345 reputation
115
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location United States
age 33
visits member for 2 years, 2 months
seen yesterday

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


Sep
24
awarded  Autobiographer
Jul
2
awarded  Curious
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
accepted Permutation cycles in Jacobson's Basic Algebra I.
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
28
asked Permutation cycles in Jacobson's Basic Algebra I.
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
revised When does something become a “mathematical object”?
added 983 characters in body
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
24
awarded  Yearling
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
revised prependicular Vs prependicular bisector
The [tag:geometry] tag should not have been removed.
Apr
22
suggested suggested edit on prependicular Vs prependicular bisector
Apr
22
comment prependicular Vs prependicular bisector
Sorry, glanced up at the wrong name while writing my answer. Fixed.
Apr
22
answered prependicular Vs prependicular bisector
Apr
22
answered When does something become a “mathematical object”?
Apr
22
answered Algebra problem stumping me