From: Zack M. Davis Date: Sat, 23 Aug 2025 01:15:21 +0000 (-0700) Subject: drafting "College Was Not ..." X-Git-Url: https://zackmdavis.net/blog/source?a=commitdiff_plain;h=6b6629a3eb24a2444bbf57ac15902cd3e70abea5;p=An_Algorithmic_Lucidity.git drafting "College Was Not ..." --- diff --git a/college_was_not_that_terrible_now_that_im_not_that_crazy.md b/college_was_not_that_terrible_now_that_im_not_that_crazy.md index 45689a1..b9eff57 100644 --- a/college_was_not_that_terrible_now_that_im_not_that_crazy.md +++ b/college_was_not_that_terrible_now_that_im_not_that_crazy.md @@ -70,9 +70,7 @@ The textbook was _An Introduction to Analysis_ (4th edition) by William R. Wade, The assignments were a lot of work, but that was good. It was what I was there for—to prove that I could do the work. I could do most of the proofs with some effort. At SFSU in 2012–2013, I remembered submitting paper homework, but now, everything was uploaded to Canvas. I did all my writeups in LyX, a GUI editor (I know) for LaTeX. -One thing that had changed very recently, not about SFSU, but about the world, was the availability of large language models, which had in the GPT-4 era become good enough to be useful tutors on standard undergrad material. They definitely weren't reliable, but it was so convenient. - -I adopted the policy that I was allowed to consult LLMs for a hint when I got stuck, citing the fact that I had gotten help in my writeup. Prof. Schuster didn't object when I inquired about the propriety of this at office hours. (I also cited office-hours hints in my writeups.) +One thing that had changed very recently, not about SFSU, but about the world, was the availability of large language models, which had in the GPT-4 era become good enough to be useful tutors on standard undergrad material. They definitely weren't totally reliable, but human tutors aren't always reliable, either. I adopted the policy that I was allowed to consult LLMs for a hint when I got stuck on homework assignments, citing the fact that I had gotten help in my writeup. Prof. Schuster didn't object when I inquired about the propriety of this at office hours. (I also cited office-hours hints in my writeups.) Prof. Schuster held his office hours in the math department conference room rather than his office, which created a nice environment for multiple people to work or socialize, in addition to asking Prof. Schuster questions. I came almost every time, whether or not I had an analysis question for Prof. Schuster. Often there were other students from "Real II" or Prof. Schuster's "Real I" class there, or a lecturer who also enjoyed the environment, but sometimes it was just me. @@ -94,7 +92,7 @@ In addition to the rarified math-math of analysis, the practical math of probabi Like "Real II", "Probability Models" was also administratively cross-listed as both a graduate ("MATH 742", "Advanced Probability Models") and upper-division undergraduate course ("MATH 442"), despite no difference whatsoever in the work required of graduate and undergraduate students. After some weeks of reviewing the basics of random variables and conditional expectation, the course covered Markov chains and the Poisson process. -The textbook was _Introduction to Probability Models_ (12th edition) by Sheldon M. Ross, which, like Wade, felt in bad taste for reasons that are hard to precisely articulate. Lectures were punctuated with recitation days on which we took a brief quiz and then did exercises from a worksheet for the rest of the class period. There was more content to cover than the class meeting schedule could accomodate, so there were also video lectures on Canvas, which I mostly did not watch. (I attended class because it was a social expectation and because attendance was 10% of the grade, but I preferred to learn from the book. As long as I was completing the assignments, that shouldn't be a problem ... right?) +The textbook was _Introduction to Probability Models_ (12th edition) by Sheldon M. Ross, which, like Wade, felt in bad taste for reasons that were hard to put my finger on. Lectures were punctuated with recitation days on which we took a brief quiz and then did exercises from a worksheet for the rest of the class period. There was more content to cover than the class meeting schedule could accomodate, so there were also video lectures on Canvas, which I mostly did not watch. (I attended class because it was a social expectation and because attendance was 10% of the grade, but I preferred to learn from the book. As long as I was completing the assignments, that shouldn't