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I am a recent graduate in applied mathematics at UCLA and currently trying to break into the quantitative investment/trading industry while also continuing to pursue advanced graduate-level mathematics as both a hobby and career necessity.


4h
comment Proving that if $f$ is Riemann integrable and $1/f$ is bounded then $1/f$ is Riemann integrable
If you wanted to make it all workout to $\epsilon$ at the end, then just refine $P$ (if necessary) so that $|U(P,f)-L(P,f)|<(m_{f})^{2}\epsilon.$ But understand that this is not necessaty, since in general a quantity bounded by $C\epsilon$ for a constant that does not depend on $\epsilon$ is as good as being bounded by $\epsilon$ since both upper bounds can be made arbitrary small by sending $\epsilon\to0$.
4h
comment Proving that if $f$ is Riemann integrable and $1/f$ is bounded then $1/f$ is Riemann integrable
No - consider the case where $(m_{f})^{-2}<1$.
4h
comment Proving that if $f$ is Riemann integrable and $1/f$ is bounded then $1/f$ is Riemann integrable
Not sure what you mean.
4h
answered Proving that if $f$ is Riemann integrable and $1/f$ is bounded then $1/f$ is Riemann integrable
Oct
21
answered Measure of the graph of a function such that the graph does not have measure zero.
Oct
21
answered derivative of $y=\sqrt{10^{5-x}}=u^{1/2}$
Oct
21
revised Analytic skills in applied math
added 606 characters in body
Oct
21
answered Analytic skills in applied math
Oct
14
comment 2. Differential equation with initial condition
$\int(y-1)^{-1}\;dy\neq\ln(y-1)$ without further specifying $y$. Note that with $y=-3$ we get $\ln(-4)$ which is undefined.
Oct
14
answered 2. Differential equation with initial condition
Oct
10
comment When computing the CDF from a PDF, why is the integral bound a different variable? $F(x) =\int_{-\infty}^x f(t)\,dt$
The properties of a function remain the same whether you use $t,x,y,\alpha,u,etc.$ as the name for the dependent variable. It is strictly a matter of choice/convenience and to keep things clear for the exposition. $t$ in this case has nothing to do with time.
Oct
10
comment Evaluating $ \sum\frac{1}{1+n^2+n^4} $
What do you mean evaluate? This sum has no easily attainable closed form, but it evidently converges by comparing to $a_{n}=n^{-2}.$ To get a sense of the challenges you face in evaluating this sum analytically, see math.stackexchange.com/questions/8337/… for the simpler case $\sum n^{-2}.$
Oct
10
answered When computing the CDF from a PDF, why is the integral bound a different variable? $F(x) =\int_{-\infty}^x f(t)\,dt$
Oct
9
answered Discount rates vs. Interest rate problem.
Oct
8
revised Given $\displaystyle f(x,y) = \frac{\sin (xy)}{x}$, $x \neq 0$, make $f(0,y)$ continuous.
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Oct
8
answered Given $\displaystyle f(x,y) = \frac{\sin (xy)}{x}$, $x \neq 0$, make $f(0,y)$ continuous.
Oct
8
revised limit of solution of a autonomous differential equation at infinitive is a stationary point
added 26 characters in body
Oct
8
answered limit of solution of a autonomous differential equation at infinitive is a stationary point
Sep
22
answered When to use $\mathbf{P}$ , and when to use $\mathbb{P}$ as the symbol for probability?
Aug
30
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