Rutgers University is offering the 6-week "Analyzing the Universe" course free on Coursera, and it has just kicked off today:
https://class.coursera.org/analyze-002
This one looks like it is fairly analytical, but shouldn't be impossible if you remember a bit of your high school physics and maths.
For people who are looking for something at a bit more "introductory" level, the highly-regarded Duke University "Introduction to Astronomy" course is starting again on December 1 2014, and is open for enrolments on Coursera now:
https://www.coursera.org/course/introastro
Earlier this year, I did the "AstroTech" course offered by Edinburgh University https://class.coursera.org/astrotech-001, which was a really good introduction to the technology used by modern astronomers - this one had a pretty light "theory" load, so would suit amateur astronomers with any level of formal science / maths education.
For something which was a lot more challenging, but absolutely fascinating, take a look at "The Science of the Solar System" https://class.coursera.org/solarsystem-001, presented by "Pluto Killer" Mike Brown http://en.wikipedia.org/wiki/Michael_E._Brown of CalTech.
If you're not familiar with Coursera https://www.coursera.org/, don't be afraid to take a look and enrol. There is a huge variety of courses being offered by universities all over the world, and it's all free. (Some courses give you the option of signing up to earn a formal certificate for a modest fee, but I haven't bothered with this, as I am doing these courses purely for my own self-education, not for any formal recognition.)
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