ok got all my alignments done.. now to get my proofreading in check and then put the diagrams and models in... well I already drawn and got them... so it's mostly proofreadng and citing stuff
nguh anyone know how to increase the font size on a report
I got \documentclass[a4paper]{article}
\usepackage[english]{babel} \usepackage[utf8x]{inputenc} \usepackage{amsmath} \usepackage{graphicx} \usepackage[colorinlistoftodos]{todonotes} how do I increase the font.. I want to increase it to 14 point
I know I have made very small text, I probably had a package to help me. I was printing off a document a couple times after I revised it, so decided to save on paper with very small text
@usukidoll It depends but normally you have a separate file with all your references and load it ( I think there is a way to do it all in one file though). These are things that you should really look up, since it is all easily searchable
So all matrices in $GL_2(\Bbb F_p)$ are similar to the three jordan forms $\begin{bmatrix} a&0\\0&a\end{bmatrix}$,$\begin{bmatrix}a&1\\0&a\end{bmatrix}$,$\begin{bmatrix}a&0\\0&b\end{bmatrix}$$
I want to find how many elements there are in each of these conjugacy classes
Hey @pjs36! Excellent, glad to hear it. It's dense stuff, so it takes time (at least for me, haha). Let me know if you want to talk about any parts of it!
Nothing might be wrong at all - not everyone likes it. Definitely happy to talk through parts of it, if that interests you. I'm also writing some companion notes which are a little less brief than A&M's style, which I'm happy to share.
Ah, I see, that is interesting! Well, I studied quite a bit of group theory, but my profs were all finite group theorists, and I don't remember spending much time on rings; I just never digested a lot of the material
So perhaps I don't have enough examples of rings to play with, or perhaps it's just excessively dry in the beginning
Lol, Balarka was none too happy about that either. It's a bit dry, to be sure, and that doesn't seem to change throughout. A&M aren't chatty, and this is personally to my taste, but others may well disagree.
A solid grounding in basic ring theory will help a lot here, both for examples and appreciating the results.
Wow finite group theorst? I am sort of ignorant of finite group theory outside of the classic, classification of finite simple, representation of finite group, and computational stuff. What sort of things do they research nowadays? @pjs36
@DiscipleofBarney One was working on representations of the symmetric group over finite fields; he was interested in a lot of combinatorial group theory as well (I can't remember, generalizing some kind of Moon and Moser result; I can't quite remember what it was about)
The other was a $p$-group man; I know he had one of his (master's) students working on something to do with wreath products, and another working on bounding degrees of characters, in some context
They both got their PhD's under Isaacs, whose advisor was Schur, and whose advisors were Frobenius and Fuchs, so the group theory was strong with them, to say the least!
The textbook says that given an open covering $A$ of $X$, there is some element $U$ of $A$ containing $0$. The set $U$ contains all but finitely many of the points $\frac1n$
Then we can take every point of $X$ not in $A$ and stuff it into an element of $A$ that contains it. This collection $A$ along with the element $U$ is a finite subcollection that covers $X$, done
So they put infinitely many points without specifying into a set and then took finite elements to finish it up
I don't see how this proof even used any other fact that $0$ being in $X$ and seems like it could be applied to pretty much anything, which makes no sense to me
Munkres page 164 if you have it handy, or I can screenshot
It uses that any open set around $0$ will contain all but finitely many points (which I will assume you understand), then you only need finitely many more open sets to cover the finite number of points left over (and you know you can pick those since we are talking about an open cover)
If you tried this on $\Bbb R$ or $[0,1)$ we would have a different story, since neither of those are compact.
@MikeMiller right, i was being stupid. $Y \stackrel{g}{\to} \bar{X}$ be the induced isomorphism of $X \otimes Y \stackrel{f}{\to} k$. Then the following diagram is commutative :
$$X \otimes Y \to X \otimes \bar{X} \\ \!\!\!\! \downarrow \;\;\;\;\;\;\;\;\;\;\;\;\,\,\, \downarrow \\ \!\!\!\! k \;\;\; \longrightarrow \;\;\; k$$
The top map is $\text{id}_X \otimes g$, the bottom map is $\text{id}_k$. The side maps are $f$ and $eval$ respectively.
Since the top and bottom maps are commutative, $f$ is necessarily equivalent to $eval$.
@robjohn The comment by Ron was a bit annoying, he said "No need to reference Barnes G-functions. These are integers after all.", but at the same times he employed a lot of stuff to get the answer.
@robjohn I think you're somewhat like me in terms of solving problems, and you simply don't attend the things you don't like much. :-) I also refer to some of my problems that you probably don't like that much.
@robjohn I'm very confident you can do a lot of stuff, much more than you say you can do. Maybe you don't like things that become ugly at some points. :-)
@Chris'ssis I also deal with ones I can handle easier first, then save the harder ones for later. However, sometimes I start on one of the harder ones and work for a long time one it.
@Chris'ssis I definitely like things that have simpler proofs, but I have tackled some pretty ugly things.
@robjohn However, no matter how things go, every such work is precious, maybe you meet some new results, interesting approaches, see connections with other problems met in the past.
@WillHunting robjohn is the mind that impressed me the most on this site. When he wants, he can come up with amazing answers such as those you never think of.
I think we can use a remarkable limit $$\lim_{n\to\infty} \frac{\displaystyle \left(\prod_{k=1}^{n}\binom{n}{k}\right)^{1/n}}{e^{n/2} n^{-1/2}}=\frac{e}{\sqrt{2\pi}}$$
I'm doing some programming-related stuff, and I need to test some code for different numbers, but I want different numbers to show up at different frequencies. I'm not sure exactly what I want, though. So I want to play with it a bit.
@WillHunting I don't know. Maybe we're not talking about the same thing. Some of those things are pretty complicated, but in general they're fairly straight-forward.
I really can't believe how quickly I forgot probability. I got a great grade and everything. Used to like it. It's like all the rest of the courses pushed it out of my head. I guess it's as good a time as any to remember.
Well. In the internet there are a lot of relics, so some videos require ancient things like quicktime or windows media player streaming. But in general, that's true. You don't need flash for most up to date things.
Well, in the new version of HTML (HTML5, you probably heard of it) the people who make the internet standards incorporated video playback into it. And now all the browsers are implementing that standard themselves, instead of using flash.
So up to date things use the new HTML5 commands. Older things still require flash because they haven't been updated. Still older things use different streaming technologies.
@WillHunting Google Maps discontinued their "Classic Maps" compatibility mode, so now everyone is forced to use the newer version. This may have had an effect on our chat map.
@MatsGranvik The floor always confuses me; vertigo.
@Mew I see you and you see me. I know it's my destiny. I have to catch you and squeeze you into a ball no larger than my fist. Then, I'm going to torture you until you become a rabid fighting monster who can destroy every challenger. Oh, you're my best friend in a world we must destroy.
