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Jul
4
comment GRE Math subject test prep
If I recall the Princeton Review one is okay. I think Agarwal & Elsner has some mistakes but is still fairly useful. I could be mixing these up, though, as it has been a while since I've looked at them and the newer editions may be better. Also, when I registered for the GRE they sent me a CD with at least one practice exam on it. Not sure if they still do that.
Jul
3
comment open problems regarding functions
It would help if you were a lot more specific about what kind of functions you are interested in.
Jul
3
comment open problems regarding functions
This is a little bit vague, since any problem can be phrased in terms of a function. e.g., is there a function $f: \mathbb{R} \rightarrow \mathbb{R}$ so that $\lim_{x \rightarrow \infty} f(x) = \infty$ and so that $f(x)$ is less than the size of the set $\{ n < x: n \text{ is a twin prime}\}$? This is equivalent to the twin prime conjecture...
Jul
3
comment Is there a name for the function of a semicircle?
I don't think there's a special name for this. It's fine to just label it $S(x)$ or whatever.
Jul
2
comment values of sin of multiples of 10?
I would also guess that your professor means $\sin(1\pi), \sin(10\pi)$, etc. In my experience, it's very common for students to confuse the $\pi$ in expressions such as $\sin (3 \pi)$ for a unit like in,cm etc. rather than the number $\pi = 3.14159...$
Jun
29
comment Any shortcut to calculate factorial of a number (Without calculator or n to 1)?
You could calculate $n! = \exp(\log(1) + \log(2) + \ldots + \log(n))$ using a log table.
Jun
26
comment Proof: Derivative of $(-1)^{x}$
The expression $(-1)^x$ is not defined in general. You can interpret it to mean $e^{ \pi x i}$, and the formula follows from that. But you could just as easily assume that it means $e^{3 \pi x i}$ which has the derivative $3 \pi ie^{3 \pi x i}$.
Jun
25
comment Linear extension of a set
I think what Miriam wants is to see all of the ordered pairs of the relation given by the linear extension written out explicitly.
Jun
25
comment What does it actually mean by a “Characteristic Polynomial”?
@Ian: The characteristic polynomial and its roots go hand in hand, so I don't see how one could be more significant than the other. In any case, the coefficients of the characteristic polynomial can be useful as well, especially for the Laplacian of a graph where they give the number of spanning forests (although this is too far afield to be an answer to the OP.)
Jun
25
comment What does it actually mean by a “Characteristic Polynomial”?
The characteristic polynomial of $M$ is $p(x) = \det(Ix - M)$. It's only defined for matrices, although there are numerous other unrelated things also called the "characteristic polynomial" in different contexts.
Jun
24
comment Show that $f$ is continuous mathematically.
@AjmalW, you could also just do the two cases separately as in the text. As I said, either way is okay.
Jun
23
comment Show that $f$ is continuous mathematically.
Looks good to me. Defining $\delta$ first for both cases is not really necessary but it is fine either way.
Jun
13
comment Finding conjugacy classes
$(12) = (21)$. They're both the permutation that switches $1$ and $2$.
Jun
5
comment What Constitutes a Pattern
You may be interested in definable numbers which include the computable numbers (the ones generated by Turing machines) and a bit more.
Jun
5
comment What Constitutes a Pattern
Nice question! It reminds me of the old joke: Theorem: Every number is interesting. Proof: Let $S$ be the set of interesting numbers. Then $S$ has a minimum element $n$. But then $n$ has a the very interesting property that it is the least noninteresting number, a contradiction.
Jun
4
comment Finding $\lim_{n\rightarrow \infty }\left(1-\frac{1}{n^2}\right)^n$
Intuitively: We know $\lim_{n\rightarrow \infty }\left(1-\frac{1}{n}\right)^n = e.$ But if you have $n^2$ on the inside without an $n^2$ in the exponent, the inside part converges faster to $1$ and the inside part "wins".
Jun
4
revised What is the technical difference between a formal and informal power series?
deleted 2 characters in body
Jun
4
answered What is the technical difference between a formal and informal power series?
Jun
3
comment Work of Ted Kaczynski
I wonder if complex analysts are somehow predisposed to murder. See André Bloch
Jun
1
comment Limit involving tetration
For any particular $C$?