Hello!!! When is the expectancy of max{n-q,q-1} , where n is a fixed number and q is in [0,n] , so max{n-q,q-1} is in [n/2,n], equal to $\frac{\frac{n}{2}+n}{2}=\frac{3n}{4}$? @quid @DavidWheeler @robjohn @DanielFischer @ThomasAndrews
@Chris'ssis nope ... I only wrote those answers because I didn't have to think much or invest a lot of time .. I am busy with my studies (got to make sure I pass the courses :P)
@Chris'ssis I'm having a meeting tomorrow morning with my academic advisor (who is also a math professor), during which I will share my notebook filled with all of the math work I've been doing independently for the past several months. I'm both terrified and excited
@Chris'ssis I am ultra nervous with an interview I gave a few days ago .. they asked me 4 simple questions and that was it ,, it was so short that it made my head spin ,, I am confused and not sure why did they ask me just 4 questions while I heard they asked other interviewees more questions :( ..
@teadawg1337 I'm not that secretive. It's not bad to cooperate with some people you may trust. Also here I posted enough of my work, but I trusted the guys here. :-)
@teadawg1337 my profs usually mildy scold me when I don't attend their lectures and my solutions in the final exam has little to do with the materials taught in class .. (independent ideas) .. but I can see they are always secretly pleased :P .. but for the same reason I have never got a full grade in any of the papers :P lol
I love doing independent math work as well, but this is the first time I've truly stepped out of my comfort zone... If the professor doesn't appreciate my work, then I don't know where I'll find future motivation. I'm completely terrified
If I become a prof some day (pun) .. I'll keep students who disregard my methods and work on their own at the problems closer .. (keeping friends close but enemies closer :P lol)
I don't think that there is a possible event, or a person ever that might be able take my self-confidence away and the strong belief in my work. I don't say I'm special, but I prefer to put trust in myself and be honest with me. I'm usually the toughest person with myself. As regards my work, I don't ever expect someone to be nice with me, but to be just honest.
If the meeting goes extremely well, then I would have more motivation to continue my work and I'll probably be more productive doing it. I just worry about the opposite scenario...
@teadawg1337 don't worry before the meeting has happened .. you'll have lots of tangible reasons to worry about after the meeting .. (i.e. the true nature of the problem will be revealed after the meeting ... no point in worrying now)
@teadawg1337 Be very careful about what a bad scenario might be. Mathematics is hard, there is a long way to go for getting good result, there is a price to pay, there might be moments when you think you're alone and maybe it's hard for you to continue, but it's important to never give up. Don't expect miracles. Just do your best.
When is the expectancy of $max \{n-q,q-1\}$ , where $n$ is a fixed number and $q$ is in $[0,n]$ , so $\max\{n-q,q-1 \}$ is in $[\frac{n}{2},n]$, equal to $\frac{\frac{n}{2}+n}{2}=\frac{3n}{4}$?
It can be fixed fairly easily (if they pay attention to responses...) by pointing out that you can't do algebraic manipulation with things that are ill-defined. There are, of course, fancy explanations like Banach limits by which these things make sense; I don't really think one should mention them in these discussions.
@Chris'ssis I'm having a meeting tomorrow morning with my academic advisor (who is also a math professor), during which I will share my notebook filled with all of the math work I've been doing independently for the past several months. I'm both terrified and excited
@Ted She got a double Bachelor's degree in Math and English from the University of Michigan, and her Master's in Mathematics from... Bowling Green State
OK, @teadawg .... Michigan is good, and Bowling Green is ok. But you're doing stuff that's pretty recondite. So don't be upset by a neutral reaction (like you'd get from me :)).
By all means express your enthusiasm and passion for mathematics, @teadawg.
Well, @Ted, I've only got two sources of income: stuff on a W2 and stuff on a 1098T. Even if I'd moved here from a second state it wouldn't have been hard to consolidate the two. I bet yours has a lot more, and hence will be much more tear-inducing...
