1. You should list all of the subjects on the home page not just 6 of them!!! The only way to view classes by subject is via search. But I want to be able to browse! Search is too much effort. Use this as an opportunity to list the highest rated classes by each subject. Put your data to good use.
2. The only way to browse all classes by subject is by un-checking the subject box in a search results page, but if your browser width is over 1200px the filter results tab becomes static and you can't see all of the subjects and filters :(
3. What is the main benefit of signing up? Add a CTA in between the search box and browse courses section of the homepage. Maybe also add a screenshot of the learning path, so I immediately know what benefit I am getting/why I shouldn't just use your site to find courses on coursera or udacity.
4. Have landing pages per subject with a CTA to sign up.
PS I wouldn't have taken the time to write this if I wasn't absolutely in love with your site and what you are doing.