220 reputation
16
bio website education.msu.edu/search/…
location Ann Arbor, MI
age
visits member for 1 year, 10 months
seen Aug 5 at 1:30

I am an Assistant Professor at Michigan State University, with a joint appointment in the Dept. of Teacher Education (in the College of Education) and the Program in Mathematics Education (in the College of Natural Sciences). My Ph.D (2009) is from the University of Michigan, and was a joint degree in Mathematics and Education awarded by the Mathematics Department and the School of Education.

My dissertation focused on the capacity of the secondary Geometry course to faithfully represent authentic mathematical values and practices, and the extent to which school mathematics can cultivate a mathematical sensibility in students. Current research interests include an analysis of the secondary "Algebra 2" course, and an investigation into the mathematics education practices of home-educated students.


Mar
31
awarded  Quorum
Mar
22
awarded  Yearling
Mar
21
awarded  Nice Question
Mar
21
awarded  Supporter
Mar
21
accepted Rings for which no polynomial induces the zero function
Mar
21
comment Rings for which no polynomial induces the zero function
Let $R$ be the ring $\mathbb{Z}/p \mathbb{Z}$ with infinitely many elements $u_i$ adjoined, each satisfying the relation $u_i^p -u_i = 0$. Then the polynomial $p=x^p-x$ satisfies $\hat{p}=0$.
Mar
21
comment Rings for which no polynomial induces the zero function
P Vanchinathan, yes, that was one of my examples. More precisely if $R$ is a ring that has my desired property, than $R \times R$ also has the desired property, even though it is not a domain. So that shows that "infinite domain" is not necessary for this property.
Mar
21
awarded  Editor
Mar
21
revised Rings for which no polynomial induces the zero function
added 10 characters in body
Mar
21
asked Rings for which no polynomial induces the zero function
Oct
21
comment Lost soul: loneliness in pursing math. Advice needed.
When I was in my 1st year of grad school I got married; in my 3rd year we had our first child. I missed a lot of classes, and a lot of deadlines, and was worried that he consequences might be dire. But my professors all -- all, without exception -- told me not to worry: "Some things are more important than math", said one, and that advice has kept me (reasonably) sane and balanced. I hope it helps you too.
Oct
15
comment A weird function related to the denominators of rational squares
Only in the most elementary case: \sigma (a) = 2 iff $a=n^2 + n$ for some $n$.
Oct
12
awarded  Scholar
Oct
12
comment A weird function related to the denominators of rational squares
Thanks -- those citations will be very helpful, I think. I am a total newbie when it comes to the OEIS; is there a way to search for papers / pages that discuss or reference a specific OEIS sequence?
Oct
12
accepted A weird function related to the denominators of rational squares
Oct
12
comment A weird function related to the denominators of rational squares
Plus I've got a list of 20 special cases that have the form: If $a=n^2 + $ [something], then $\sigma (a) = $ [some specific linear polynomial in n with simple coefficiets]. But I can't find a way to tie those 20 special cases together into a general statement.
Oct
12
comment A weird function related to the denominators of rational squares
(4) The lower bound is harder to state, but: If $a$ is not a perfect square, write $a=n^2 + b$ and $a=m^2 - c$ where $n^2$ and $m^2$ are the closest squares below and above $a$, respectively. Then: $\sigma (a) \geq \underline{ max \left \{ \frac{n+\sqrt{a+1}}{b+1}, \frac{m+\sqrt{a}}{c} \right \} } + 1$.
Oct
12
comment A weird function related to the denominators of rational squares
Maybe I should give some more detail on what I have already found so that people don't waste their time re-inventing my wheel. (1) For all $a$, $\sigma (a) \leq \overline{\frac{8a\sqrt{a}}{4a-1}}$, where the overbar denotes the ceiling function. (2) When $a=n^2$ the upper bound above is sharp, and simplified to $\sigma (n^2) = 2n+1$. (3) When $a=n^2 + n$ we have $\sigma(n^2 + n) = 2$.
Oct
12
awarded  Student
Oct
12
asked A weird function related to the denominators of rational squares