I grow old, I grow old

I got an emergency email from a good friend from college (now in grad school at MIT) who is going to soon be meeting with a professor to talk about Number Theory (honestly, I have no idea why she needs to meet him; she does material science!).

She needs a crash course in it, and wanted a recommendation for a textbook. Of course, I go digging around online to find out what book I used, to no avail. I distinctly remember the cover, but I can’t find that on Amazon either. So I finally go to my last resort… digging through my 30 or so binders (from high school (!) and college) looking for the syllabus from that class.

I find the binder, but the syllabus doesn’t have the name of the textbook on it, even though it has 3 pages of assigned problems from the textbook.

My friend is, sadly, out of luck.

But here’s the horrible, horrifying part. Once I started looking through the old binder, I felt dumb. Like really, really dumb. For a number of reasons which I will enumerate here:

1. My three test scores (I don’t know what I got on the final) were 28/40, 29.5/40, and 32/40. [1]

2. One of the tests has a depressing, terse note from the professor “1 [point] for effort”

3. My class notes are completely beautiful but, for me today, totally incomprehensible. I mean, I don’t even remember most of the basic terms that I’m writing about.

Hensel’s Lemma: Let $f(x) \in Z[x]$. $f(a) \equiv 0 \mod p^j$, and $f'(a) \not\equiv 0 \mod p$. Then there exists a unique $t \mod p$ such that $f(a+tp^j) \equiv 0 \mod p^{j+1}$.

Did I ever understand that? Yeah, I know. If I had a month and the textbook, I would be able to figure out what that meant again. Which is (very) slightly heartening. But how sad it is that all my hard work in college is so fleeting? I wish it weren’t all so temporary.

PS. The subject line is from this poem.

[1] Okay, here I’m being a bit disingenuous. I remember that for at least one of them I scored the highest grade in the class. There were only 10-15 students in the class, and the teacher used to write up on the chalkboard the highest score, the lowest score, the mean, the median, the mode, and the standard deviation. Yikes. Those were scary moments, after the professor wrote that on the board, but before he returned the exams. But somehow, after teaching high school, scores in this form look bad. Even though they were probably fine. (I ended up with an A in the class.)