Someone recently asked a question in mitmit about the difference between two probability classes – one taught by the EECS department and the other by the math department. I didn't take the one offered by the math department, so I was curious to see if there were any differences between the two classes. In one of the readings for the math department's version, Stirling's formula is proved, then used in some examples. I vaguely recalled that it was used in the algorithms class to prove something about sorting, but I couldn't remember what it was. (Good thing no one's asked me this on an interview.) A few quick searches turned up the answer: it's used to derive the least number of comparisons necessary to sort a list by any method that compares pairs of list elements.

Some time ago, I wrote that I was going to make a remark about the different levels at which material is presented in a class like 6.001, but I might as well do that here. Sometimes, the multiple levels at which the material is presented in such a class can make it seem very difficult. In the probability class, for example, there is the factual material (such as knowing what Stirling's formula is), there is the method by which the theorem is proved, and there are the many ways in which the theorem can be used to derive or prove other results. If you apply this to all the topics that are covered in a given class, it can add up to a lot of information to process. Multiply this by the four or more classes one usually takes per semester or quarter, and, well, you get the idea. It can be difficult to prepare for quizzes and such because you can't always cover all the material plus do enough practice problems that are representative of what you'll be tested on.