@JMoravitz I have a presentation at the end of the semester and I have chosen the topic of the Ackermann function... What could I talk about?? One thing could be the proof that the Ackermann function is recursive but not primitive recursive, right?? But what else could we talk about?? Do you know if there is any exemplar of this topic so that I can see how it has to look like??
You could discuss some of the results which use ackermanic functions, such as the previous proofs of the Hales-Jewett theorem or Van der Waerden theorems I suppose,
The proofs before Shelah's (which uses a wowzer function)
well, it depends on what you mean by category theory. it's certainly good to be comfortable with categories and functors, but I don't really know that learning adjoint functor theorems or anything will help.
oh, just in general functors and the like. I feel like I have a grasp on what the elements of $C_n(X)$ and $H_n(X)$ look like and how $\partial$ maps from one level to the next, though I'm still not very comfortable with $H^n(X)$ and $Ext(\cdot)$,
It feels like geometric intuition starts getting buried when going into cohomology,
Though, that may just be my own inexperience talking.
Sure, sure. Comfortability with Ext is more (classic) algebra than category theory, I think. And H^n is, like the many isomorphic flavors of singular homology you learned, just the homology of a new chain complex.
(Not isomorphic to singular homology, of course.) It might be a good idea to push forward past all the universal coefficient theorem algebra, assuming the result, and coming back later. I think that's what I did, or at least I read the proof but only understood what was going on later.
@MaryStar if you search well enough for a pdf you might find an illegit copy online, else it should be available at most university libraries., the text I was referring to is Ramsey Theory (Second Edition) by Ronald L. Graham, Bruce L. Rothschild, and Joel H. Spencer. isbn: 0-471-50046-1
The pages where he describes the ackermann hierarchy start on page 60, and the previous section deals with the Hales-Jewett theorem and related theorems
Suppose that $f(x), \phi(x)$ are continuous functions on $[a,b]$ where $\phi(x)$ has the following property
$$
\int_a^b x^k \phi(x) dx = 0
$$
for all $k\in \mathbb{N}$. Show that $\int_a^b f(x)\phi(x) dx = 0$.
Certainly, $\int_a^b x^k \phi(x) dx = 0$ if $\phi(x)=0$ for all $x$. However, for a no...
Cheat : $Z(G)$ is normal in $G$ for any group $G$. Thus, via simplicity and nonabelianity of $A_n$, $Z(S_n)$ is forced to be trivial. — Balarka Sen5 hours ago
Hi I am trying to solve this question I don't know where to begin but I have an idea so we have
$$Z(G) = \{x \in G \space |\space xy = yx \space\forall y \in G\}$$
We must show that for all $\sigma$ $\in S_n$ such that $\sigma \neq (1)$
Then there exists y $\in S_n$ such that $\sigma * y$ $\...
The "regular" way, as Mike Miller suggests (as per the linked answer), boils down to considering what happens to just 3 letters (elements of the permuted set).
Are any of you good at finding probability distributions and expected values? I have a problem that I've been trying to solve for the past two hours which I seem to be getting close to solving, but can't figure it out
Fun facts: ABC is back from yearlong suspension; Internet sheriff's suspension is over in less than 24 hours. Grab some popcorn or whatever snack you prefer.
Math SE, and SE in general, is overly obsessed with these kinds of minutiae. People argue passionately, and often acrimoniously, over anything reputation-connected.
Some things go from being minutiae to problems on a grand scale; I see mass posting of PSQs in this category, and how someone votes far from being in this category.
Problem statement question. Homework with no input of thought whatsoever. Degrades the quality of the site, and I now only glance at two or three tags because of it.
Yes, people do that, a lot. Sometimes because they are lazy, sometimes because they aren't socially savvy enough to look at and read other questions to model theirs by. Sometimes because they do not know any better.
I see quite a few people down-voting questions for that very reason. The nature of the site makes communication about problems difficult. Whether that leads to more quality or not, is something that I feel ambivalent about.
Thank you. I guess that the author has then simply not stated the domain $\Omega$ in the equality $$J_{\pi}(x_0) = \int g(x_1,\mu_1(x_1))p(dx_1 | x_0,\mu_0(x_0)).$$
@Chris'ssis Well, obviously the past cannot be changed, just do the best for the future, but the future is difficult. You know, I told her this: I have only a 1 per cent chance of getting well.
@Chris'ssis I now live on every day holding on to that 1 per cent chance.
