Today's a Monday, which for me means four lectures in a row, almost without break (there is generally a fifteen minute break between classes, but with going to the restroom, maybe going to another building or buying something to eat, this vanishes quickly). Each lecture is two hours long (roughly), so it's quite a long block of note-taking from 8 a.m. to 4 p.m. But today, each of my math professors have just been so...mathematician-y that I felt the need to use one of my fifteen minute breaks to write this.
One such hilarious (to me) moment today already made its appearance in the title of this post. In Analysis II (very abstract calculus, roughly explained) this morning, we worked our way at one point through a very tedious example. Lots of indices — let me say what I mean by indices. Indices (plural of index) are the subscripts we use to know which entry of a particular vector we are talking about.
For example, the vector x:
The first entry in that vector is 5, the second 4, and the third -1. In math speak, we would write x1=5, x2=4, etc. This vector has three entries in it, so we say it has length 3 . Alright? Bear with me now, it’s going to get complicated. First, imagine you have a vector of length n. What’s n? Could be anything. Got that? Kinda? Good. Now imagine that you don’t have just one vector of length n but a whole series (or list) of them. So, now we might want to talk about the entry at index i of the kth vector in that sequence…You get the idea. Subscripts of subscripts of indices.
Most people in class were either pulling on bits of their hair as they tried to keep track of all the tiny k's and n's and x's, or they were just staring into space after having given up. (Let me note -these kinds of details are not, in my opinion, what makes math difficult. They are not abstract concepts that you need to wrap your head around. Rather, they are the tiny details (that are indeed very important) that we use to be incredibly precise about what it is we are calculating and though they are not in themselves difficult, these tedious indices and things like them certainly can, and do, make math problems discouraging). Finally, we finished the example in the lecture and the professor smiled at us and said we were about to do a different example now that was "ähnlich kompliziert", which means 'similarly complicated'. Also complicated, and in exactly the same way. Sometimes phrases just catch my eye (or ear) and I think they are worth noting in their perfect suitableness.
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