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A mediocre professor at a top-notch university making mediocre contributions to this top-notch community


Apr
21
comment Prove or disprove isomorphic graphs
It should be classified as "group theory" instead of "graph theory." Even if this problem came from graph theory, your presentation of it leaves no trace of that evolution and you've given it as a pure group theory problem.
Apr
21
answered Prove or disprove isomorphic graphs
Apr
10
answered Classifying Algebraic Structures as Fields
Mar
25
comment Explain to me what these symbols mean.
The confusion often arises from the fact that many writers call $dy/dx$ a "symbol" as if it were atomic, but then later start doing algebra with it. This leads to the question, "well, then what is $dy$ really?"
Mar
10
comment Summation of element of a subset and divition
I think your two added assumptions are reasonable enough to make the original question interesting. But 8 feels quite arbitrary now.
Mar
8
comment Summation of element of a subset and divition
Technically, it is true: the empty set is always a subset of $A$ and 8 divides 0.
Mar
6
revised How to prove $\det(e^A) = e^{\operatorname{tr}(A)}$?
edited title
Mar
1
comment Continued Fraction [1,1,1,…]
You're welcome. This is the cutest (and most elementary) solution I could think of. Good luck.
Feb
26
answered Continued Fraction [1,1,1,…]
Feb
26
comment Continued Fraction [1,1,1,…]
I think this is the argument the OP already has but is worried about. But thanks for the lovely typesetting nonetheless. :)
Feb
16
awarded  Yearling
Feb
14
answered Prove that if $n$ is a composite and $p \gt \sqrt[3]n$, then $n/p$ is a prime.
Jan
19
comment Given $N$, find $ab = N$ with $a$ and $b$ as close as possible
Correct, which is why I was careful to not claim that it was. If you know an efficient (meaning poly-time) factoring algorithm, please send me a private note and we'll write a paper. Or start a company. Or be captured/assassinated before we can do either...
Jan
19
comment Given $N$, find $ab = N$ with $a$ and $b$ as close as possible
Factoring is thought to be hard. Knapsack is NP-Hard, and therefore thought to be hard. If $P = NP$ then all of these are poly-time solvable, but that's unlikely. The best known general factoring algorithms are super-polynomial (on a conventional computer; quantum algorithms are polynomial-time).
Jan
19
answered Given $N$, find $ab = N$ with $a$ and $b$ as close as possible
Dec
30
accepted Derivation of $e$
Dec
30
revised Derivation of $e$
added 75 characters in body
Dec
30
comment Derivation of $e$
@JonasMeyer: I think the way math evolved was to use some informal versions of infinite series without any rigorous notions of limits (see for example the Madhava series, used around 1400CE, en.wikipedia.org/wiki/Madhava_series). In any case, in my question I meant "how can we derive a method to calculate digits of $e$ from the definition of Bernoulli, but without resorting to the Taylor series".
Dec
29
asked Derivation of $e$
Dec
28
revised question about derivative of exponential function
deleted 4 characters in body