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  2. $\\operatorname{Aut}(\\mathbb Z_n)$ is isomorphic to $U_n$.

    Aug 3, 2023 · 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 …

  3. Mnemonic for Integration by Parts formula? - Mathematics Stack …

    Nov 11, 2018 · 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 …

  4. Expectation of Minimum of $n$ i.i.d. uniform random variables.

    Apr 25, 2017 · To calculate the expected value, we're going to need the density function for Y Y. To get that, we're going to need the distribution function for Y Y. Let's start there. By definition, …

  5. Calculate the cohomology group of $U(n)$ by spectral sequence.

    May 31, 2015 · 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 ∗ …

  6. Mathematics Stack Exchange

    Q&A for people studying math at any level and professionals in related fields

  7. 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 …

  8. Equation of a rectangle - Mathematics Stack Exchange

    Oct 2, 2011 · I need to graph a rectangle on the Cartesian coordinate system. Is there an equation for a rectangle? I can't find it anywhere.

  9. 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 …

  10. How many possible combinations in 8 character password?

    I need to calculate the possible combinations for 8 characters password. The password must contain at least one of the following: (lower case letters, upper case letters, digits, …

  11. Find the sum of the series $\\sum \\frac{1}{n(n+1)(n+2)}$

    Mar 26, 2015 · I got this question in my maths paper Test the condition for convergence of $$\sum_ {n=1}^\infty \frac {1} {n (n+1) (n+2)}$$ and find the sum if it exists. I managed to show …