From: Zack M. Davis Date: Fri, 22 Aug 2025 04:28:05 +0000 (-0700) Subject: drafting "College Was Not ..." X-Git-Url: https://zackmdavis.net/blog/source?a=commitdiff_plain;h=a0b4859740e0b4c32a3d4e3ece9af469980b21db;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 e0f4210..45689a1 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 @@ -54,7 +54,7 @@ But it didn't hurt this time, because I had a sense of humor about it now—and The undergraduate mathematics program at SFSU has three tracks: for "advanced studies", for teaching, and for liberal arts. My student record from 2013 was still listed as on the advanced studies track. In order to graduate as quickly as possible, I switched to the liberal arts track, which, beyond a set of "core" courses, only requires five electives numbered 300 or higher. The only core course I hadn't completed was "Modern Algebra I", and I had done two electives in Fall 2012 ("Mathematical Optimization" and "Probability and Statistics I"), so I only had four math courses (including "Modern Algebra I") to complete for the major. -#### Real Analysis II (Fall 2024) +#### "Real Analysis II" (Fall 2024) My last class at SF State in Spring 2013 (before getting rescued by the software industry) had been [Real Analysis I"](https://math.sfsu.edu/courses/370) with Prof. Alex Schuster. I regret that I wasn't in a state to properly focus and savor it at the time: I [had a pretty bad sleep-deprivation-induced psychotic break in early February 2013](http://zackmdavis.net/blog/2013/03/religious/) and for a few months thereafter was [mostly just trying to hold myself together](http://zackmdavis.net/blog/2013/04/prodrome/). I withdrew from my other classes ("Introduction to Functions of a Complex Variable" and "Urban Issues of Black Children and Youth") and ended up getting a B−. @@ -66,7 +66,7 @@ The official University Bulletin officially titled the course "Real Analysis II: "Real II" was an intimate class that semester, befitting the SFSU's status as a [garbage-tier institution](https://en.wikipedia.org/wiki/List_of_research_universities_in_the_United_States#Map_of_R2_institutions): there were only seven or eight students enrolled. It was one of many classes in the department that were cross-listed as both a graduate ("MATH 770") and upper-division undergraduate course ("MATH 470"). I was the only student enrolled in 470. The university website [hosted an old syllabus from 2008](http://archive.today/2025.08.14-233957/https://math.sfsu.edu/courses/470) which said that the graduate students would additionally write a paper on an approved topic, but that wasn't a thing the way Prof. Schuster was teaching the class. Partway through the semester, I was added to Canvas (the online course management system) for the 770 class, to save Prof. Schuster and the TA Sean Hadley the hassle of maintaining both. -The textbook was _An Introduction to Analysis_ by William R. Wade, the same book that had been used for "Real I" in Spring 2013. It felt in bad taste for reasons that are hard to precisely articulate. I want to say the tone is patronizing, but don't feel like I could defend that judgement in debate against someone who doesn't share it. What I love about Schröder is how it tries to simultaneously be friendly to the novice (the early chapters sprinkling analysis tips and tricks as numbered "Standard Proof Techniques" among the numbered theorems and definitions) while also showcasing the fearsome technicality of the topic in excruciatingly detailed estimates (proofs involving chains of inequalities, typically ending on "< ε"). In contrast, Wade often feels like it's hiding something from children who are now in fact teenagers. +The textbook was _An Introduction to Analysis_ (4th edition) by William R. Wade, the same book that had been used for "Real I" in Spring 2013. It felt in bad taste for reasons that are hard to precisely articulate. I want to say the tone is patronizing, but don't feel like I could defend that judgement in debate against someone who doesn't share it. What I love about Schröder is how it tries to simultaneously be friendly to the novice (the early chapters sprinkling analysis tips and tricks as numbered "Standard Proof Techniques" among the numbered theorems and definitions) while also showcasing the fearsome technicality of the topic in excruciatingly detailed estimates (proofs involving chains of inequalities, typically ending on "< ε"). In contrast, Wade often feels like it's hiding something from children who are now in fact teenagers. 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. @@ -84,9 +84,9 @@ One of my signature gripes was about the way people in the department habitually There were two examinations: a midterm, and the final. Each involved stating some definitions, identifying some propositions as true or false with a brief justification, and writing two or three proofs. A reference sheet was allowed, which made the definitions portion somewhat farcical as a test of anything more than having bothered to prepare a reference sheet. (I objected to Prof. Schuster calling it a "cheat sheet." Since he was allowing it, it's wasn't "cheating"!) -I did okay. I posted a 32.5/40 (81%) on the midterm. I'm embarrassed by my performance on the final. It looked easy, and I left the examination room an hour early after providing an answer to all the questions, only to realize a couple hours later that I had completely botched a compactness proof. Between that gaffe, the midterm, and my homework grades, I was expecting to end up with a B+ in the course. (How mortifying—to have gone back to school almost specifically for this course and then _not even get an A_.) But when the final grades came in, it ended up being an A: Prof. Schuster only knocked off 6 points for the bogus proof, and had a policy of discarding