360 reputation
18
bio website math.joedub.net
location Phoenix, AZ
age 25
visits member for 2 years, 3 months
seen 10 hours ago

I'm a graduate student in Mathematics program at Arizona State University. My research interests lie in algebraic topology and hyperbolic geometry.


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 suggested 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?
Dec
5
revised Commutator subgroup of a dihedral group.
Tidied up TeX and, in general, attempted to make it more readable.
Dec
5
comment Groups elements
Hmm, since $\langle (123) \rangle$ is cyclic, that notation really should be $(\tau \bmod (123), n \bmod 2)$. I've edited my response.
Dec
5
revised Groups elements
edited body
Dec
5
suggested suggested edit on Commutator subgroup of a dihedral group.
Dec
5
comment Groups elements
Yes, $G$ has order $24$, but that's not particularly relevant to your three homework questions. See my answer for a more complete response to your homework questions.
Dec
5
answered Groups elements