@JasperLoy Live like a winner, like you decide about everything. Maybe you cannot change everything in your life, but you can change the way you look at all these things.
@Chris'ssis I know that many many people in this world have it worse than me, but still I think I was born into the wrong family and the wrong country.
@Chris'ssis But I am grateful that at least right now I still have food and shelter.
@JasperLoy Happiness shouldn't depend on the things we have or not. Happiness is a state of mind and one should necessarily find the reasons to be happy.
@Chris'ssis I think people who have lost too much won't be able to say that.
:20829518 Can you say a bit more? For me, I lost my career, my money, my chance to study in a top university, and my sanity, and my peace of mind. Every moment is filled with anxiety.
@JasperLoy Look, for instance if you never apply for a certain position within a company you will never receive that position. First you need to believe in yourself and then apply for it.
@Chris'ssis One of the problems with my anxiety is that every time I try to solve one part of it, another new part pops up. I need to somehow stop new things from popping up too often.
@Chris'ssis No, my OCD is mostly the checking type, not the cleaning type. And I have no social anxiety. I used to be very shy but I have overcome that with time.
@Chris'ssis Let me give you an example. If you have a fear that someone is trying to kill you, you won't be able to work, just an example. So when the fears get to that level, you cannot function.
@Chris'ssis You've no doubt heard of the Gaussian defined as $f(x)=a\exp\left(\frac{-(x-b)^2}{2c^2}\right)$. Perhaps you know that allowing $c=g(x)=\frac{x-b}{\sqrt{2\log((x-b)^2)}}$ yields $f(x)=\frac{a}{(x-b)^2}$. I'm currently studying functions of the family $g(x)$ as defined above, specifically of the general form $\frac{h(x)}{\sqrt{2\log((h(x))^2)}}$
Nothing interesting has come up thus far, but who knows?
@Chris'ssis By the way, my meeting went well yesterday. My advisor, the person I met with, is going to find someone who can analyze my work in greater detail. I should hear back from them within the next week
@Chris'ssis If everything goes well, I'm hoping that I can be directed towards someone who can help me publish some of my work (assuming it's substantial enough). I just need to stop hiding my work from everybody, it's time to find out if it has any value or importance
@teadawg1337 Personally I wouldn't care of such opinions, but I understand you. I think after doing a lot of math you can realize alone if your work is precious or not. For instance, you might discover integrals and series unknown, and solutions to the unsolved integrals and series. Of course, they should be published.
In the end it doesn't depend only on you, of course, a certain magazine can publish your work or not.
The article to the Au-Yeung series AMM rejected was approved by another magazine and it's going to be published soon.
A rejected paper doesn't mean your work is not precious either. As I told you, you need to be careful about these things.
@Chris'ssis But I seriously don't know any mathematicians to collaborate with yet, that's why I set up the meeting yesterday in the first place! They know who to talk to in the math department, I don't
@Valery: The point is that robjohn computed the integrals over the intervals $[\pi/2,\pi]$, $[\pi, 3\pi/2]$, $[3\pi/2,2\pi]$ by substitution all in terms of the interval $[0,\pi/2]$. Use the rules for $\cos(\alpha\pm\beta)$.
I'm not sure what constitutes as interesting to you but I couldn't prove that if X is compact and f: X -> R is continuous, that there cannot be a sequence {x_n} in X with f(x_n) = n^2
I made a claim that the sequence n^2 is not convergent but I couldn't prove it
It's good to get used to using theorems rather than trying to prove everything from scratch. But you should make sure you can do the exercise I just put (a few lines up). I have to go teach for 2 1/2 hours. You have fun!
Did anybody here learn trigonometry with lookup tables? Back before calculators became common, we had big printed tables of numbers. To find $\sin 11.5^o$, you had to look up lines $11$ and $12$ in a table, and interpolate between the two values. I learned that technique when I was in high school way back in 1980, but that was in the day when calculators were becoming more easily available.
@Balarka It went well, I should get an email from her within the next six days with information to contact someone who can review my work in more detail
Hi I am trying to solve this question I don't know where to begin but I have an idea so we have
$$Z(G) = \{x \in G \space |\space xy = yx \space\forall y \in G\}$$
We must show that for all $\sigma$ $\in S_n$ such that $\sigma \neq (1)$
Then there exists y $\in S_n$ such that $\sigma * y$ $\...
