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  • $\\operatorname{Aut}(\\mathbb Z_n)$ 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
  • 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
  • Expectation of Minimum of $n$ i. i. d. uniform random variables.
    You'll need to complete a few actions and gain 15 reputation points before being able to upvote Upvoting indicates when questions and answers are useful What's reputation and how do I get it? Instead, you can save this post to reference later
  • Calculate the cohomology group of $U(n)$ by spectral sequence.
    We have Ep,q2 ≅ Λ[c1,c3] E 2 p, q ≅ Λ [c 1, c 3] By lacunary reasons, this spectral sequence collapses on the second page, and so we deduce H∗(U(2)) ≅ Λ[c1,c3] H ∗ (U (2)) ≅ Λ [c 1, c 3] In general, the spectral sequence for the fiber bundle U(n − 1) → U(n) → S2n−1 U (n 1) → U (n) → S 2 n 1 always collapses on the second page, and you can use induction to prove
  • Mathematics Stack Exchange
    Q A for people studying math at any level and professionals in related fields
  • 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
  • When is the group of units in $\\mathbb{Z}_n$ cyclic?
    Let Un U n denote the group of units in Zn Z n with multiplication modulo n n It is easy to show that this is a group My question is how to characterize the n n for which it is cyclic Since the multiplicative group of a finite field is cyclic so for all n n prime, it is cyclic However I believe that for certain composite n n it is also cyclic Searching through past posts turned up this
  • 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?
















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