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Hopeful mathematics student with some competition level problem solving experience. Studying algebraic topology and algebraic geometry at the moment, but I feel like anyone who know anything know more than I do.


18h
comment Suppose $F$ is a finite field of characteristic $p$. Prove $\exists u \in F$ such that $F = \mathbb{F}_{p}(u)$.
Equality is an isomorphism, but isomorphisms aren't always equalities. So equality is stronger.
1d
revised Isomorphism between quotient groups with normal subgroups
added 33 characters in body
1d
comment How to prove that $\sup(A\cup B)=\max\{\sup(A),\sup(B)\}$?
What are your own thoughts?
1d
comment How can I prove that the inverse of $n-1$ in $U(n) = \mathbb{Z}_n^{\times}$ is $n-1$?
Calculate $(n-1)^2$.
1d
revised In proving “if a set is compact, then it must be closed”, why does the finite subcover behave differently than the infinite open cover?
added 40 characters in body
1d
answered In proving “if a set is compact, then it must be closed”, why does the finite subcover behave differently than the infinite open cover?
2d
comment how to calculate $f(D(0,\delta) - \{ 0 \})$ with $f(z)=z\sin(\frac{1}{z})$?
You can do better than that. The neighbourhood around an essential singularity misses at most one value.
2d
comment Showing $\mathbb{H}$ is isomorphic to a subring of $M_2(\mathbb{C})$ as $\mathbb{R}$-algebras
$\Bbb H$ is generated as an $\Bbb R$-algebra by $1, i, j, k$ with identities like $i^2 = -1$ and $ij = k$. Find four matrices in $A$ that fulfill the same relations.
2d
comment What are all different (non-isomorphic) field structures on $\mathbb R \times \mathbb R$
Do you have any restrictions? Because if you just want a field structure on the set $\Bbb R^2$ then any field $F$ of the same cardinality has a (set) bijection $\Bbb R^2$, which gives a field structure.
2d
comment Find number of elements of order p in a group
What's the order of the element $p.q$?
2d
answered Find 3rd point in 3D space based on position of 2 points
2d
comment Finding maximum points by constrain optimization (multivariable calculus)
The Lagrange multiplier method is for finding extreme points along a border. For extreme points within the circle, you just need to solve $\nabla f=0$.
2d
comment Prove By Induction (Fibonacci Sequence)
What are your own thoughts?
2d
comment Do the given vectors span $\mathbb{R}^3$?
Calculate $2v_1 +v_2$.
2d
comment Prove that sequences $\frac{a_n}{b_n} = 0$
$b_n$ doesn't have to converge just because it's bounded. The sequence $|\sin(n)|$ is bounded by $1$, but it doesn't converge to anything.
2d
comment Put B balls in C containers. How many combinations have box(es) with exactly 2 balls?
I think you should go the other way: First, there are $\binom{C}{n}$ ways to choose which $n$ containers are to have exactly $2$ balls. Then use a modified stars and bars to calculate the number of ways to distribute the remaining $B-2n$ balls with none of the $C-n$ containers containing $2$ balls.
2d
comment Find a basis for the subspace of polynomials of degree 3
What are your own thoughts on this problem?
Oct
21
answered Linear map problem
Oct
21
revised Linear map problem
TeX-ed the pictures
Oct
21
revised “Evaluated at” or “at” notation
added 40 characters in body