AJAX for jquery

I plan on using jquery to modify the behaviors on my page, and I like the idea of using AJAX to supply the jquery code, instead of loading a .js file, etc. to my server..

Can anyone verify that my list below will work?

1) create a new header.php to put in my child theme folder
2) put in this code before the </head> in the header.php file:
<script src=”https://ajax.googleapis.com/ajax/libs/jquery/1.6.1/jquery.min.js”></script&gt;
3) Write the rest of my scripting code(s) below this.