A Skill search within the people search dialog would have made searching easier and would eliminate at least some poorly targeted messages. (Why isn't it there??)
Recently - finally! - LinkedIn Recruiter accounts got skills search, as part of theNext-generation Recruiter. With the Recruiter subscription, we can select skills and and look for profiles with one or more of the selected skills. (There's still no way to search for skill1 AND skill2 etc.)
Here is an example. In Recruiter, select major = computer Science, location = San Francisco Bay Area, company = Google OR Apple OR Facebook OR Yahoo OR LinkedIn OR IBM - and see the Skill selection:
It's little known, but we have been able to search by skill from a personal account for a while now - not in the main search dialog, but in the "Field of Study Explorer".
If we know what college major we are looking for in our prospects, we can change it using the "Explore more button...
...and search for skills.
Try the same search as above using your personal account - major = computer Science, location = San Francisco Bay Area, compan....
Here's what searching for skills from a personal account using the Field of Study Explorer looks like:
Just as in Recruiter, this is an OR search for skills. As an example, you can search for skills= Python OR Perl OR PHP.
(Note: To have the Skills column included in the Field of Study search, you will need some sort of a premium personal account; unfortunately, the skill selection is no longer displayed when searching from a basic account. I don't think it's documented).
If you'd like to get more people with all of the skills (vs. one of those), you can add the skills in the keyword section: skills= Python OR Perl OR PHP, keywords = Python, Perl, PHP
Conclusion: Got a college major, will search by skills.