Numbers
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start, begin  These numbers contain different sets of digits, which suggests they might be in different bases. Try using an online tool like WolframAlpha to convert them to base ten. Only the right base will result in a reasonably short number. 
If you don't immediately recognize that these numbers share some property, try googling some of them together, and remember that this is the MIT Mystery Hunt you're solving. 

order  The numbers start sorted in numerical order, which suggests we'll need to reorder them. The bold number suggests that rather than having an ordering, they make a cycle and we should use that to order them. Can you find any way to match numbers into a cycle? The base the numbers are written in is as important as the number itself. 
You've determined that these are MIT course numbers, and you have the cycle to order them. You haven't yet used the names of the classes, or the parts of their numbers after the decimal point. Try to use those. And remember that the ordering we have could go in either direction. 
5.0415304153041530415304153041530415304153041530415304153042...
6.0020256154331304414600202561543313044146002025615433130442...
8.14j4j4j4j4j4j4j4j4j4j4j4j4j4j4j4j4j4j4j4j4j4j4j4j4j4j4j4j4...
9.148036a259148036a259148036a259148036a259148036a259148036a3...
21.001141414141414141414141414141414141414141414141414141414...
22.012172702436560507534121727024365605075341217270243656051...
26.023774205602377420560237742056023774205602377420560237742...
111.00000011100101011000000100000110001001001101110100101111...