1,874 reputation
413
bio website math.uga.edu/~amaurer
location United States
age 22
visits member for 2 years
seen Nov 24 at 5:34

Graduate student in mathematics. Interested in many things, particularly algebraic geometry.


Nov
28
awarded  Yearling
Nov
10
comment Show a curve has no factor of degree 1 or 2
Hint: Polynomial rings over fields are PIDs, and we like that. So instead of looking at this as a problem in $k[x,y]$ (whatever $k$ is...), try looking at this as a problem in $k(x)[y]$.
Oct
8
comment How to combine OR linear inequality with absolute value
My example wasn't intended to be the exact same as your question. Try out some examples, and see if all the inequalities you can think of can be written in that form.
Oct
8
comment Algebraic topology in high school?
Ah, the book is by Hilbert, and available here: amazon.com/Geometry-Imagination-CHEL-Chelsea-Publishing/dp/… and notes by Rob Kusner are available here: gang.umass.edu/~kusner/class/462hw
Oct
8
comment Algebraic topology in high school?
This seems really interesting to do. The only thing is that I'm not sure how one would present algebraic objects to high school students and have time to do interesting topology. I've heard of a book (haven't read it) called "Geometry and the Imagination". A professor at my undergrad taught a course with the same title, so I'll look for any notes on that and let you know if I find any.
Oct
8
comment How to combine OR linear inequality with absolute value
Try doing some examples -- which $x$ satisfy $|x-2| < 1$?
Oct
8
comment How to combine OR linear inequality with absolute value
The way I think about this is that $x$ is at most ___ away from the midpoint of $-10$ and $15$ (remember that absolute value tells distance).
Oct
7
comment Suppose that the sequence ${a_n}$ is monotone. Prove that it converges iff ${a_n^2}$ converges.
@frank000 duly noted, thanks
Sep
30
awarded  Explainer
Sep
28
answered How do you define Dimensions in general?
Sep
26
comment What does $p_j(x)$ mean?
@andre Yes, oops
Sep
25
comment What does $p_j(x)$ mean?
So essentially the author is choosing a specific basis for the vector space of all polynomials in $M$ variables of degree less than or equal to $D$.
Sep
25
comment What does $p_j(x)$ mean?
The binomial symbol is used in $\LaTeX$ by writing \binom{n}{k}.
Sep
25
comment What does $p_j(x)$ mean?
It looks like $\binom{M+D}{M}$ is the number of monomials of degree less than or equal to $D$ in $M$ variables. So $J$ would then be an enumeration of them. EDIT: I misunderstood what your question was asking. That symbol is the binomial symbol, and you can find information (now that you know its name) on Wikipedia.
Sep
25
comment Exponential Functions Proof
To get $5^{x+h}$ replace your parentheses with curly braces {}.
Sep
25
revised For any two Ideals $A$ and $B$,$A+B=\langle A \cup B \rangle$
deleted 5 characters in body
Sep
24
comment For any two Ideals $A$ and $B$,$A+B=\langle A \cup B \rangle$
@spectraa An "additive subgroup" is just a subset $S \subseteq X$ that is closed under addition -- $a + b \in S$ whenever $a$ and $b$ are both elements of $S$. As Nimda mentioned, any subring must be an additive subgroup, simply by the definition of ring. So the statement I mentioned can be read as "Whenever $S$ is a subset of $X$ that contains $A$ and $B$, and is closed under addition (in particular $S$ could be a subring of $X$ containing $A$ and $B$), $S$ must contain the ideal $A + B$."
Sep
23
answered For any two Ideals $A$ and $B$,$A+B=\langle A \cup B \rangle$
Sep
23
comment How to construct a smooth curve whose range is dense in $\mathbb R^2$?
My first thought is to use the topologist's sine curve in some way.
Sep
23
answered Summable enumerations of $\Bbb Q$