This semester I'm taking a class titled 18.05 Introduction to Probability and Statistics. The math class I took last semester was 18.03 Differential Equations.
Prior to this semester, in almost every math class I've taken (at least since high school, because I don't remember too much detail about my classes before then), the homework assignments have basically been: "OK, so you did this problem illustrating the fundamentals of this concept? Good. Now do 20 more problems just like that with different numbers." Sure, there were a couple word problems here and there, but those were extremely straightforward as well and didn't really require a whole lot of thought.
Now, however, all the problems are word problems, and as evidenced by the recent problem sets, they require quite a bit more thought and interpretation. They look like they are very open-ended (i.e. any answer could be right), but the truth is that there is only one fairly specific way to solve a problem. For example, there was one question on the last problem set that almost seemed like it was asking for my personal opinion, but it really was a cleverly-disguised question asking me to construct a Poisson approximation with the data provided in the problem. The emphasis now is not on the mathematical techniques, because those are fairly basic and there isn't any new math being taught here; now, the emphasis is on being able to correctly parse what the question is asking and apply the correct mathematical tools to reach a solution. Plus, this is made a little bit more difficult by the fact that many people including myself subconsciously resort to intuition to answer questions of probability, and when it comes to probability, human intuition has been repeatedly shown to be very, very wrong; I think this is because people instinctively try to look for patterns rather than looking at the bigger picture of chances, and this is something I do too.
I think it'll be a fun class, but even now it's certainly a little bit more challenging than previous math classes. I don't think it should be that bad though!
Prior to this semester, in almost every math class I've taken (at least since high school, because I don't remember too much detail about my classes before then), the homework assignments have basically been: "OK, so you did this problem illustrating the fundamentals of this concept? Good. Now do 20 more problems just like that with different numbers." Sure, there were a couple word problems here and there, but those were extremely straightforward as well and didn't really require a whole lot of thought.
Now, however, all the problems are word problems, and as evidenced by the recent problem sets, they require quite a bit more thought and interpretation. They look like they are very open-ended (i.e. any answer could be right), but the truth is that there is only one fairly specific way to solve a problem. For example, there was one question on the last problem set that almost seemed like it was asking for my personal opinion, but it really was a cleverly-disguised question asking me to construct a Poisson approximation with the data provided in the problem. The emphasis now is not on the mathematical techniques, because those are fairly basic and there isn't any new math being taught here; now, the emphasis is on being able to correctly parse what the question is asking and apply the correct mathematical tools to reach a solution. Plus, this is made a little bit more difficult by the fact that many people including myself subconsciously resort to intuition to answer questions of probability, and when it comes to probability, human intuition has been repeatedly shown to be very, very wrong; I think this is because people instinctively try to look for patterns rather than looking at the bigger picture of chances, and this is something I do too.
I think it'll be a fun class, but even now it's certainly a little bit more challenging than previous math classes. I don't think it should be that bad though!
