4,831 reputation
924
bio website math.uwaterloo.ca/~j2rosen
location Waterloo, Ontario
age 29
visits member for 2 years, 3 months
seen 1 hour ago

I am a postdoctoral fellow in the department of Pure Mathematics at the University of Waterloo


20h
answered The ring $R$ is a field iff there exist some kind of $R$-module
1d
comment Find the probability that a matrix is diagonalizable
In the computation for part (b), a diagonalizable matrix can have 0 as an eigenvalue, so the number of central diagonal matrices is $p$, and the number of diagonal increasing non-central matrices is $p(p-1)/2$.
1d
revised Find the probability that a matrix is diagonalizable
deleted 50 characters in body
1d
answered Find the probability that a matrix is diagonalizable
Jul
22
comment Is every affine scheme the complement of the closed point $x$ of the spectrum of a local ring $A$?
For $R$ algebraic over its prime field, it's not true in general that every subring of $R$ is a field (e.g. $R=\mathbb{Q}$, $A=\mathbb{Z}_{(p)}$). The argument still works for $R=\mathbb{F}_p$, though.
Jul
22
comment Is every affine scheme the complement of the closed point $x$ of the spectrum of a local ring $A$?
(1) A finite field cannot be the ring of fractions of a DVR. (2) There's a classification of those topological spaces homeomorphic to the spectrum of a ring, and I think it implies there always exists local $A$ with Spec$(A)\backslash\{m\}$ homeomorphic to Spec$(R)$ (en.wikipedia.org/wiki/Spectral_space)
Jul
2
awarded  Curious
May
14
reviewed Approve suggested edit on The determinant of a special matrix
May
9
reviewed Approve suggested edit on Density on the square, expected value
May
3
reviewed Reject suggested edit on Prove that $\operatorname{rank}(A) + \operatorname{rank}(B) \ge \operatorname{rank}(A + B)$
Apr
23
revised Challenge: Demonstrate a Contradiction in Leibniz' differential notation
deleted 74 characters in body
Apr
23
reviewed Approve suggested edit on What is wrong with this exercise in do Carmo's Differential Geometry?
Apr
22
answered Challenge: Demonstrate a Contradiction in Leibniz' differential notation
Apr
21
reviewed Approve suggested edit on Probability of getting a working product from three groups of products…
Apr
20
reviewed Approve suggested edit on $\sum\limits_{n=1}^\infty n(\frac{1}{2})^{n}$
Apr
9
reviewed Approve suggested edit on Confusion related to k neighborly polytope
Apr
6
reviewed Approve suggested edit on Parabolic Branch Cut
Apr
6
reviewed Approve suggested edit on contour integration of a function with two branch points .
Apr
5
awarded  Yearling
Apr
2
reviewed Approve suggested edit on Bounding $\sum_{n=n_1}^\infty x^n (n+1)^2$