebra of U(N) and SO(N) - Mathematics Stack Exchange
U(N) and SO(N) are quite important groups in physics I thought I would find this with an easy google search Apparently NOT! What is the Lie algebra and Lie bracket of the two groups?
- $\\operatorname{Aut}(\\mathbb Z_n)$ is isomorphic to $U_n$.
It might be using ring theory in a non-essential way, but it is conceptually simpler because the endomorphisms are easier to describe than the automorphisms, and since the invertible elements of Zn Z n are by definition Un U n, we obtain the result without having to understand what Un U n actually looks like
- Equation of a rectangle - Mathematics Stack Exchange
I need to graph a rectangle on the Cartesian coordinate system Is there an equation for a rectangle? I can't find it anywhere
- Calculate the cohomology group of $U(n)$ by spectral sequence.
with fibre U(n − 1) U (n − 1) Then, we try to use spectral sequence and Leray's theorem to calculate Although it seems that we should calculate it by induction, I don't know how to continue Moreover, someone could use any other method as long as it work
- How do we calculate factorials for numbers with decimal places?
I was playing with my calculator when I tried 1 5! 1 5! It came out to be 1 32934038817 1 32934038817 Now my question is that isn't factorial for natural numbers only? Like 2! 2! is 2 × 1 2 × 1, but how do we express 1 5! 1 5! like this?
- When is the group of units in $\\mathbb{Z}_n$ cyclic?
Let Un denote the group of units in Zn with multiplication modulo n It is easy to show that this is a group My question is how to characterize the n for which it is cyclic Since the multiplicative group of a finite field is cyclic so for all n prime, it is cyclic However I believe that for certain composite n it is also cyclic Searching through past posts turned up this, where there was
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