Reputation
377
Next privilege 500 Rep.
Access review queues
Badges
1 9
Newest
 Caucus
Impact
~5k people reached

Mar
26
comment Help with old exam question relating a spanning set of covectors of $T_{p}^{*} M$ to a coordinate chart containing $p$.
Doh! That makes perfect sense and is so much cleaner than what I was trying to do. Thank you very much.
Mar
26
accepted Help with old exam question relating a spanning set of covectors of $T_{p}^{*} M$ to a coordinate chart containing $p$.
Mar
26
asked Help with old exam question relating a spanning set of covectors of $T_{p}^{*} M$ to a coordinate chart containing $p$.
Dec
11
awarded  Caucus
Nov
29
asked Counting tamely ramified Galois extensions of $\mathbb{Q}_p$ with a given Galois group.
Aug
18
comment If G is a group of order n=35, then it is cyclic
As others have said, this proof does not work because you don't know <i>a priori</i> that it is abelian. It's entirely possible that $gh$ has infinite order (see: above matrix example). Let $n_p$ denote the number of Sylow $p$-subgroups of $G$. We know that $n_p \equiv 1 \pmod p$ and $n_p \mid 35$. We deduce from this that $n_5 = n_7 = 1$, so both the $5$-subgroup, $C_5$, and $7$-subgroup, $C_7$, are normal in $G$. By normality, we have that $C_5 C_7 < G$. Moreover, since $C_5 \cap C_7 = \{1\}$, $C_5 C_7 = C_5 \times C_7 \cong C_{35}$, and finiteness of $G$ implies that $G = C_{35}$.
Jul
2
awarded  Curious
Apr
30
accepted Help Understanding/Completing Proof of Prop 3.18/3.19 in Hatcher's Algebraic Topology
Apr
30
answered Help Understanding/Completing Proof of Prop 3.18/3.19 in Hatcher's Algebraic Topology
Apr
15
asked Help Understanding/Completing Proof of Prop 3.18/3.19 in Hatcher's Algebraic Topology
Feb
5
comment Open sets are $\mu*$-measurable in a metric space with a given condition
Notice that it's from your second approach, where you strive for contradiction. You already have that $\mu^{*}(E) < \mu^{*}(E \cap U) + \mu^{*}(E \cap U^{C})$, so the suggestion was to find a $U' \subseteq U$ that is just big enough to maintain the inequality $\mu^{*}(E) < \mu^{*}(E \cap U') + \mu^{*}(E \cap U^{C}) \leq \mu^{*}(E \cap U) + \mu^{*}(E \cap U^{C})$, and just small enough to also yield $d(E \cap U', E \cap U^{C}) > 0$. From there, your calculation shows that the inequality cannot be strict, and therein lies your contradiction.
Dec
13
comment Anti-Derivative where f(n) = m
According to the original post, $f'(1)=1$, so $C=3$.
Dec
13
revised For the mapping $\varphi: \Bbb{Z}+\Bbb{Z} \to \Bbb{Z}$ given by $(a,b) \to a-b$, describe the set $\varphi^{-1} (3).$
TeXified it
Dec
13
comment Anti-Derivative where f(n) = m
Almost had it. When you take the antiderivative of a constant $C$ (with respect to $x$), you end up with $Cx+D$, where $D$ is another constant. You should plug in for your constants along the way once you've solved for them. So the first derivative becomes $f'(x)=4x^3 - 6x^2 + 3$. Then take the antiderivative of that and find the new constant based on the initial values.
Dec
13
suggested approved edit on For the mapping $\varphi: \Bbb{Z}+\Bbb{Z} \to \Bbb{Z}$ given by $(a,b) \to a-b$, describe the set $\varphi^{-1} (3).$
Dec
8
accepted Compact hypersurface of $\mathbb{R}^{n+1}$ with positive curvature is diffeomorphic to $S^n$.
Dec
8
asked Compact hypersurface of $\mathbb{R}^{n+1}$ with positive curvature is diffeomorphic to $S^n$.
Dec
7
accepted Volume of a complete, simply connected Riemannian manifold of constant negative curvature
Dec
7
asked Volume of a complete, simply connected Riemannian manifold of constant negative curvature
Dec
5
comment Groups elements
I would prefer to keep contact here on StackExchange so that other users can chime in while I'm away. What exactly is it that you're still stuck on?