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Freshman Graduate Student in Mathematics


Jul
25
comment Approximate solution for the root of a non-linear function
Are you trying to solve some problem where you are trying to find out all points in time where a certain system satisfies a particular given property and hence you actually want the time closest to it because it is the next time the event happens or something similar? In this case the property satisfied at the time of happening of event is , \begin{equation} e^{t_1} (g\cos(\omega t_1) + b) = e^{t_0} (g\cos(\omega t_0) + b) \end{equation} Because, basically your problems seems to find out all such events given one particular event.
Jul
25
comment Complete undergraduate bundle-pack
You would be lucky to read all of them in next three years.
Jul
25
comment How many decimal places are needed for incremental average calculation?
by $d$ decimal digits, you mean, $d$ significant figures right? It would also probably help if you can specify the the smallest allowed exponent, because then we can implement the formula in some special way to make use of the higher exponent available while still requiring only d significant digits For example, I would like the value of $n$ in the following expression and I guess the $d$ which you mention is as I have described. number = $a.a_{1}a_{2}...a_{d} \ \times \ 10^{-n}$
Jul
25
comment Good problem book on Abstract Algebra
I am now reading the Berkeley Problems in Mathematics and it seems good. Lets see how well can I solve the problems now.
Jul
25
comment Good problem book on Abstract Algebra
Thanks Francis. The thread was useful. Fraleigh's book seems interesting. The solutions are exactly what I want. Since I am self-studying in isolation, it is useful to verify the solutions.
Jul
25
comment Good problem book on Abstract Algebra
I admit they are really good. Still, I believe it is better to look around just to see what problems do other people see around. I am not a math major and my college/university does not have these courses, so I am really scarce on exposure.
Jul
25
comment Good problem book on Abstract Algebra
Hi, thanks for your comments. Herstein does have a fresh perspective of problems and exposition. I read it and already like how he presented the three different proofs of Sylow Theorems including the very basic combinatorial one. Thanks
Jul
25
comment Continuous mappings pull back closed sets to closed sets
I was not taught that way, not using that or equivalent definition, I was taught as I wrote in that comment. While, I did learn the new definition, once in a while the old habit unconsciously takes over. I hope, I get used to the new one fast enough though :-)
Jul
24
comment Continuous mappings pull back closed sets to closed sets
Okay, then it is trivial. You just take the complements and get done. Somehow, now, the question is something else, while the actual difficulty was something else. I guess, I would edit the question and someone can edit his answer and then, I would accept it so that it represents what actually happened?
Jul
24
comment Continuous mappings pull back closed sets to closed sets
I am very sorry, I meant to use $G'$, will correct it if possible.
Jul
24
comment Continuous mappings pull back closed sets to closed sets
I guess, I am not using the definition of $f^{-1}\left(G\right)$ properly. I am using the definition that $f^{-1}\left(G\right)$ exists only when $f$ is onto and if it is not then $f^{-1}\left(G\right)$ is a loose term for $f^{-1}\left(H\right)$ where $H$ is the range. If someone one can make it more clear to me, it would be better.
Jul
24
comment Continuous mappings pull back closed sets to closed sets
So lets say, $Z \in Y$ is the "range" of $f$ so that $f:X \rightarrow Z$ is an onto mapping. Then, if $G$ is closed in $Y$, then $G^{-1}$ is open in $Y$, but we are now considering $H = G^{-1} \bigcap Z$, how do I know that is also open? As far as I know, $H$ is open as a subset of $Z$ (which should be a subspace of $X$) in and only if it is the intersection with $Z$ of an open set which it is, but what about $H$ in $X$?
Jul
24
comment Continuous mappings pull back closed sets to closed sets
Definition of closed is that the a contains all its limit points where $a$ is a limit point of $X$ if for every open sphere $S_{\epsilon}\left(a\right)$ there exists an $x \in X$ such that $x \in S_{\epsilon}\left(a\right)$
Jul
24
comment Continuous mappings pull back closed sets to closed sets
Your second step would be true only for onto mappings, while the textbook says $f$ is an into mapping, or am I missing something?
Jul
24
comment Continuous mappings pull back closed sets to closed sets
But the mapping is an into mapping, how do I know $f^{-1}$ exists for all Y
Jan
17
comment Difficulties with Chapter 2 in Rudin
@Adam: I tried to have a go ;-). Was not very comfortable. Will try again after reading some more.
Jan
12
comment Difficulties with Chapter 2 in Rudin
thanks... expecially for the problems, though I will need some time. But I'll get back to you as soon as I can.
Jan
12
comment Difficulties with Chapter 2 in Rudin
"Because the subject is relatively standard, other texts may provide a different perspective on a topic that provides you with that "ah-ha" moment -- why have one teacher when you can have many? " Yeah, though so, but I was afraid, (see my comment on answer by Samuel Reid about multivariable calculus book.) Hence, I was kind of reluctant. But, I will try now, I have Royden with me. I will get korner if possible and see.
Jan
12
comment Difficulties with Chapter 2 in Rudin
thanks for the clarification, was just browsing through one of the multivariate calculus book, they said the same thing about compactness as described by Samuel Reid, so I had an idea, but kahen's explanation clarifies it. Thank You! Anyway, that is cleared now. But, boy, was I confused when I read that book!!
Jan
12
comment Difficulties with Chapter 2 in Rudin
+1 : Thanks. I am an electrical engineer too. I was good in mathematics in school and have a decently good olympiad experience, and so thought that I may be able to handle Rudin well ;-). I will take your advice of keeping other books as supplement. Thanks for your advice.