be a problem ... right?) In contrast to what I considered serious math, the course was very much school-math about applying particular techniques to solve particular problem classes, taken to the parodic extent of quizzes and tests re-using worksheet problems verbatim. (You'd expect a statistics professor to know not to test on the training set!) @@ -124,27 +122,47 @@ I assumed that the ask to share with the department "eventually" was polite bull #### "Measure and Integration" (Spring 2025) -I had a busy semester planned for Spring 2025, with two graduate-level (true graduate-level, not cross-listed) analysis courses plus three gen-ed courses that I needed to graduate. (Following Prof. Schuster, I'm humorously counting "Modern Algebra I" as a gen-ed course.) I only needed one upper-division undergrad math course other than "Modern Algebra I" to graduate, but while I was at the University for one more semester, I was intent on getting my money's worth. I aspired to get a head start (ideally on all three math courses) over winter break and checked out a complex analysis book with exercise solutions from the library, but only ended up getting much traction on measure theory, doing some exercises from chapter 14 of Schröder, "Integration on Measure Spaces". +I had a busy semester planned for Spring 2025, with two graduate-level (true graduate-level, not cross-listed) analysis courses plus three gen-ed courses that I needed to graduate. (Following Prof. Schuster, I'm humorously counting "Modern Algebra I" as a gen-ed course.) I only needed one upper-division undergrad math course other than "Modern Algebra I" to graduate, but while I was at the University for one more semester, I was intent on getting my money's worth. (The registration webapp initially rebuffed me with "Must be graduate students [_sic_] to enroll in this course", but Prof. Schuster was happy to give me a permission code, and Prof. Lai offered no resistance when I asked for one at the end of the first class, pointing out that I had gotten A in "Real II" the previous semester.) I aspired to get a head start (ideally on all three math courses) over winter break and checked out a complex analysis book with exercise solutions from the library, but only ended up getting much traction on measure theory, doing some exercises from chapter 14 of Schröder, "Integration on Measure Spaces". -Prof. Schuster was teaching "Measure and Integration" ("MATH 710"). It was less intimate than "Real II" the previous semester, with a number of students in the teens. The class met at 9:30 a.m. on Tuesdays and Thursdays, which I found inconveniently early in the morning given my hour-and-twenty-minute BART-and-bus commute. I was late the first day. After running into to the room, I put the printout of my exercises from Schröder on the instructor's desk and said, "Homework." Prof. Schuster looked surprised for a moment, then accepted it without a word. +[TODO: temporal sequencing of the registration anecdote; readers haven't been introduced to Prof. Lai yet] -The previous semester, Prof. Schuster said he was undecided between using _Real Analysis_ by Royden and _Measure, Integration, and Real Analysis_ by Sheldon Axler (of _Linear Algebra Done Right_ fame, and also our former department chair at SFSU) as the textbook. He ended up going with Axler, which for once was in good taste. (Axler would guest-lecture one day when Prof. Schuster was absent. I got him to sign my copy of _Linear Algebra Done Right_.) We covered Lebesgue measure and the Lebesgue integral, then skipped over the chapter on product measures (which Prof. Schuster said was technical and not that interesting) in favor of starting on Banach spaces. +Prof. Schuster was teaching "Measure and Integration" ("MATH 710"). It was less intimate than "Real II" the previous semester, with a number of students in the teens. The class met at 9:30 a.m. on Tuesdays and Thursdays, which I found inconveniently early in the morning given my hour-and-twenty-minute BART-and-bus commute. I was late the first day. After running into to the room, I put the printout of my exercises from Schröder on the instructor's desk and said, "Homework." Prof. Schuster looked surprised for a moment, then accepted it without a word. +The previous semester, Prof. Schuster said he was undecided between using _Real Analysis_ by Royden and _Measure, Integration, and Real Analysis_ by Sheldon Axler (of _Linear Algebra Done Right_ fame, and also our former department chair at SFSU) as the textbook. He ended up going with Axler, which for once was in