5,157 reputation
1731
bio website Workingonit...
location Pasadena, CA
age 20
visits member for 1 year, 10 months
seen 2 hours ago

Undergraduate sophomore at Caltech. PROMYS student and counselor.

Things I am confused about, in the form of media titles:

  • The Trouble with Tensors
  • My Little Functor: Category Theory is Magic

Nov
10
comment Fun results from modular arithmetic
This isn't really a "number fact", but a description of RSA and a proof that it works would be an interesting, motivated result.
Nov
9
comment Can we start studying number theory before abstract algebra?
Good comment, solid advice, PROMYS mentality, 3wise5me, 10/10 would +1 again.
Nov
9
comment Product of numbers that remains invariant repeatedly when adding one to all of them
+1 for the velociraptor
Nov
9
comment Group, QR, QNR, Product of distinct primes
For the first question: what is $1 + 1 + \cdots 1$ ($p$ times). Second question: If a QR times a QNR gave you a QR, what would that imply? QNR times QNR is a bit more interesting...
Nov
6
comment Vector coordinates in terms of magnitude and angles with axes
Yep, it does! What're two ways of writing $\vec{v} \cdot \vec{v}$? (Hint: distribute)
Nov
6
revised Suplementary law and reciprocity
added 9 characters in body; deleted 1 character in body
Nov
6
comment Suplementary law and reciprocity
It's not Euler's Criterion; there's a separate theorem that $2^{(p-1)/2} \equiv (-1)^{(p^2 - 1)/8} \pmod 8$, but I can't remember the name offhand.
Nov
5
comment Suplementary law and reciprocity
Well, if $p = 8k + r$, $\omega^p = \omega^8k \omega^r = \omega^r$, so for part i), we only need to check two cases: plus and minus one.
Nov
5
answered Suplementary law and reciprocity
Nov
5
comment Suplementary law and reciprocity
Which part are you stuck on? There are several ideas coming together in this proof.
Nov
3
comment Possible subspace dimensions of $\mathbb{R}^n$?
Yep, correct on all counts. For any $k$ between $0$ and $n$ inclusive, there are subspaces of dimension $k$. In particular, $\mathbb{R}^0$ is the zero vector, and $\mathbb{R}^n$ is the whole space.
Nov
3
comment Multiply point by scalar in elliptic curve group
If this notation seems unusual, just recall that when our group operation is $\cdot$, we often use exponention by a scalar: $g^n = g \cdot g \cdot \underbrace{\cdots}_{n-3} \cdot g$. So for groups where $+$ is the operation, we use multiplication by a scalar instead.
Nov
3
answered Let n be a three digit number. Prove or give a counter example: 9|n if and only if the digits of n sum to a multiple of 9.
Nov
2
answered Complex numbers in my system of equations
Oct
28
awarded  Popular Question
Oct
25
answered When are cancellations allowed in ring?
Oct
13
comment Difficulty understanding the solutions to $x'' = -\omega^2 x$
The second example really made it click. Thanks so much!
Oct
13
accepted Difficulty understanding the solutions to $x'' = -\omega^2 x$
Oct
13
comment Difficulty understanding the solutions to $x'' = -\omega^2 x$
This definitely explains how a linear solution can arise with particular boundary conditions, and it's satisfying in some ways, but there's still something troubling me: you say the general solution is $A \cos (\omega t) + B \sin (\omega t)$. But that's still not true for $\omega = 0$. I guess I was looking for a derivation that makes it clear why things break there. Perhaps there's a division by $\omega$ or by $x''$ that shows up somewhere.
Oct
13
revised Difficulty understanding the solutions to $x'' = -\omega^2 x$
added 2 characters in body; edited title