New Posts

I got started later than I should have when it came to writing up stochastics posts, so I’m trying to get started early with new posts for this semester.  Most of my posts will be about algebra, starting from the beginning with basic definitions (definitions and examples of semigroups, monoids, and groups will be posted shortly after this post), as my next prelim will be in algebra.  Most of these posts will come from my in-class notes and the Dummit & Foote book.  I may post some on topology and partial differential equations too, as these are the other classes I’m taking this semester.

Analysis Prelim Passed!

The analysis prelim was one week ago today, and I just received an email a little bit ago saying that I passed it, so I’m happy.  Classes don’t start until August 22 (or so), so this blog will probably not have much of any posts until then, as I plan on just kind of taking it easy for the next couple of weeks.

I’ll plan start studying for stochastics much earlier this time around though, and so stochastics posts will probably start sometime around the start of the semester.  See you then.

Question about LaTeX on WordPress

Hola.  Does anyone know if there’s a way to do something like eqnarray inside of WordPress’ LaTeX?  If not, what’s the preferred method of listing a long string of equalities?

Basic Analysis Page

I’ve added a page on “Basic Analysis” that lists some definitions and basic theorems that you should be familiar with if you’re going to read the posts here.  I’ll probably add to this if I want to post something that assumes some other “basic” definition or theorem I’ve not mentioned before, but will be sure to put up a post saying that that page has been updated.

A Note on Notation

For the moment I’m just going to be writing straight up LaTeX in my posts because I don’t want to take the time to generate images of everything.  (If you know of an easy solution though, let me know!)  There are a few custom aliases I use for things that I write over and over again, so here they are.

\def\R{\mathbb{R}}      % The reals
\def\N{\mathbb{N}}      % The naturals
\def\Q{\mathbb{Q}}      % The rationals
\def\C{\mathbb{C}}      % The complex plane
\def\M{\mathcal{M}}     % Measurable sets
\def\B{\mathcal{B}}     % Borel sets
\def\O{\mathcal{O}}     % Open sets
\def\F{\mathcal{F}}     % A sigma algebra F
\def\Fx{\mathcal{F}_X}  % Sigma algebra F generated by random var. X
\def\A{\mathscr{A}}     % Script A
\def\W{\Omega}          % Capital omega
\def\w{\omega}          % Lowercase omega
\def\L{\mathscr{L}}     % Lebesgue-integrable functions
\def\esssup{\text{ess sup}}  % Essential supremum
\def\iff{\Leftrightarrow}    % If and only if
\def\implies{\Rightarrow}    % Implies
\def\e{\epsilon}             % Epsilon
\def\d{\delta}               % Delta

Update Thanks for all the comments about how to put LaTeX code in WordPress!  I’ll fix the existing posts this morning and will be sure to use that in upcoming posts too.

Hello, World!

Hi.  I’m working on studying for the mathematics preliminaries at Clemson University.  My experience has been that you have to really know your stuff in order to explain it to someone else, so that’s what this blog is an attempt to do.  The plan is to  write up my notes on reading and problem solving as I go, trying to fill in the gaps that books like to leave for readers to figure out.

Currently I’m studying for the analysis prelim, which has three parts: basic real analysis, functional analysis and measure theory.  I’ve completed the real analysis and most of the functional analysis I want to, but may write up my notes for that anyway as I go back over them.  Anyway, stick around, and there will be lots of posts over the next couple fo weeks.