good taste. (Axler would guest-lecture one day when Prof. Schuster was absent. I got him to sign my copy of _Linear Algebra Done Right_.) We covered Lebesgue measure and the Lebesgue integral, then skipped over the chapter on product measures (which Prof. Schuster said was technical and not that interesting) in favor of starting on Banach spaces. (As with "Several Variables" the previous semester, Prof. Schuster did not feel beholden to making the Bulletin course titles not be lies; he admitted late in the semester that it might as well have been called "Real Analysis III".) + I would frequently be a few minutes late throughout the semester. One day, the BART had trouble while my train was in downtown San Francisco, and it wasn't clear when it would move again. I got off and summoned a Waymo driverless taxi to take me the rest of the way to the University. We were covering the Cantor set that day, and I rushed in with more than half the class period over. "Sorry, someone deleted the middle third of the train," I said. -Measure theory was a test of faith which I'm not sure I passed. Everyone who reads _Wikipedia_ knows about the notorious axiom of choice. This was the part of the curriculum in which the axiom of choice becomes relevant. It impressed upon me that as much as I like analysis as an intellectual activity, I ... don't necessarily believe in this stuff? We go to all this work to define sigma-algebras in order to rule out pathological sets whose elements _cannot be written down because they're defined using the axiom of choice_. You could argue that it's not worse than uncountable sets, and that alternatives to classical mathematics just end up biting different bullets. (In computable analysis, equality ends up being uncomputable, because there's no limit on how many decimal places you would need to check for a tiny difference between two almost-equal numbers. For related reasons, all computable functions are continuous.) But I'm not necessarilly happy about the situation. +Measure theory was a test of faith which I'm not sure I passed. Everyone who reads _Wikipedia_ knows about the notorious axiom of choice. This was the part of the curriculum in which the axiom of choice becomes relevant. It impressed upon me that as much as I like analysis as an intellectual activity, I ... don't necessarily believe in this stuff? We go to all this work to define sigma-algebras in order to rule out pathological sets whose elements _cannot be written down because they're defined using the axiom of choice_. You could argue that it's not worse than uncountable sets, and that alternatives to classical mathematics just end up biting different bullets. (In computable analysis, equality ends up being uncomputable, because there's no limit on how many decimal places you would need to check for a tiny difference between two almost-equal numbers. For related reasons, all computable functions are continuous.) But I'm not necessarily happy about the situation. + +I did okay. I was late on some of the assignments (and didn't entirely finish assignments #9 and #10), but the TA was late in grading them, too. I posted a 31/40 (77.5%) on the midterm. I was expecting to get around 80% on the final based on my previous performance on Prof. Schuster's examinations, but I ended up posting a 48/50 (96%), locking in an A for the course. + +#### "Theory of Functions of a Complex Variable" (Spring 2025) + +My other graduate course was "Theory of Functions of a Complex Variable" ("MATH 730"), taught by Prof. Chun-Kit Lai. I loved the pretentious title and pronounced all seven words at every opportunity. (Everyone else, including Prof. Lai's syllabus, said "complex analysis" when they didn't say "730".) -I did okay. I was late on some of the assignments (and didn't entirely finish assignments #9 and #10), but the TA was late in grading them, too. I posted a 31/40 (77.5%) on the midterm. I was expecting to get around 80% on the final based on my previous performance on Prof. Schuster's examinations, but I ended up posting a 48/50 (96%). +The content lived up to the pretension of the title. This was unambiguously the hardest school class I had ever taken. Not in the sense that Prof. Lai was particularly strict about grades or anything; on the contrary, he seemed charmingly easygoing about the institutional structure of school, while of course taking it for granted as an unquestioned background feature of existence. He was just pitching the material to a higher level than Prof. Schuster or Axler. -#### Theory of Functions of a Complex Variable (Spring 2025) +The textbook was _Complex Analysis_ by Elias M. Stein and Rami Shakarchi, volume II in their "Princeton Lectures in Analysis" series. Stein and Shakarchi leave a lot to the reader. It wasn't to my taste—but this time, I knew the problem was on my end. My distaste for Wade and Ross had been a reflection of the ways in which I was spiritually superior to the generic SFSU student; my distaste for Stein and Shakarchi reflected the grim reality that I was right where I belonged. +I don't think I was alone in finding the work difficult. Prof. Lai gave the entire class an extension to rebsubmit assignment #2 because the average performance had been so poor. +Prof. Lai didn't object to my LLM hint usage policy when I inquired about it at office hours. I still felt bad about how much external help I needed just to get through the assignments. The fact that I footnoted everything meant that I wasn't being dishonest. (In his feedback on assignment #7, Prof. Lai wrote to me, "I like your footnote. Very genuine and is a modern way of learning math.") It still felt humiliating to turn in work with _so many_ footnotes: "Thanks to OpenAI o3-mini-high for hints", "Thanks to Claude Sonnet 3.7 for guidance", "Thanks to [classmate's name] for this insight", "Thanks to the "Harmonic Conjugate" _Wikipedia_ article", "This is pointed out in Tristan Needham's _Visual Complex Analysis_, p. [...]", _&c._ +If I were just trying to learn, it wouldn't have been an issue. I look things up all the time when I'm working on something I care about, but the institutional context of submitting an assignment for a grade seemed to introduce the kind of moral ambiguity that had made school so unbearable to me, in a way that didn't feel fully mitigated by the transparent footnotes. +I told myself not to worry about it. Prof. Lai had said in class and in office hours that he trusted us, that he trusted me. The purpose of the "assignment" was to help us to learn about the theory of functions of a complex variable, and I was doing that. If I had wanted to avoid this particular source of moral ambiguity at all costs, but still wanted a Bachelor's degree, I could have taken easier classes for which I wouldn't need so much external assistance. But that would be insane. The thing I was doing now, of jointly trying to maximize math knowledge while also participating in the standard system to help with that, made sense. Minimizing perceived moral ambiguity (which was all in my head) would have just been a really stupid goal. Now, so late in life at age 37, I wanted to give myself fully over to not being stupid, even unto the cost of perceived moral ambiguity which was all in my head. +Prof. Lai eschewed in-person exams in favor of take-homes for both the midterm and the final. He said reasonable internet reference usage was allowed, as with the assignments. I didn't ask for further clarification, but resolved to myself that for the take-homes, I would allow myself static websites but obviously no LLMs. (I had already neurotically asked for clarification about the assignments once more than was necessary. I suspect he would have allowed LLMs if I had asked—I didn't get the sense that he yet understood the edge that the latest models offered over mere books and websites—but even asking would have been undignified.) +I got a [TODO: lookup score] on the midterm. [TODO: describe errors] -#### Modern Algebra I (Spring 2025) +[TODO: expository paper] + +There were only 9 assignments during the semester (contrasted to 12 in "Measure and Integration") to give us time to work on it. + +[TODO: Discord log of Prof. Lai's reaction to frontier LLMs] + +#### "Modern Algebra I" (Spring 2025) One of the quirks of being an autodidact is that it's easy to end up with an "unbalanced" skill profile relative to what school authorities expect. As a student of mathematics, I consider myself more of an analyst than an algebraist and had not previously prioritized learning abstract algebra nor (what the school authorities cared about) "taking" an algebra "class", neither last semester nor in Fall 2012/Spring 2013. (Over the years, I had taken a few [desultory swings at Dummit & Foote](http://zackmdavis.net/blog/2019/05/group-theory-for-wellness-i/), but never got very far.) @@ -160,11 +178,8 @@ Prof. Ross is a better teacher, but Prof. Schuster is a better person, because D * algebra tutoring and punch card - - ### Not Sweating the Fake Stuff (Non-Math) - #### Queer Literatures and Media (Fall 2024) ["I could if I wanted to"](https://www.youtube.com/watch?v=GUuU99c_9mY)