Yup, life was trivial when I was a grad student, @Mike.
@Gridley: The first thing that comes to mind is a book I've recommended a lot on here for geometry. It's a bit sophisticated, but I'll bet you can handle it. Look at Pedoe's Geometry: A Comprehensive Course. There's also Hartshorne's introductory book.
@TedShifrin Thanks, I'll look into it. The only Geometry book I have used so far is one by the British Olympiad called 'plane Euclidean geometry' which goes up to inversion. Most of my Olympiad experience comes from actually trying (and sometimes failing) past questions, by sophisticated do you mean theory intensive?
Positive integers of the form $3 * 2^n - 1$ are called Thâbit ibn Kurrah numbers.
and if those numbers are prime they are called Thâbit ibn Kurrah primes.
Now if for a fixed positive integer $n$ , $3 * 2^n - 1$ and $3 * 2^n - 5$ are both prime then we have a Thâbit ibn Kurrah cousin prime.
Con...
@r9m when you have more free time work on that, you won't regret any minute spent there. I'm planning to develop another similar integral, slightly modified, but that again is very special for some reasons. :-)
@r9m that article with Au-Yeung series is going to be published soon. Unfortunately, to publish an article takes so incredibly much. I have more stuff to be published but all goes terribly slowly. I need that stuff for my book.
There are two versions of the Knapsack problem, the integer and the fractional one.
The difference between the integer and the fractional version of the Knapsack problem is the following: At the integer version we want to pick each item either fully or we don't pick it. At the fractional versio...
@DanielFischer Could I ask you something about an algorithm? I want to write a $O(n \lg k)$-time algorithm in order to merge k sorted lists into one sorted list, where n is the total number of the elements in all the input lists.
I thought the following:
We put in a min-heap of length k the first elements from the k sorted lists. Then, we heapify and delete the root , which will be the smallest element and put it at a new list, and at this position we put the second element from the list from which the smallest element came from. Then we heapify and continue the same procedure till the li…
I searched him up on Google and saw 'Evil' as a sub search. Naturally, I went straight to the images! It's been a while since I've been on here. How've you been, @r9m?
It's interesting that a Google search for "is used in such generality" (with quotation marks) only turns up one result. Five very common words, and of the entire internet, only one page has those words in that order.
There are two versions of the Knapsack problem, the integer and the fractional one.
The difference between the integer and the fractional version of the Knapsack problem is the following: At the integer version we want to pick each item either fully or we don't pick it. At the fractional versio...
Google NGRAM, which searches books, has it occurring about 1/100th of the times that the word "general" does.
I'd evaluate it as $$\lim \frac{\sin(2x+2y)-2x-2y}{2x+2y} \frac{2x+2y}{\sqrt{x^2+y^2}}$$ The first is going to have limit $0$, so you need to show that $\frac{2x+2y}{\sqrt{x^2+y^2}}$ is bounded.
Oh, no, the first bit is $0$. You can see that by showing $\frac{\sin(h)-h}{h}\to 0$ as $h\to 0$. That is a case for L'Hopital. Or rewriting $\frac{\sin(h)-h}{h} =\frac{\sin(h)}{h}-1\to 0$.
When is the expectancy of $max \{n-q,q-1\}$ , where $n$ is a fixed number and $q$ is in $[0,n]$ , so $\max\{n-q,q-1 \}$ is in $[\frac{n}{2},n]$, equal to $\frac{\frac{n}{2}+n}{2}=\frac{3n}{4}$?
Positive integers of the form $3 * 2^n - 1$ are called Thâbit ibn Kurrah numbers.
and if those numbers are prime they are called Thâbit ibn Kurrah primes.
Now if for a fixed positive integer $n$ , $3 * 2^n - 1$ and $3 * 2^n - 5$ are both prime then we have a Thâbit ibn Kurrah cousin prime.
Con...
