I get this error whether I put the jQuery $.ajax call in a $(document).ready(function() { or not. This is on a ASP.NET MVC .cshtml file.
$(document).ready(function() {
On a server on the local network with IE 11, it can also be a compatibility view issue.
See my answer to this question for more details: '$' is undefined. How to use jQuery 2.0.1 in empty ASP.NET MVC 4 project?