2,607 reputation
1514
bio website
location Berkeley, CA
age
visits member for 2 years, 1 month
seen 3 mins ago

1m
comment Inverse Trigonometry proof
$\pi/4, 3\pi/4, \pi, 5\pi/4, 7\pi/4$
23h
comment can $u^8-u^4-u^2+u-35=0$ be simplified?
Using Galois theory, one finds that this equation can not be solved by radicals.
Jul
3
comment Improper Rotations in Even Dimensions
@jdizzle Since the rotations $SO(n)$ have index 2 in the group $O(n)$ then any improper is the block matrix identified above multiplied by any rotation.
Jul
2
comment Improper Rotations in Even Dimensions
Use a block matrix $\begin{pmatrix}0 & I_n\\I_n&0\end{pmatrix}$.
Jun
21
comment Find the last two digits of $9^{{9}^{9}}$
From your calculation you want the exponent $\mod 40$. So you want $9^9 \mod 40$, but as you show $9^2=1 \mod 40$ so $9^9=9 \mod 40$ and then $9^{9^9}=9^9 \mod 100$
Jun
20
comment Show that a sequence of fields exists
Use that a finite p-group has a normal subgroup of index p.
Jun
7
comment What does $Z_2(S)$ mean where $S$ is a group.
Maybe it is the second center, Z(G/Z).
Jun
7
comment Compute $\int_0^1 \frac{\arcsin(x)}{x}dx$
Maple gives an answer of $\frac{\pi}{2} \ln (2)$.
May
1
comment Rank of $(G/H)/(G/H)_t$ where $G$ is finitely generated abelian and $H$ is a subgroup.
Try using the elementary divisor structure theory.
Feb
9
comment $x^5-x^2+1$ is separable over all fields
Yes, the gcd is x+2 and x=-2 is a root mod 7.
Dec
27
comment Consider the sequence 01110100…
Look for DeBruijn sequences or Huffman code.
Dec
23
comment Can the n-string sphere braid group embed in to the (n+1)-string sphere braid group?
Oh, I see, it is not the usual braid group, but on the sphere.
Dec
23
comment Can the n-string sphere braid group embed in to the (n+1)-string sphere braid group?
What if you add n+1 strand so that there is no interaction with the n-braid?
Dec
21
comment Interesting GRE problem
There is a root between 74 and 75.
Dec
19
comment Axiomatic characterization of the rational numbers
Smallest field containing the natural numbers.
Dec
18
comment Find the rotation axis and angle of a matrix
As a start, find the eigenvector with eigenvalue 1.
Dec
16
comment Peculiar presentation of Symmetric group of degree 10
The presentation seems garbled and the obvious fix makes it the trivial group.
Dec
16
comment Subgroups in $S_4$ are normal or not
How does the cycle structure of an element $x$ relate to the cycle structure of $axa^{-1}$?
Dec
12
comment Help in establishing the Cayley table of $\text{Gal}(L/\mathbb{Q})$
In this case, the Galois group is the direct product of the Galois groups of the factors. It is cyclic of order 6.
Dec
10
comment Determining all intermediate fields of $X^3-3$
Subfields correspond to subgroups of the Galois group $S_3$. So you should be looking for 3 quadratic subfields, and one cubic subfield.