the midterm grade when the final exam grade was higher. It still seemed to me that that should have probably worked out to an A− rather than an A, but it wasn't my job to worry about that. +I did okay. I posted a 32.5/40 (81%) on the midterm. I'm embarrassed by my performance on the final. It looked easy, and I left the examination room an hour early after providing an answer to all the questions, only to realize a couple hours later that I had completely botched a compactness proof. Between that gaffe, the midterm, and my homework grades, I was expecting to end up with a B+ in the course. (How mortifying—to have gone back to school almost specifically for this course and then _not even get an A_.) But when the final grades came in, it ended up being an A: Prof. Schuster only knocked off 6 points for the bogus proof, for a final exam grade of 44/50 (88%), and had a policy of discarding the midterm grade when the final exam grade was higher. It still seemed to me that that should have probably worked out to an A− rather than an A, but it wasn't my job to worry about that. -#### Probability Models (Fall 2024) +#### "Probability Models" (Fall 2024) In addition to the rarified math-math of analysis, the practical math of probability seemed like a good choice for making the most of my elective credits at the university, so I also enrolled in Prof. Mujamdar's "Probability Models" for the Fall 2024 semester. The prerequisites were linear algebra, "Probability and Statistics I", and "Calculus III", but the registration webapp hadn't allowed me to enroll, presumably because it didn't believe I knew linear algebra. (The linear algebra requirement at SFSU was four units. My 2007 linear algebra class from UCSC, which was on a quarter system, got translated to 3.3 semester units.) Prof. Mujamdar hadn't replied to my 9 July 2024 email requesting a permission code, but got me the code after telling me to send a followup email after I inquired in person at the end of the first class. @@ -94,13 +94,13 @@ 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. -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 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?) 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!) It was still a lot of work, which I knew needed to be taken seriously in order to do well in the course. The task of quiz #2 was to derive the moment-generating function of the exponential distribution. I had done that successfully from the recitation worksheet earlier, but apparently that and the homework hadn't been enough practice, because I botched it on the quiz day. After the quiz, Prof. Mujamdar wrote the correct derivation on the board. She had also said that we could re-submit a correction to our quiz for half-credit, but I found this policy confusing: it felt morally questionable that it should be possible to just copy down the solution from the board and hand that in, even for partial credit. (I guess the policy made sense from the perspective of schoolstudents needing to be nudged and manipulated with credit in order to do even essential things like trying to learn from one's mistakes.) For my resubmission, I did the correct derivation at home in LyX, got it printed, and bought it to office hours the next class day. I resolved to be better prepared for future quizzes (to at least not botch them, minor errors aside) in order to avoid the indignity of having an incentive to resubmit, and mostly succeeded. -I would end up doing a resubmission for quiz #8, which was about how to sample from an exponential distribution (with λ=1) given the ability to sample from the uniform distribution on [0,1] by inverting the exponential's cumulative distribution function. (It had been covered in class, and I had gotten plenty of practice on that week's assignments with importance sampling using exponential proposal distributions, but I did it Rust and used the rand_distr library rather than what was apparently the intended method of implementing exponential sampling from a uniform RNG "from scratch".) I blunted the indignity of my resubmission recapitulating the answer written on the board after the quiz by also inverting by myself the CDF of a different distribution, the Pareto. +I would end up doing a resubmission for quiz #8, which was about how to sample from an exponential distribution (with λ=1) given the ability to sample from the uniform distribution on [0,1] by inverting the exponential's cumulative distribution function. (It had been covered in class, and I had gotten plenty of practice on that week's assignments with importance sampling using exponential proposal distributions, but I did it Rust and used the rand_distr library rather than what was apparently the intended method of implementing exponential sampling from a uniform RNG "from scratch".) I blunted the indignity of my resubmission recapitulating the answer written on the board after the quiz by additionally inverting by myself the CDF of a different distribution, the Pareto. I continued my practice of using LLMs for hints when I got stuck on assignments, and citing the help in my writeup; Prof. Mujamdar seemed OK with it when I mentioned it at office hours. (I went to office hours occasionally, when I had a question for Prof. Mujamdar, who was kind and friendly to me, but it wasn't a social occasion like Prof. Schuster's conference-room office hours.) @@ -108,11 +108,11 @@ I was apparently more conscientious than most students. Outside of class, the gr The student quality seemed noticeably worse than "Real II", at least along the dimensions that I was sensitive to. There was a memorable moment when Prof. Mujamdar asked which students were in undergrad. I raised my hand. "Really?" she said. -I was only late in the semester that I was alerted by non-course reading (specifically a footnote in the probabilistic graphical models book by Daphne Koller and the other guy) that the stationary distribution of a Markov chain is an eigenvector of the transition matrix with eigenvalue 1. (And taking such a linear-algebraic view has interesting applications: for example, the mixing time of the chain is determined by the second-largest eigenvalue, which is less than one, because any starting distribution can be expressed in terms of an eigenbasis, and the coefficients of all but the stationary vector decay as you keep iterating.) +It was only late in the semester that I was alerted by non-course reading (specifically a footnote in the Daphne Koller and the other guy book) that the stationary distribution of a Markov chain is an eigenvector of the transition matrix with eigenvalue 1. Taking such a linear-algebraic view has interesting applications: for example, the mixing time of the chain is determined by the second-largest eigenvalue, which is less than one, because any starting distribution can be expressed in terms of an eigenbasis, and the coefficients of all but the stationary vector decay as you keep iterating. -The feeling of enlightenment was outweighed by embarrassment that I hadn't independently noticed that the stationary distribution was an eigenvector (we had been subtracting one off the main diagonal and solving the system for weeks; the operation should have _felt familiar_), and, more than either of those, annoyance that neither the textbook nor the professor had deigned to mention this relevant fact _in a course that had linear algebra as a prerequisite_. When I tried to point it out during the final review session, it didn't seem like Prof. Mujamdar had understood what I said—not for the lack of linear algebra knowledge, obviously—let alone any of the other students. +The feeling of enlightenment was outweighed by embarrassment that I hadn't independently noticed that the stationary distribution was an eigenvector (we had been subtracting one off the main diagonal and solving the system for weeks; the operation should have _felt familiar_), and, more than either of those, annoyance that neither the textbook nor the professor had deigned to mention this relevant fact _in a course that had linear algebra as a prerequisite_. When I tried to point it out during the final review session, it didn't seem like Prof. Mujamdar had understood what I said—not for the lack of linear algebra knowledge, I'm sure—let alone any of the other students. -I can only speculate that the occurrence of a student pointing out something about mathematical reality that wasn't on the test or syllabus was so unexpected, so beyond what everyone had conditioned to think school was about, that no one had any context to make sense of it. A graduate statistics class at San Francisco State University just wasn't that kind of space. I did get an A. +I can only speculate that the occurrence of a student pointing out something about mathematical reality that wasn't on the test or syllabus was so unexpected, so beyond what everyone had been conditioned to think school was about, that no one had any context to make sense of it. A graduate statistics class at San Francisco State University just wasn't that kind of space. I did get an A. #### The Putnam Exam @@ -122,14 +122,27 @@ As the email headers at the top of the post indicate, the post was originally co I assumed that the ask to share with the department "eventually" was polite bullshit on Hsu's part to let me down gently. (Probably no one gets to be department chair without being molded into a master of polite bullshit.) Privately, I didn't think the rationale made sense—it's just as easy to delete a long unwanted mailing list message as a short one; the email server wasn't going to run out of _paper_—but it seemed petty to argue. I replied that I hadn't known the rules for the mailing list and that he should feel free to share or not as he saw fit. -#### Measure and Integration (Spring 2025) +#### "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". +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. + +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. + +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%). #### Theory of Functions of a Complex Variable (Spring 2025) - * the course numbers are actually informative + + + + + #### Modern Algebra I (Spring 2025) @@ -139,6 +152,8 @@ But "Modern Algebra I" was a graduation requirement, so I found myself in Prof. Dusty Ross + * the course numbers are actually informative + Prof. Ross is an outstanding schoolteacher, the best I encountered at SFSU. I choose my words here very carefully. _My_ favorite professor was Alex Schuster. Prof. Ross is a better teacher, but Prof. Schuster is a better person, because Dusty Ross _believes_ in San Francisco State University; Alex Schuster just works there. @@ -173,3 +188,10 @@ Prof. Ross is a better teacher, but Prof. Schuster is a better person, because D * being more aggressive about working the system * Peter Verdone * it was chance that I ended up deciding to finish before moving; finishing at Reno would be harder + + +Afterwards, Prof. Schuster encouraged me via email to at least consider grad school, saying that I seemed comparable talent-wise to his peers in the University of Michigan Ph.D. program (which was ranked #10 in the U.S. at that time in the late '90s). I demurred: I said I would consider it if circumstances were otherwise, but in contrast to the last two semesters to finish undergrad, grad school didn't pass a cost-benefit analysis. + +What was significant (but not appropriate to mention in the email) was that now the choice to pursue more schooling _was_ a matter of cost–benefit analysis, and not a prospect of torment or betrayal. + +I wasn't that crazy anymore.