The solution:
1) Use Google CDN to load jQuery
<script type="text/javascript" src="http://ajax.googleapis.com/ajax/libs/jquery/1.5/jquery.min.js"></script>
2) As far as I know about the Cycle Plugin, It is compatible with jQuery v1.5-v1.7 because most of the methods were deprecated in jQuery 1.8+ . This is the reason I've used v1.5 of Google CDN jquery in point 1. Most of the examples on cycle plugin use jquery 1.5.
3) Clear Your browser cache, It is the main culprit most of the times.
4) PLease check the loading of jquery using the code below
if(typeof jQuery!=='undefined'){
console.log('jQuery Loaded');
}
else{
console.log('not loaded yet');
}
Major Edit:
The reason for the error is fairly simple:
You have called the cycle method before the jquery is loaded.
call cycle plugin on DOM ready..
$(document).ready(function(){
$('#slider').cycle({
fx: 'scrollHorz',
speed: 'fast',
next: '#next',
prev: '#prev'
});
});