I want to count the number of characters within a brief essay, like an abstract or summary thesis, including math symbols. Is there a command like the one in microsoft word (preferences, statistics) that count characters?
As already mentioned by Sean in the comments, you can use TeXcount: either through the web-service or by running the Perl script (which may already have come along with your TeX installation) using the option
Note that this counts letters only, i.e. not including punctuation and spaces (although some special characters are permitted as part of words and thus counted along with letters). An estimate of the number of spaces could be the word count for the same document.