I'm taking a different Coursera course right now. I completed the first homework assignment on my own, but I would have loved to see how other people solved the problem. I definitely felt like I had some ugly hacks in my solution. Posting solutions online would be a great way for me to learn.
I'd recommend that they get rid of the certificate. There is no way to prove that 1) the person who took the course is who they say they are, and 2) they didn't cheat. Copying and pasting from a solution online is only one way to cheat. You could also have a friend finish the assignment. Maybe some day we can get past the point where education is simply a list of achievements, and more about who you have become as a person.
I'd recommend that they get rid of the certificate. There is no way to prove that 1) the person who took the course is who they say they are, and 2) they didn't cheat. Copying and pasting from a solution online is only one way to cheat. You could also have a friend finish the assignment. Maybe some day we can get past the point where education is simply a list of achievements, and more about who you have become as a person.