340 reputation
114
bio website
location United States
age 32
visits member for 1 year, 10 months
seen Jul 4 at 8:48

I'm earning my PhD in mathematics and have been employed as an analyst since graduating college in 2003.


May
1
comment Union of the conjugates of a proper subgroup
How are there at most $n$ distinct conjugates? Every time I try to see this, I either come up with a maximum of $k$ or $kn$ distinct conjugates, depending on how I look at it. It's clear that there are $n$ left or right cosets of $H$, but it's not clear to me that this must be a maximum for the number of distinct conjugates.
Apr
28
comment Permutation cycles in Jacobson's Basic Algebra I.
@rschwieb Ah. I have to go $(1\to n_1, n_1 \to n_k, n_k \to \dots)$ not $(1\to n_1, 2 \to n_2, 3 \to n_3 \dots)$. I find this text so unclear as to be almost unreadable. I've been getting through this class by supplementing my reading with other texts.
Apr
28
comment Permutation cycles in Jacobson's Basic Algebra I.
@MichaelHardy How do you get $(13452)$? Following the mapping from top to bottom: $$\begin{pmatrix} 1 & 2 & 3 & 4 & 5 \\ 2 & 1 & 3 & 4 & 5 \\ 3 & 2 & 4 & 5 & 1 \\ 3 & 1 & 4 & 5 & 2 \end{pmatrix}$$
Apr
24
comment 5 digit number $a6a41$ divisible by 9
@user108104 As squeamish points out, the first step is subtracting 9 from both sides. $0 - 9 = 0$ in mod 9 arithmetic. The second step can be seen as dividing both sides by zero. $0 / 2 = 0$, remains true in any arithmetic.
Apr
24
comment Is the determinant differentiable?
All of the answers so far treat the determinant as a polynomial in the matrix entries $(a_{ij})$. However, just as we can take the derivative of $\vec{y}=f(\vec{x})$ as the vector $\vec{x}$ varies, it would be nice to see someone answer the question from the perspective of $$\frac{d}{dA} det(A).$$
Apr
24
comment Algebra problem stumping me
I find it funny that my first (wrong) coded answer (incorrect assumption) received an upvote, but this correct coded answer hasn't yet. (Of course the manual solution is the best because it leads to understanding.)
Apr
23
comment Algebra problem stumping me
I'm new enough to Mathematica that I don't follow your code. Since you have 2 solutions, I'm guessing you didn't use $A-H>F$? Your second solution matches the others here; your first satisfies the sum equations, but not that inequality.
Apr
22
comment Algebra problem stumping me
@user144808 Just for fun I tried doing it with only symbols, no words, and remain clear. ;-) I couldn't find an obvious and universal contradiction symbol.
Apr
22
comment prependicular Vs prependicular bisector
Sorry, glanced up at the wrong name while writing my answer. Fixed.
Apr
22
comment Algebra problem stumping me
$y$ is $7$, not $5$. But you did beat me to the other letters by a bit.
Apr
22
comment Algebra problem stumping me
@DanielV See 2 comments up, 2 minutes before your comment. "Let me check $total=RHS$." :)
Apr
22
comment Algebra problem stumping me
@user144808 I meant missing from my formula, not your question. ;-)
Apr
22
comment Algebra problem stumping me
Yep, None of those 31 satisfy uniqueness. (For $total=45$. Let me check $total=RHS$.)
Apr
22
comment Algebra problem stumping me
@DanielV The output is basically just a text string (display wise). There may be functions that would do that, but I'm still new to Mathematica. The fastest way for me to try that would be to dump it into Excel. (But the long time makes me think none of those 31 satisfy the uniqueness condition.)
Apr
22
comment Algebra problem stumping me
@user144808 Hmm, with the 36 inequalities enforcing uniqueness it's taking too long to run, to expect a good solution. (For either interpretation of $total$.)
Apr
22
comment Algebra problem stumping me
@Keith The sum of the RHS view gives 45 possibilities (before enforcing uniqueness). Give me a bit to encode the uniqueness.
Apr
22
comment Algebra problem stumping me
Ah, yes! A missing assumption.
Apr
22
comment Algebra problem stumping me
@MattAllegro No, $E\in \{1,2\}$. I'll paste what I've got as an answer.
Apr
22
comment Algebra problem stumping me
In all 31 cases, $C=1$. $E$ is either a $1$ or $2$ (with approximately equal likelihood).
Apr
22
comment Algebra problem stumping me
In only 1 of those 31 cases, is the first $?$ a $2$. In the other 30 cases, it's a $1$.